WO2024124266A1 - Method for controlling a technical system - output variable model - Google Patents

Abstract

The invention relates to a method for adjusting an output variable (y) of a technical system (1), the temporal behaviour of which is influenced by a disturbance variable wi, to a reference variable (r), in which method a mathematical state model (ZM) of the technical system (1) is extended by an output variable model (AM), which describes the temporal behaviour of the output variable (y) influenced by the at least one disturbance variable (wI), to create an output-state model (AZM), and a current disturbance variable estimate ŵi of the disturbance variable wI is determined by means of a state observer (ZB) designed on the basis of the output-state model (AZM).

Description

Method for controlling a technical system - output variable model

The present invention relates to a method for controlling a technical system with n state variables, at least one input variable acting on the technical system and influencing the temporal behavior of the n state variables, an output variable to be controlled and at least one disturbance variable acting on the system and influencing the temporal behavior of the output variable, wherein a mathematical state model is specified to describe the temporal change of the n state variables and wherein a controller determines a manipulated variable in predetermined control time steps from a control error which describes a deviation between a predetermined reference variable and the output variable, which manipulated variable is specified to the technical system as an input variable in order to regulate the output variable to the reference variable.

The treatment of disturbances or disturbance variables when controlling a technical system is a central topic in the field of control engineering. Specifically, disturbance variables can affect a technical system to be controlled in different ways. In the control engineering literature, a distinction is made between disturbance variables that affect the input, the output or the state of the system to be controlled (input disturbance, output disturbance, state disturbance). In addition to input, output and state disturbances, there are a number of other disturbances relevant to control engineering that can arise, for example, from model errors or parameter uncertainties. The terms disturbance and disturbance variable are used synonymously in the following explanations.

In the context of this application, a "technical system" is understood to mean a system (device, system, device, machine, object, test bench, actuator, inverter, converter, DC-DC converter, DC/DC converter, etc.) that can be influenced by at least one input variable. By influencing the at least one input variable, at least one state variable and/or at least one output variable of the technical system is influenced. An output variable is typically a measurable or measured variable and is usually a variable that is to be regulated by the control system, for example a load current or a load voltage or another current or another voltage in a DC/DC converter. "Regulating" means that the output variable is adjusted to a predetermined reference variable of the control system at any time or at any control time step. A state variable is typically an internal variable of the technical system that is often not measurable or not measured, for example currents and/or voltages in the example of a DC/DC converter. The input variable acts on the system via an actuator. technical system, whereby the actuator is of course dependent on the type of input variable. For this purpose, the controller of the technical system determines a manipulated variable with which the actuator is controlled, for example, in the case of a DC/DC converter, a PWM pattern for switching semiconductor switches in the DC/DC converter or switching pulses. These relationships are well known in the field of control engineering.

In control engineering, there are different approaches to dealing with disturbances affecting a technical system. A classic method is the so-called disturbance compensation, in which, to put it simply, a control variable determined by a controller is superimposed with a suitable compensation variable in order to (at least partially) compensate for the effect of the disturbance. The compensation variable is typically derived from the disturbance. If, for example, an input disturbance affects the input of the system to be controlled, it is often sufficient to subtract the value of the input disturbance from the control variable determined by the controller in order to (at least largely) compensate for the effect of the input disturbance. In the case of disturbances affecting the state (state disturbances) or the output (output disturbance), however, it may be necessary to take into account the transfer behavior of the system to be controlled (i.e. how the input affects the output or the state) when determining a compensation variable.

A problem that has received a lot of attention in this context is the question of how to enable a disturbance feedforward control even in scenarios in which a disturbance cannot be measured directly and is therefore unknown. Various approaches are known to solve this problem, with the disturbance observation method in particular proving to be a universally applicable and often particularly precise approach. Typically, an estimator (in control engineering and subsequently referred to as an "observer" or specifically as a "disturbance observer") is used to provide an estimate of the disturbance, which is then used for compensation. However, even in cases in which a disturbance is measurable, it can be advantageous or even necessary to determine an estimate of the disturbance, e.g. because the measurement of the disturbance is delayed or distorted due to dirt effects that occur in practice.

In general, high control quality, in particular high control accuracy, a short rise time, low overshoot or the use of little control energy, can be mentioned as common requirements in control engineering. If a disturbance affects a system to be controlled and the disturbance is to be estimated using a disturbance observer and then compensated on the basis of the estimate, it is often necessary to take control quality requirements into account when designing disturbance observers. As will be explained in detail below, In particular, the requirement for high control accuracy can have an impact on the estimation and compensation of disturbances. The control accuracy evaluates the deviation or control error between a variable to be controlled, usually an output variable of the system to be controlled, and a reference variable specified for this variable to be controlled (a specified setpoint). As is well known, a high control accuracy stands for a low, ideally negligible, control error.

In the present context, disturbances are often a major cause of inadequate control accuracy. Specifically, for example, in the case of output variables with disturbances, the shifted variable "output variable plus output disturbance" is controlled instead of the actual output variable to be controlled, which results in a deviation between the actual output variable and the reference variable by the amount of the output disturbance. In the control engineering literature, this is referred to as an "offset". The more precisely and dynamically an output disturbance can be estimated, the more precisely and dynamically an offset caused by the output disturbance can be corrected. Accuracy requirements with regard to control accuracy are therefore in many cases directly transferable to accuracy requirements with regard to disturbance observation and compensation.

In order to meet the accuracy requirements mentioned above, modern approaches, such as those published in “Offset-free reference tracking with model predictive control” Automatica 46, 1469-1476, Maeder, U., & Morari, M., 2010, “Offset-free tracking MPC: A tutorial review and comparison of different formulations” European Control Conference (ECC). Linz, Austria, Pannocchia, G., 2015, or “Offset-free MPC explained: novelties, subtleties, and applications” 5th I FAC Conference on Nonlinear Model Predictive Control. Seville, Spain, Pannocchia, G., & Gabiccini, M., & Artoni, A., 2015, rely on increasingly complex concepts for disturbance compensation. In the cited documents, an already existing state observer, as is common in control engineering for observing non-measurable state variables of a system, is supplemented by further (observer) components for observing disturbance variables.

The components added to the state-of-the-art state observers are in many cases complex and mathematically complex due to the accuracy requirements mentioned above. When evaluating the resulting observer equations, one often encounters the real-time capability limit, which is important in practice, in real operation, especially in systems with limited computing capacity. Complex and complex disturbance observers cannot therefore often be used, especially in combination with control strategies that are already computationally intensive, such as Model Predictive Control (MPC), Adaptive Control (AC) or other optimization-based control algorithms. This is made even more difficult by the fact that modern Control systems are using increasingly higher clock rates and therefore increasingly shorter sampling intervals. Even if powerful computer architectures are used to implement the control and/or observation techniques mentioned, the shortening of the time available between two control time steps, in which all calculations required for control and/or observation must be carried out, often leads to bottlenecks in terms of real-time capability. Real-time capability means that the manipulated variables can be determined by the controller within a specified time period.

Another problem that is not sufficiently addressed in the state of the art arises when disturbances influence the temporal behavior or the temporal change of an output variable to be controlled. In particular, when output variables disturbed in this way are in dynamic interaction with the state variables of a technical system, the question often arises as to how a suitable mathematical model can be specified for the given output variables. Mathematical models or mathematical descriptions for output variables to be controlled are often a necessary prerequisite for the design of a suitable controller for controlling one or more output variables. In the scenario of disturbed output variables described above, it is therefore important to ensure that the temporal behavior of the output variables themselves is described precisely, i.e. that the influence of the disturbances is accurately represented, but that the interaction with the other state variables is also correctly represented, whereby it is important to ensure that the mathematical complexity of a model does not reach a level that could endanger the real-time capability already discussed. This problem area is also only inadequately addressed in the state of the art.

It is therefore an object of the present invention to provide a precise but nevertheless computationally efficient method for estimating and compensating disturbances acting on a system to be controlled.

This object is achieved for a method mentioned at the outset by the features of the characteristics of the independent claims. The independent claims describe a method for controlling a technical system and a technical system.

Specifically, the invention assumes a technical system with n state variables, with at least one input variable acting on the technical system and influencing the temporal behavior of the n state variables, an output variable to be controlled and at least one disturbance variable acting on the system and influencing the temporal behavior of the output variable. As in control engineering As is usual, a mathematical state model is specified to describe the temporal change of the n state variables. In order to adjust the output variable to a specified reference variable, a controller determines a manipulated variable in specified control time steps from a control error that describes a deviation between the reference variable and the output variable, which is then specified to the technical system as an input variable for control.

According to the invention, it is provided for such a system that the mathematical state model is expanded to form an output state model by an output variable model that describes the temporal behavior of the output variable influenced by the at least one disturbance variable. The output variable model has a dynamic component that depends on the output variable and an error component that depends on the output disturbance. During a current control time step, a current disturbance variable estimate for the at least one disturbance variable is determined using a state observer designed on the basis of the output state model. The determined disturbance variable estimate is also fed to the controller during the current control time step, so that the controller can take the disturbance variable estimate into account when determining a current manipulated variable.

In addition to a number of advantages discussed below, the method according to the invention allows model-based observation or estimation and/or model-based control to be used in situations in which the use of model-based concepts is otherwise difficult. Reasons for making it difficult to use a model-based concept can be that the dynamic behavior of an output variable to be controlled is strongly influenced by disturbances, or that the dynamics of an output variable to be controlled are unknown or change very quickly. Within the scope of the invention, it was recognized that in a large number of cases in which modeling the output variable to be controlled proves difficult, it is possible to integrate a model approach according to the invention for the output variable with a dynamic component and an error component into an existing state model. This makes model-based observation and control possible, which in many practical applications leads to sometimes significant improvements, in particular with regard to the suppression of disturbances affecting output variables and control accuracy.

In a particularly advantageous manner, it can be provided that the dynamic component is designed to be exclusively dependent on the output variable and that the error component is designed to be exclusively dependent on the at least one disturbance variable. In this way, the variables influencing the dynamic behavior of the output variable are separated, so that when designing a disturbance variable observer that monitors the disturbance variables on the output variable acting disturbance is observed, only the error component needs to be taken into account. The design of observers can be made significantly easier in this way.

The selected structure of the output variable model not only allows the output variable to be controlled to be described in a model. Due to the structure of two separate model parts, it is possible, among other things, to use particularly advantageous structures of state observers and disturbance variable observers to estimate disturbance variables that affect output variables in particular.

Specifically, it can be provided to first determine a current state estimate for at least one of the n state variables of the technical system during the current control time step using a state observer. Based on this, a current disturbance variable estimate can be determined using a disturbance variable observer designed on the basis of the initial state model, taking into account a current control error and/or at least one past control error, as well as from the current, at least one state estimate determined with the state observer, and from known state estimates from at least one past control time step. This disturbance variable estimate can preferably be the disturbance variable acting on the output variable. In an equally advantageous manner, however, other disturbance variables can also be estimated in the course of this estimation and subsequently used in the control.

This particular approach to determining disturbance estimates has the special feature that control errors are taken into account during observation, particularly during disturbance observation. This approach is based on the remarkable insight that particularly accurate estimates of disturbances can be determined by using control errors as additional correction terms in a disturbance observer. Although the approach of using control errors when estimating disturbances can sometimes lead to significant improvements in accuracy, and this with only a negligible increase in the complexity of the resulting control loops, this idea does not emerge from the cited prior art or from the relevant control engineering literature. It is precisely due to the special structure of the output variable model according to the invention with an error component to describe the output variable that it is possible to link the described procedure for disturbance observation based on control errors with the method according to the invention.

Another important advantage of the method according to the invention is its flexibility, especially in the advantageous embodiment based on the described combination of State observer and disturbance variable observer. The invention can be adapted precisely to different applications with usually only minor changes.

Specifically, the described state observer can of course also determine state estimates for all of the n state variables. For this purpose, the state observer can be supplied with a number of measured values of the input variable and/or the output variable and/or state variables that correspond to the number of disturbances affecting the technical system in order to meet particularly high accuracy requirements.

Furthermore, a control time step immediately preceding the current control time step can be used as a past control time step in order to be able to provide accurate estimates of the disturbance variables even in highly dynamic or very fast technical systems, i.e. in systems with small time constants. If, on the other hand, a technical system has large time constants, it can be advantageous to use control time steps that are further apart from each other for the estimation. Of course, a plurality of past control time steps can also be used, for example to take into account an average over a temporal progression of the state variables when estimating disturbance variables in the disturbance variable observer.

Another point in which the invention in the advantageous embodiment based on a combination of state observer and disturbance variable observer can be adapted particularly flexibly to the specific requirements of a special application is the way in which the control errors are taken into account when estimating the disturbance variables. A particularly advantageous approach has proven to be to take the current control error into account as a current control error weighted by at least one linear weighting factor when determining the disturbance variable estimates. As will be shown in detail below, this creates a connection to the state control that is well known from control engineering. For example, the linear weighting factors mentioned can be selected in a particularly simple manner using means for designing state controllers, for example using the well-known Ackermann formula.

A further significant advantage of the structure of cascaded observers and a controller as described above is the continued simplicity of the resulting overall system and the associated short execution times, whereby in particular the achievable control accuracy is not impaired.

Furthermore, the object underlying the invention is achieved by a control circuit for controlling a technical system in which a control unit for implementing of the method steps according to the invention. It was recognized that the previous statements can be applied in particular to test bench systems for the development and testing of battery systems, in particular battery systems for electric drive trains. In the course of the development of such battery systems, so-called hardware-in-the-loop (HiL) tests are often carried out on hardware-in-the-loop test bench systems (HiL test benches) in order to enable the parallel development of components of electric drive trains and thus shorten development times. Components of electric drive trains include in particular battery systems (energy storage devices such as accumulators or batteries or on-board batteries), but also electric motors, transmissions, drive shafts and electrical converters.

In HiL tests, physically existing components are actually built on a HiL test bench and physically non-existent components are replaced by corresponding mathematical simulation models. Highly dynamic actuators are used to adjust reference values or time profiles of reference values that result from a calculation of the simulation models in real time during operation of the HiL test bench and that describe the temporal behavior of the physically non-existent components. In a known manner, the environment expected in real operation can be simulated or "emulated" for components to be tested that are actually present on the HiL test bench. The load on the HiL test bench corresponds to the real load expected in real operation, even though several components are not physically present.

Applied to the present invention, a highly dynamic actuator mentioned above can be understood as a technical system to be controlled. Specifically, a highly dynamic actuator can be in the form of an electrical power converter, e.g. as a step-up converter, step-down converter (also called a buck converter, “interleaved buck converter”), inverter, frequency converter, etc., which simulates the load of a battery system to be tested, e.g. an on-board battery. The load of a battery system to be tested typically results from the operating state of the electric drive train supplied by the battery system and the electrical energy consumed by the electric drive train, whereby the electric drive train is not physically present in the case of a HiL test and is advantageously simulated in a simulation model.

As the requirements for battery tests are becoming increasingly demanding, battery test systems must also be designed to be more dynamic, precise and computationally efficient. A wide variety of disturbances can also affect a battery test system, with the in many cases unknown reaction of the object to be tested being of particular importance. Battery system on the highly dynamic actuator can represent a significant disturbance. The sometimes very high sampling rates in modern electric drive trains, in combination with complex simulation models and complex disturbance observers, can lead to the problems mentioned above with regard to real-time capability. For these reasons, among others, battery test systems are a predestined field of application for the method according to the invention, which is explained in detail below.

The present invention is explained in more detail below with reference to Figures 1 to 5, which show exemplary, schematic and non-limiting advantageous embodiments of the invention.

Fig.1 a coupling plan for controlling a technical system,

Fig.2 a coupling plan for controlling a technical system with a cascade of a state observer and a disturbance observer,

Fig.3 a bidirectional DC/DC converter,

Fig.4 an equivalent circuit diagram of a bidirectional DC/DC converter,

Fig.5a, 5b show results obtained with the method according to the invention and with a method according to the prior art.

Fig.1 shows a coupling plan for controlling a technical system 1. The technical system 1 shown in Fig.1 has n>1 state variables xi, ..., x _n and at least one input variable u, which acts on the technical system 1 and influences the temporal behavior of the n state variables xi, ..., x _n . The disturbance variables wi, W2, W3 also act on the technical system 1. Within the scope of the invention, it is not necessary that all disturbance variables wi, W2, W3 always act; it is sufficient if at least the disturbance variable W2 acts. The disturbance variable wi acts as an input disturbance, the disturbance variable W2 as a state disturbance and the disturbance variable W3 as an output disturbance, which is additively superimposed on the output variable y. The number p of disturbance variables is referred to below as p, whereby it should be noted that the number is not restricted to p=3. Within the scope of the invention, any number between 1 and n of disturbance variables can be effective, whereby it is also conceivable that the said disturbance variables wi, W2, W3 themselves represent several disturbance variables, so that W2 can, for example, stand for several state disturbances.

For the following explanations, it is important that the disturbance variable W2 influences the temporal behavior of the output variable y. This circumstance is taken into account by way of example and purely schematically by blocks 11 and 12 provided in the system 1 to be controlled. Block 11 represents the formation of a temporal derivative y of the output variable y, and block 12 an integration, by means of which the output variable y is determined from the said derivative y.

A state variable Xj (i serves here as an index to generally reference the n state variables) is used to describe the internal behavior of a technical system 1 . Typically, several state variables xi, x _n are required to characterize the state or to characterize the internal behavior of a technical system 1. Several state variables x are typically combined to form a state vector X = [xi, X2, ..., x _n ] ^T (vectors and matrices are preferably written in capital letters and bold below). The number of state variables xi, ..., x _n determines the order of a technical system 1. A vector notation is also used below for the disturbance variables wi, W2, W3 that are important for the present explanations, and the disturbance variables acting 1 < p < n are collectively referred to as the disturbance variable vector W = [wi, W2, ..., w _p ] ^T. Also for disturbance variables wi, W2, W3 the designation wi can be specified for a single disturbance variable using the index 1=1,...,p.

In technical systems 1 such as the one shown in Fig.1, the aim is to use a controller R to adjust an output variable y of the technical system 1 to a value specified by a given reference variable r, i.e. to adjust the output variable y to be controlled to the reference variable r. For this purpose, the controller R determines in predetermined control time steps, usually in the microsecond to millisecond range, from a control error e _y , which describes a deviation between the reference variable r and the output variable y, e.g. as a difference e _y =ry, a manipulated variable v, which is specified to the technical system 1 as an input variable u, and by means of which the control error e _y is ideally brought to zero.

As is usual with control loops such as the one shown in Fig.1, in the context of the present invention it is assumed that measured variables of at least some of the variables given in the control loop 200 are recorded. Consequently, the at least one input variable u and/or the at least one output variable y and/or at least one of the n state variables xi...x _n can be measured and further processed for control. For this purpose, one or more suitable measurement data acquisition units can be provided, such as sensors or voltage sensors or current sensors or speed sensors or position sensors, etc., which is of course well known to the person skilled in the field of control technology. Typically, in control loops such as the one shown in Fig.1, the input variable u and the output variable y of the technical system 1 are measured, but it is also conceivable that selected state variables Xj are also measured in addition. or that instead of the input variable u and the output variable y, only state variables Xi are measured.

During operation of a control loop 100 as shown in Fig.1, the reference variable r is usually specified continuously, which leads to a temporal progression of the reference variable r. In the case of a control implemented on a digital computer, “continuous” is to be understood as a specification of the reference variable r in predetermined control time steps of the control. In the following, it is assumed that sampling takes place with a sampling time T _s . As is known, sampling using a sampling time T _s defines discrete points in time t _k = k • T _s , which define the actual control time steps. As is usual in digital technology, in the following, to refer to a discrete control time step tk, often only the index k is used, which defines a discrete control time step tk in accordance with the above rule. In the following explanations, state variables xi...x _n or disturbance variables wi, w ₂ , W3 or input variables u etc. are explicitly assigned to a specific control time step tk at several points, for which the corresponding index is given in the subscript of the corresponding variables, e.g. xi,k.

In the case shown in Fig.1, a state observer ZB is also provided for estimating state variables Xj and disturbance variables wi. Starting from the reference variable r, an estimated value of the state vector X determined by the state observer ZB, where X is a vector X =

■■■ ] ⁷ of state estimates of the state variables Xj, and an estimate W of the disturbance vector W determined by the state observer ZB, where W represents a vector of disturbance estimates W = [w _1; w ₂ , w _p ] ^T of the disturbance variables wi, the controller R in the case shown in Fig.1 determines the manipulated variable v, which is given to the technical system 1 as input variable u. Various control laws can be used to implement the controller R, such as model predictive control (MPC), adaptive control (AC), linear quadratic regulators (LQR), or other optimization-based control algorithms, but also control algorithms such as sliding mode control, backstepping control or flatness-based controllers, whereby the choice of control law is irrelevant for the invention.

As shown in Fig.1, the controller R can also access a measured output variable y directly, which is indicated by the dashed input in the controller R. However, if the controller R is supplied with estimated state values X from the state observer ZB anyway, on the basis of which the controller R can carry out the control, direct access to the output variable y is often not necessary. In practice, the state observer ZB for estimating state variables Xj and disturbance variables wi is often State observers such as the so-called Luenberger type are used, although other types of observers can also be used, such as Kalman filters.

In the coupling plan shown in Fig.1, a combined estimation of state variables Xj and disturbance variables wi is carried out. In the state of the art, this is often done as follows: Based on so-called disturbance variable models, i.e. models of the dynamic or temporal behavior of the disturbance variables wi to be estimated, an existing mathematical model of the technical system 1 to be controlled (referred to as state model ZM in the context of this application) is expanded to include the aforementioned disturbance variable models, so that the disturbance variables wi are taken into account as further state variables Xj in the expanded state model ZM. As is known, a mathematical state model ZM of a technical system 1 can be given as a state model ZM in the form of a vector-valued state differential equation or state difference equation, which typically describes the temporal change of the state vector X = [xi, X2, ..., x _n ] ^T (in the case of an extension by a disturbance model, temporal change of an extended state vector X ⁺ = [xi, X2, ..., x _n , wi, W2, ...,w _p ] ^T ). A vector-valued time-discrete difference equation and a vector-valued time-continuous differential equation can be given as linear or nonlinear equations.

Known state-of-the-art approaches provide for the design of a state observer ZB for such an extended state model ZM, which determines estimated values for the state variables xi, X2, ..., x _n and for the disturbance variables wi, W2, ... , w _p . Disturbance estimates determined in this way

w ₂ , ...,w _p can subsequently be used in a controller R for disturbance compensation, for example by using the disturbance estimates

w ₂ ,... , w _p are superimposed on a manipulated variable resulting from a control law without compensation, for example by addition or subtraction or weighted addition or weighted subtraction of the disturbance variable estimates w ₂ , w ₃ . Before such a superimposition, the disturbance variable estimates can also be subjected to filtering.

In practice, one is often confronted with the case that disturbance variables wi have a decisive influence on the temporal behavior or the temporal change of an output variable y to be controlled. In particular, when an output variable y disturbed in this way is in dynamic interaction with the state variables of a technical system 1, the question often arises as to how a suitable mathematical model for the given output variable y can be specified. An accurate description of the output variable y is also usually required for the control of the output variable y. In many cases, this results in a combination of two problems: On the one hand, the need to estimate a disturbance variable wi itself, on the other hand, the question of how the dynamics, i.e. the temporal behavior, of an output variable y that is influenced to a significant extent by this disturbance variable wi can be modeled, because a model of the output variable y is required for the control of the output variable y. The state of the art does not offer any approaches to solving these problems, in contrast to the present invention, which can be used for this purpose.

Specifically, according to the invention, in a first step, a mathematical state model ZM, which describes the temporal behavior of state variables Xj, is expanded to form an output variable model AM, which describes the temporal behavior of the output variable y influenced by the at least one disturbance variable wi, to form an output state model AZM. In contrast to methods known from the prior art, in which a state model ZM, as mentioned, is expanded to include disturbance variable models, within the scope of the invention the state model ZM is supplemented by a model of the output variable y. According to the invention, the output variable model AM has a dynamic component AM1 dependent on the output variable y and an error component AM2 dependent on the output disturbance wi.

Based on the described initial state model AZM, the invention provides for a further step to determine a current disturbance variable estimate w _tk for the at least one disturbance variable wi during a current control time step tk using a state observer ZB designed on the basis of the initial state model AZM and to feed this to the controller R, so that the controller R can take the disturbance variable estimate w _tk into account when determining a current manipulated variable v. The state observer ZB can be designed as described using the methods from the prior art. It is crucial that a model of the output variable y to be controlled is incorporated according to the invention.

The invention makes it possible to solve the problems mentioned in a combined manner: On the one hand, a model of the output variable y is specified, and on the other hand, the at least one disturbance variable is taken into account in the output state model. This aspect can be implemented in an advantageous manner by designing the dynamic component AM1 in the output model as being exclusively dependent on the output variable y, and the error component AM2 as being exclusively dependent on the at least one disturbance variable wi.

A particularly advantageous embodiment of the present invention based on the above statements is shown in Fig.2. Specifically, Fig.2 shows a block diagram of a control circuit 100 with a state observer ZB and a disturbance variable observer SB separate from the state observer ZB. In the case shown in Fig.2 the disturbance variable observer SB and the state observer ZB form a cascade structure. The estimation of at least one disturbance variable wi is divided into two subtasks, on the one hand an estimation of state variables x, which is carried out by the state observer ZB, and on the other hand the estimation of the disturbance variable wi based on the estimated state variables Xj, which is carried out by means of the aforementioned disturbance variable observer SB. The state observer ZB and the disturbance variable observer SB are designed on the basis of the inventive initial state model AZM.

In this way, the state observer ZB does not have to estimate disturbance variables in cases where state estimates are also to be determined. It should be noted that a state observer ZB can estimate all state variables Xj of the technical system 1, or only selected state variables Xj of the technical system 1, or only a single state variable Xj of the technical system 1. Different requirements can arise in different application cases. The same applies to the disturbance variables wi, where all disturbance variables wi can be estimated in a disturbance variable observer SB, or only selected ones. In any case, however, the disturbance variable w ₂ influencing the output variable y is estimated. Specifically, the disturbance variable observer SB in the design shown in Fig.2 is arranged after the state observer ZB, so that the state observer ZB only estimates state estimates X =

which due to the

Extension to the initial state model AZM but can include an output variable of the technical system 1, needs to be determined and output as output variables of the state observer ZB, the disturbance variable observer SB, on the other hand, only has to determine disturbance variable estimates W = [w _1; w ₂ , w _p ] ^T. The statements made for Fig.1 regarding disturbance variables wi, w ₂ , W3, ... , w _p state variables xi, ..., x _n , input variable u, output variable y, controller R, manipulated variable v, vectorial notation, measurement, etc. are still valid with regard to the coupling plan shown in Fig.2.

Within the framework of the coupling plan shown in Fig.2, it is specifically intended to first determine current state estimates X k = [x _lk ,x _{2 k} , ...,x _m fc] ⁷ for a number of at least m state variables Xj of the n state variables x of the technical system 1 during a current control time step _tk by means of the state observer ZB designed on the basis of the initial state model AZM.

In a further step, also during the current control time step tk, the disturbance variable observer SB is used to calculate the current at least m determined state estimates X _k = [x _1:k ,x _{2 k} , ...,x _mk ] ^T , from a current control error e _y ,k and/or from at least one past control error e _y .kj, from known at least m past state estimates X _fe-7 = [x _lk _j,x _{2 k} _j, ... , x _mk _j] ' from a past control time step tk-j, and, if m is smaller than p, from at least a number of pm current measured values of the input variable u and/or the output variable y and/or of state variables xi...x _n , for which no state estimate x _{l fe} , x ₂ ,/<> -,x _mk has been determined by the state observer ZB, current disturbance variable estimates lV _k = [w _lk , w _{2 k} , w _Pife ] ^T for the p disturbance variables wi are determined.

It was recognized that, for example, in order to form a system of equations from which p disturbance estimates for p disturbance variables wi can subsequently be determined, it is sufficient to provide the disturbance observer SB with only p variables, such as in particular p state estimates X _k = [x _lk , x _{2 k} , ... , x _Pife ] ⁷ , which the state observer ZB has previously determined and from which the disturbance observer SB determines the disturbance estimates (in this case m=p).

Within the scope of the invention, however, it was recognized that it is possible to use the state observer ZB to determine fewer than p state estimates, so that m is smaller than p. In order to be able to provide the disturbance variable observer SB with p input variables in this case too, the disturbance variable observer SB can be supplied with measured values of the input variable u and/or the output variable y and/or state variables xi .. ,x _n , for which no state estimate x _lik ,x _2ik , ...,x _mk has been determined by the state observer ZB, instead of the pm state estimates that are missing in this case. However, estimates for all n state variables can of course also be determined and supplied to the disturbance variable observer SB, so that the disturbance variable observer SB can access a complete estimate of the state of the technical system 1. In this context, it was recognized within the scope of the invention that good results can be achieved in particular in cases in which estimated values are determined for all n state variables and all of these n estimated values are fed to the disturbance variable observer SB. Likewise, the disturbance variable observer SB can also be fed with a combination of state estimated values and measured values that make up a total of more than p variables, e.g. p state estimated values and np measured values.

If, as described above, only a single disturbance variable wi is estimated, which influences the temporal behavior of the output variable y, it is therefore sufficient to determine an estimated value x _t only for one state variable xi.

It should also be noted that the past control error e _y ,kj and the known at least m state estimates X _fe-7 = [x _lk _j, x _{2 k} _j, ..., x _{m k-7} ] ^T preferably originate from a common past control time step tk-j, but this is not a mandatory requirement. This is a prerequisite of the invention. Likewise, for example, the control error e _y ,kj can originate from a past control time step tk-j, but the known at least m state estimates X _fe-0 = [%i,fc- ₀ , % ₂ ,fc-o< ■■■ ^Ti.fc-of can originate from a past control time step tk-o.

Following this, within the framework of the design shown in Fig.2, it is intended to calculate the determined disturbance estimates W _k = [w _{l fe} , w _{2 k} ,

to the controller R so that the controller R calculates the disturbance estimates tv _k = [w _lk ,w _{2 k} ,

can be taken into account when determining a current manipulated variable Vk.

In an advantageous manner, a control time step tk-i immediately preceding the current control time step tk can be used as a past control time step tk-j, i.e. j=1, from which the known state estimates used to determine the disturbance value estimate w _7ife

x ₂ ,fc-n ->x _n ,k- ₁ .

This approach is based on several findings. A core idea of the described method is to first generate correct state estimates X _k using a state observer ZB and without explicitly taking into account the disturbance variables wi. The determined state estimates X _k are used together with known, past at least m state estimates X _fe-7 to determine the disturbance variable estimates.

Preferably, successive state estimates X _k ,X _k-1 can be compared with each other in the disturbance variable observer SB, whereby it is checked whether the relationship between the compared, successive state estimates X _k ,X _k-1 corresponds to a disturbance-free relationship that would occur in a disturbance-free scenario and is given, for example, by the initial state model AZM without disturbances, or whether a deviation from this disturbance-free relationship exists. If two successive state vectors Xk, Xk-i of a technical system 1 are related in the undisturbed case, for example, by a general difference equation of the form Xk = g(Xk-i,Uk-i), but in the disturbed case by a difference equation of the form Xk = g(Xk-i,Uk-i)+Hwk-i, each with purely exemplary functions g and matrix H specified by the technical system 1 or by the modeling of the technical system 1, in the simplest case a difference Hwk=Xk+i - g(Xk,Uk) can simply be formed to determine this deviation. Within the scope of the invention, it was recognized that such a deviation can represent a measure of disturbance variables wi, and that the disturbance variables sought can be determined from such a deviation. In this way, it is possible, in a first step, even without detailed knowledge of the to determine precise disturbance estimates based on the dynamic behavior of the disturbances to be estimated.

Another central insight of the invention is to use control errors e _y as additional correction terms in the disturbance variable observer SB. For example, the control errors e _y mentioned, preferably weighted by a linear weighting factor L, can be taken into account when calculating the disturbance variable estimates. Here it was recognized that control errors e _y represent a further measure for the disturbance variables w to be estimated, in particular since in a technical system 1 controlled by a suitably designed controller R, in the undisturbed case, no or only insignificant control errors e _y often occur. In compact terms, these considerations can be exemplified by the purely exemplary calculation rule

which can be provided in the disturbance variable observer, for example. The parameters g, H ⁺ are derived from the above example difference equations, so that H ⁺ is an inverse or a pseudo-inverse or another inverting function of a matrix H that weights the disturbance variable Wk. In particular, the use of at least one control error e _y as a correction term brings significant advantages in terms of the achievable convergence times and the achievable robustness of the disturbance variable observer SB.

Note that the m state estimates X =

...,x _m ] ⁷ do not have to correspond to the first m state variables xi,...,x _m , but can be any m state variables xi,...,x _m of the total n state variables xi,...,x _n . This circumstance makes it possible to significantly reduce the complexity of state observers ZB in particular. It can therefore be sufficient, for example, even in a complex system 1 with a large number of state variables Xj to estimate just one state variable Xj if, for example, only one disturbance variable wi is acting.

Control circuits 100 such as those shown in Fig.1 and Fig.2 are particularly suitable for controlling bidirectional DC/DC converters 10 as a technical system 1, such as those used on HiL test benches, e.g. for the development and testing of battery systems, in particular battery systems of electric drive trains. It should be noted that, despite the advantages resulting from this, the invention is of course not limited to the control of a bidirectional DC/DC converter 10 as a technical system 1 as shown in Fig.3, but can also be applied to other technical systems 1. The control circuits specified below and associated with the discussed DC/DC converter 10 The accompanying mathematical models and descriptions are to be regarded as purely exemplary and serve only to explain the invention.

Fig.3 discloses a possible embodiment of a technical system 1 in the form of a DC/DC converter 10 with an electrical load 5. The DC/DC converter 10 takes on the role of the technical system 1. The electrical load 5 represents a test object to be tested (also known as a “unit under test” or “UUT”), with the case of an electrical load 5 in the form of a battery system being considered below. The electrical load 5 can also be an (at least partial) electrical drive train of a vehicle, or comprise certain drive train components of an electrical drive train, or even represent just a single drive train component of an electrical drive train, such as a power converter or an electrical machine. The DC/DC converter 10 provides the electrical load 5 with a load current i, which, in conjunction with the load 5, produces a load voltage V2 at the output of the DC/DC converter 10.

The DC/DC converter 10 shown in Fig.3 comprises the half-bridges HBi, HB2, HB3, HB4. A direct voltage vo is present at the inputs Ei, E2 of the DC/DC converter 10, which is smoothed by a smoothing capacitor Co that is usually present. To generate the direct voltage vo, a three-phase alternating voltage AC is rectified by means of a rectifier 4 to an input direct voltage vo.

In the embodiment shown in Fig.3, the DC/DC converter 10 is constructed as a four-phase synchronous converter. The DC/DC converter 10 can also have more or fewer phases. The applicability of the present invention is not restricted by this. The DC/DC converter 10 consists of parallel half-bridges HB1, HB2, HB3, HB4 and associated chokes Li, L2, L3, L4, whose phase currents i _Li , ii2, ii_3, ii_4 are each controlled by the switching behavior of the associated half-bridge HB1, HB2, HB3, HB4. The half-bridges HB1, HB2, HB3, HB4 each consist of an upper circuit breaker S01, S02, S ₀ 3, S ₀ 4, and a lower circuit breaker S _u i, Su2, Su3, Su4, whereby the strands with the associated chokes, Li , L2, L3, L4 are each connected between an upper and lower circuit breaker. Furthermore, as usual, associated freewheeling diodes D _oi , D _u i, D ₀ 2, D _U 2, D ₀ 3, D _U 3, D ₀ 4, D _U 4 are provided in parallel with the circuit breakers.

Thus, one half-bridge HB1, HB2, HB3, HB4 and one choke Li, L2, L3, L4 are provided for each phase, whereby the chokes Li, L2, L3, L4 are connected on the one hand between the upper circuit breakers S01, S02, S ₀ 3, S ₀ 4 and the lower circuit breakers S _ui , Su2, S _U 3, S _U 4 with one half-bridge HB1, HB2, HB3, HB4, and on the other hand are connected to each other on the output side. The output current is thus the sum of the respective phase currents i _Li , ii2, ii_3, ii_4- Ohmic resistances of the chokes Li , L2, L3, L4 are neglected in Fig.3, but can also be taken into account (as later in Fig.4).

In addition, an output filter F is usually provided, which filters the output current in the desired manner, for example smoothes it. In the embodiment according to Fig.3, the output filter F is designed in the form of an output-side smoothing capacitor C2 and an output inductance L. The output filter F receives an output current of the DC/DC converter 10 or an output voltage vi as input variable(s) and filters these.

The power switches S01, S02, S ₀ 3, S ₀ 4, S _ui , Su2, S _U 3, S _U 4 of the half-bridges are controlled by a control unit 2. Possible implementations of a control unit 2 include microprocessor-based hardware, such as microcontrollers, and integrated circuits (ASIC, FPGA). It is assumed below that the control unit 2 is clocked with a sampling time T _s so that, as mentioned, discrete control time steps t _k = k • T _s are formed, where k typically comes from the set of natural or whole numbers. The observation and control according to the invention can be implemented on a control unit 2. Of course, corresponding control units 2 are typically also provided in other technical systems 1, not only in the DC/DC converter 10 under consideration.

The upper power switches S01, S02, S ₀ 3, S ₀ 4 and the corresponding lower power switches Sui, S _U 2, S _U 3, S _U 4 of a half-bridge HB1, HB2, HB3, HB4 are basically switched alternately to prevent potentially damaging short circuits in the half-bridges. To specifically control the power switches S01, S02, S ₀ 3, So4, Sui, Su2, Su3, S _U 4, a control method is implemented in the control unit 2, usually a well-known pulse width modulation (PWM). As is well known, pulse width modulation can be used to specify a duty cycle d, which describes the duration of the input voltage vo being switched through via a half-bridge in relation to a specified switching period T _s . The reciprocal of the switching period T _s determines the switching frequency f _s = —.

^T s

The control of half-bridges HB1, HB2, HB3, HB4 and the principle of PWM are well known in power electronics, which is why these points will not be discussed in more detail here. It should be noted that other control methods can also be used to implement the method according to the invention, such as pulse frequency modulation (PFM).

The DC/DC converter 10 can of course also be implemented in a different design or circuit topology, e.g. with fewer or more strings, with fewer or more power switches (also per half-bridge), etc. It is also conceivable that the rectifier 4 is integrated in the DC/DC converter 10. In each embodiment, however, the DC/DC converter 10 comprises at least one power switch which is controlled by a control unit 2 in order to set a load current i or a load voltage V2.

To operate the DC/DC converter 10, it can be provided to determine the load current i and/or the load voltage V2, e.g. by measurement or calculation or by an observer based on other known quantities, and to supply the determined load current i and/or the load voltage V2 to the control unit 2, as in the embodiment of Fig. 3. It should be noted that in practice, the measurement of the load voltage V2 in particular often proves to be difficult, and due to the usually necessary cabling of measurement setups used for measurement, the actual temporal behavior of a load voltage V2 can often only be inadequately represented in a measurement. Furthermore, an emulation model 3 of a component to be emulated (UUT) is provided in the control unit 2, for example a drive train model for describing the temporal behavior of an electric drive train or a battery model.

The emulation model 3 simulates the behavior of the component(s) to be simulated and typically calculates a reference variable r, e.g. in the form of a reference current iR (battery current) or a reference voltage UR. Such a reference voltage UR can subsequently be used as a reference variable r or as a reference variable time curve for controlling the load voltage V2. However, a reference variable r can also be specified in another way, e.g. by an operator or by reading from a table. In this case, an emulation model 3 is not necessary. An emulation model 3 also does not necessarily have to record input variables, but can also determine a reference variable r without externally specified input variables.

In order to subsequently explain how the method according to the invention can be applied to a DC/DC converter 10 as described with reference to Fig.3, it is shown in a first step how a mathematical model for the DC/DC converter 10 can be specified by means of the equivalent circuit diagram of the DC/DC converter 10 shown in Fig.4.

In Fig.4, L _b Ri stands for the average inductances of the chokes Li , L2, L3, L4 and for an internal resistance of this average inductance L C2 as before for an output-side smoothing capacitor, L as before for the already mentioned output inductance L, and R _o for an internal resistance associated with the output inductance L. Furthermore, a disturbance W2 acts, which in the present case can be given in the form of a current that is specified by the load 5, or by a model error in the description of the dynamics, i.e. the temporal behavior, of the output variable y, or by other disturbing influences, which can be represented by a disturbance variable W2. In particular, if the dynamics of the output variable y to be controlled are completely unknown, a representation such as that described in Fig.4, based on a disturbance variable W2, is often an effective way of modeling. If the load voltage V2 is to be controlled as the output variable y, the case discussed arises that the temporal behavior of the output variable y is, on the one hand, dependent to a decisive extent on the disturbance variable W2, and, on the other hand, it is not clear how a model for the output variable y should be specified, since the behavior of the load 5 or the current source shown is typically unknown, and that the output variable in the form of the load voltage V2 affects the other state variables Xj.

Starting from the equivalent circuit diagram in Fig.4, the following system of three differential equations can be derived as a mathematical state model ZM for the DC/DC converter 10 shown in Fig.3:

y = v ₂

It contains j ₂ ,

v ₂ is the sum of the phase currents, the output current, the output voltage and the measured load voltage. v ₀ ■ d is the input variable u, which is the product of the intermediate circuit voltage v ₀ and the duty cycle d. With this selection, a direct connection can be established between the manipulated variable u and the average duty cycle of the PWM signals for the power switches S _oi , S02, S ₀ 3, S ₀ 4, Sui, Su2, Su3, S _U 4 .

In order to extend the mathematical state model ZM according to the invention by an output variable model AM, which describes the temporal behavior of the output variable y influenced by the at least one disturbance variable W2, to an output state model AZM, the following output variable model AM can first be specified for the load voltage V2:

This output variable model AM has a dynamic component AM1 that depends on the output variable y=V2 and an error component AM2 that depends on the output disturbance W2. If the parameter / is set to zero, i.e. y=0, the advantageous embodiment mentioned above can be achieved in which the dynamic component AM1 depends exclusively on the Output variable y=V2 and the error component AM2 depends exclusively on at least one disturbance variable W2.

Inserted into the state model ZM mentioned above, this results in

as an inventive initial state model AZM for describing the DC/DC

Converter 10. For a more compact notation, the (now extended)

State vector, the dynamic matrix, the input vector, the disturbance input vector and the

Output vector, the abbreviations X, A, B, E, C, which are common in linear control engineering, are introduced. With the actual output state model AZM, as already discussed in detail, a state observer ZB can now be specified to estimate the state vector X, for which a variety of approaches known in control engineering can be used (Kalman filter, Luenberger observer, etc.).

In order to further implement the particularly advantageous procedure already explained based on a cascade structure consisting of a disturbance observer SB and a state observer ZB, the following procedure can be used:

First, the given initial state model can be discretized (e.g. using a forward or backward Euler method or using the Tustin method), resulting in a general, discrete initial state model of the following form:

■Xfc+1 — ^d^- k + Bd ^u k + Ed ^w 2,k-

The subscript d represents the time-discrete model description, and the index k records the time-discrete control time steps already mentioned. At this point, it should be noted again that the application of the method according to the invention is by no means restricted to the control of a DC/DC converter 10. A system such as the above linear difference equation can result from the modeling of a wide variety of technical systems 1, which indicates the universal applicability of the invention. In particular, a linear, time-discrete model as above can also result from the linearization of any non-linear model, so that the class of models or technical systems 1 to which the invention can be applied does not essentially have to be restricted. In order to adjust the output variable y=V2 to a given reference variable r or a reference variable determined by an emulation model, a non-linear or linear control law can be specified for the above model, e.g. in the form of a state controller well known in control engineering, in which the state vector X of the system to be controlled is mapped directly to the manipulated variable u by means of a controller gain K _x . A variety of methods and approaches are available for selecting the controller gain K _x , such as the state controller design according to Ackermann.

In an advantageous manner, however, a so-called optimal controller can also be used as controller R, which optimizes a predetermined quality measure J in the predetermined control time steps when determining the manipulated variable v, which preferably evaluates a time period until the output variable y is adjusted to the reference variable r and/or a control energy to be expended in the course of the control and/or a temporal course of a control error e _y = ry.

As mentioned, the estimated disturbance values determined are advantageously taken into account in the controller R when determining the manipulated variable. It should be noted that this procedure opens up the possibility of using control laws without integral components. Integrating controllers are typically used to suppress input disturbances. However, if, as provided for in the context of the invention, all effective disturbances are estimated and taken into account by means of their estimation and compensated in a suitable manner, integrators in the controller R can often be dispensed with, which has a variety of advantages in terms of dynamics and oscillation tendency of the resulting control loops (for example, integrators in controllers R can cause larger ripples and larger overshoots in step responses).

If, for example, a state controller K _x is used to adjust an output variable y to a given reference variable r, the formation law can be applied in the present case, for example

for the manipulated variable Uk, where the variable X _r is derived from the specified reference variable r according to the equation r = CX _r , and thus represents a reference state vector X _r , and u _r represents a value of _the manipulated variable u _fe that is required to keep the state vector X in the reference _state vector _{X r} . The control engineering literature can provide, ^for example, the calculation rule u _r = ( _C (I - _{A d ) ~} ¹ B _d )~ ¹ (r _- C(I - A _d ) ¹ E _d w _{2 k} ), where in particular the consideration of the disturbance estimate w _{2 k} becomes clearly evident.

The idea behind the introduction of this reference state vector X _r is to convert the state vector X into a state vector X _r in which the originally posed control problem of adjusting the output variable y to the reference variable r is solved. The reference state vector X _r is thus an auxiliary variable that is derived from the given reference variable r.

The following shows how a state observer ZB can be designed for the above model to determine the state estimate X _k . Specifically, for example, based on the time-discrete model mentioned above, the following observer equations can be set for a state observer ZB:

%k+l ⁼ Z + ^Vk + d ^u kk = ^k — My _k , y _k = DX _k

In this equation, Z _k stands for an auxiliary state from which the estimate X _k for the state vector X k to be estimated can be determined according to the second of the above equations, and y _k stands for an estimate of the output variable y k determined from the estimate X _k . The matrices N, L, G, M are to be designed in such a way that the estimation error e _xk = X _k - X _k converges, i.e. tends to e _xk = 0 for an index k tending to infinity (/c -> oo). The matrix D can correspond to the already known output matrix C, but can also be chosen differently, e.g. for reasons of observer design.

It should be noted that in the present case, in which only one disturbance W2,k is acting, the state observer ZB determines the state estimates X _k based on the output variable yk and the input variable Uk of the technical system 1. These variables, output variable yk and input variable Uk, are made available to the state observer ZB in practical implementation as measured variables. Within the scope of the invention, it was recognized that in many cases relevant to practice, in the case of a number of p acting disturbance variables wi,...,w _p, it is necessary to make at least p measured variables, e.g. the input variable u and/or the output variable y and/or state variables xi...x _n , available to a state observer ZB in order to be able to determine the desired state estimate. In the control engineering literature, this is referred to as the "existence of an observer". If, for example, two additional disturbance variables wi, W3 were to act in the present case (in total, three disturbance variables wi, W2, W3 would then act), it would be necessary to supply the state observer ZB with another measurement variable, e.g. a measurement of a state variable Xj, so that the State observer can perform the desired estimation based on three measured variables.

The dynamics (i.e. the temporal behavior) of the estimation error is based on the above model by the equation

®x,fc+l ^— e _xk , whereby the requirement of a convergent estimation error e _xk can be directly derived from a requirement for a matrix N that is stable in the sense of Hurwitz (for discrete systems: all eigenvalues of the matrix N within the unit circle, for continuous systems: all eigenvalues of the matrix N in the left open half-plane of the complex number plane). In the context of the invention, it was recognized that this requirement is met by a matrix N that satisfies the equation

Af = (Z - E _d (DE _d yD)A _d - [Q ff] _ _D( j _ _E y _DEd y _D ) _Ad . Such a state observer can be specified for any system that can be modeled by a model of the form X _{k+ 1} = A _d X _k + B _d u _k + E _d w _{2 k} and is not restricted to the DC/DC converter under consideration.

Here I stands for a unit matrix of suitable dimension, (öff _d ) ⁺ for the pseudo-inverse of D

^T and [(? ff] for matrices which, as mentioned, impose eigenvalues on the matrix N within the unit circle. Various approaches to choosing the matrices [(? ff] are known from the literature. In an advantageous way, the well-known formula according to Ackermann can be used for this purpose. For the matrix M, for example,

M = -E _d (DE _d y + R(I - (DE _d DE _d y) can be used. It should be noted that other approaches to setting up the observer equations of the state observer ZB can also be used, such as sliding mode observers, or Kalman filters or other observers. The decisive factor is that the state observer ZB allows an exact estimate of the state vector to be determined without explicitly considering the disturbance variables W2, from which the desired disturbance variable estimates can be determined in a next step in the disturbance variable observer.

How this determination of disturbance estimates can be carried out in the present application example is shown below. To do this, an obvious approach is first shown in which the difference equation for the state vector is solved for the disturbance w _{2 k} to be estimated without any further measures:

As before, the matrix E _d ⁺ stands for the pseudo-inverse E _d ⁺ = (E^E^ E _d ^T . This procedure can be interpreted as a comparison of a new estimated value x _fe+1 with a prediction of this new estimated value, whereby this prediction is carried out based on at least one previous estimated value^ and a disturbance-free model A _d x _k + B _d u _k . If there were no disturbance, the expression on the right-hand side of the equation would be zero, so x _fe+1 - A _d x,. - B _d u _k = 0 would apply. However, if a disturbance wi now acts, a deviation occurs from which an estimate for the disturbance can be determined.

Within the scope of the present invention, however, it was recognized that the described type of estimation has several disadvantages, including the fact that the estimate of the disturbance variables w _{2 k} only becomes correct once the estimate of the state vector X _k has converged. If it is not possible to ensure rapid convergence, it can sometimes take a considerable amount of time before correct disturbance variable estimates can be provided.

For this reason, another type of disturbance estimation can be used, in which the control error e _y =ry is taken into account. For this purpose, the system of equations

from which the unknown w _{2 k} can be determined. For example, if the second equation of the above system of equations is inserted into the first equation, the calculation rule after transformation is

for the disturbance vector to be estimated. This shows the effect of the additional correction term based on the control error. A significant advantage of formulating the disturbance observer SB in the form of two separate difference equations is that the choice of the gain factors Li and L2 to be determined can be made in a particularly efficient manner.

A possible and particularly elegant approach for this purpose is presented below. Specifically, the reference state vector X _r can be used again, which, as described, is derived from the reference variable r according to r = CX _r If we combine the two difference equations of the disturbance observer SB and set D = C, the following description can be given:

The choice of the gain factors L _lf L ₂ is thus reduced to the dimensioning of a vector - ¹ , which stabilizes the matrix, ie the

ensures that the eigenvalues of the matrix lie within the unit circle. Various approaches to this are known from the control engineering literature. Based on this equation, one can again choose from a variety of methods for dimensioning the gain factors Z _1; Z ₂ , whereby a well-known example is the Ackermann method, which is well known in control engineering.

Finally, Figures 5a and 5b show results that were achieved when controlling a load voltage v ₂ of a DC/DC converter 10 as shown in Fig. 3, once by means of a disturbance observer SB according to the prior art (dashed lines), once by means of the method according to the invention (solid lines).

In the scenario shown in Fig.5a, the reference voltage specified as the reference variable r for the voltage v ₂ to be regulated changes in the time interval between 2 and 2.5 seconds, initially abruptly and then in a ramp-like manner. It is clear that with the method according to the invention, the undershoot in the middle of the diagram caused by the method according to the prior art can be avoided and thus, on the one hand, a higher control accuracy can be achieved, but on the other hand, a faster transient response and thus a shorter transient response time can be achieved.

Fig.5b shows another result of a fixed value control of the voltage to be controlled to 1V with a simultaneous increase in the load current i drawn by the load 5 at time t=0 seconds, during a switchover from a so-called "constant current" operation to "constant voltage" operation. In comparison to the prior art, the advantages of the method according to the invention are clearly visible, particularly in terms of control accuracy. A significant advantage of the method according to the invention is also the lower cross-effect between different variables, as in the present case due to the load current drawn. As can be seen from Fig.5b, the voltage v ₂ to be controlled hardly changes despite the sudden increase in current.

Claims

Patent claims

1. Method for controlling a technical system (1) with n state variables (xi...x _n ), at least one input variable (u) acting on the technical system (1) and influencing the temporal behavior of the n state variables (xi...x _n ), an output variable (y) to be controlled and at least one disturbance variable wi acting on the system (1) and influencing the temporal behavior of the output variable (y), wherein a mathematical state model (ZM) is specified to describe the temporal change of the n state variables (xi...x _n ) and wherein a controller (R) determines a manipulated variable (v) in predetermined control time steps from a control error e _y , which describes a deviation between a predetermined reference variable (r) and the output variable (y), which is specified to the technical system (1) as an input variable (u) in order to regulate the output variable (y) to the reference variable (r), characterized in that the mathematical state model (ZM) is supplemented by an output variable model (AM) which describes the temporal behavior of the output variable (y) influenced by the at least one disturbance variable wi, is expanded to form an output state model (AZM), wherein the output variable model (AM) has a dynamic component (AM1) dependent on the output variable (y) and an error component (AM2) dependent on the disturbance variable wi, that during a current control time step tk a current disturbance variable estimate w _tk for the at least one disturbance variable wi is determined by means of a state observer (ZB) designed on the basis of the output state model (AZM), and that during the current control time step tk the determined disturbance variable estimate w _tk is fed to the controller (R) and the controller (R) takes the disturbance variable estimate w _tk into account when determining a current manipulated variable (v).

2. Method according to claim 1, characterized in that the dynamic component (AM1) depends exclusively on the output variable (y) and that the error component (AM2) depends exclusively on the at least one disturbance variable wi.

3. Method according to claim 1 or 2, characterized in that during the current control time step tk, a current state estimate (%i _;fe ) is determined by means of the state observer (ZB) for at least one state variable (xi) of the n state variables (xi...x _n ) of the technical system (1), and that by means of a disturbance variable observer (SB) designed on the basis of the initial state model (AZM) from a current control error e _y ,k and/or from at least one past control error e _y ,kj, as well as from the current, at least one state estimate x _iik determined with the state observer (ZB) and from known state estimates

of at least the current disturbance estimate is determined from a past control time step tk-j.

4. Method according to claim 3, characterized in that a control time step tk-i immediately preceding the current control time step tk is used as a past control time step tk-j.

5. Method according to one of claims 3 or 4, characterized in that the current control error e _y ,k is taken into account as a current control error Ze _y ,k weighted by at least one linear weighting factor Z in the determination of the at least one disturbance variable estimate w _t .

6. Method according to claim 5, characterized in that the at least one linear weighting factor L is selected such that a matrix describing the temporal behavior of the at least one disturbance variable estimate w _t has eigenvalues within the unit circle of the complex number plane or in the left open half-plane of the complex number plane and thus describes an asymptotically stable dynamic.

7. Method according to one of the preceding claims, characterized in that a controller (R) designed on the basis of the output state model (AZM) without an integral component is used to control the output variable (y), wherein the at least one disturbance variable estimate w _t is superimposed on an uncompensated manipulated variable resulting from a control law without disturbance variable compensation for the disturbance variable compensation.

8. Control loop (100) for controlling a technical system (1) with n state variables (xi...x _n ), at least one input variable (u) acting on the system (1) and influencing the temporal behavior of the n state variables (xi...x _n ), an output variable (y) and at least one disturbance variable wi acting on the system (1) and influencing the temporal behavior of the output variable (y), wherein a mathematical state model (ZM) is specified for describing the temporal change of the n state variables (xi...x _n ), wherein a control unit (2) is provided on which a controller (R) is implemented, which is designed to determine a manipulated variable (v) in predetermined control time steps from a control error e _y , which describes a deviation between a predetermined reference variable (r) and the output variable (y), and to specify the manipulated variable (v) to the technical system (1) as an input variable (u) in order to adjust the output variable (y) to the reference variable (r) to regulate, characterized in that the control unit (2) is designed to extend the mathematical state model (ZM) by an output variable model (AM), which describes the temporal behavior of the output variable (y) influenced by the at least one disturbance variable wi, to an output state model (AZM), wherein the output variable model (AM) has a dynamic component (AM1) dependent on the output variable (y) and a dynamic component (AM2) dependent on the at least one Disturbance variable wi dependent error component (AM2), that in the control unit (2) a state observer (ZB) designed on the basis of the initial state model (AZM) is provided, which is designed to determine a current disturbance variable estimate w _tk for the at least one disturbance variable wi during a current control time step tk, and that the control unit (2) is designed to supply the disturbance variable estimate w _t determined during the current control time step tk to the controller (R).

9. Control circuit (100) according to claim 8, characterized in that the technical system (1) is in the form of a bidirectional DC/DC converter (10).

10. Control circuit (100) according to claim 9, characterized in that the bidirectional DC/DC converter (10) comprises a plurality of power switches (S _oi , S02, S ₀ 3, S ₀ 4, S _ui , Su2, S _U 3, S _U 4), wherein a direct voltage (vo) is applied to the inputs (Ei , E2) of the DC/DC converter (10) and the bidirectional DC/DC converter (10) provides a load voltage (V2) and/or an output-side load current (i ) as an output variable (y), and that an emulation model (3) is provided in the control unit (2), wherein the emulation model (3) is designed to calculate a reference voltage (UR) as a reference variable (r) for control and to supply it to the control unit (2) for control.

11. Control circuit (100) according to claim 10, characterized in that the control unit (2) is designed to determine the current control error e _y ,k as the difference between the reference voltage (UR) determined by the emulation model (3) as a reference variable (r) and the load voltage (V2).

12. Control circuit (100) according to claim 10 or 11, characterized in that in the control unit (2) a linear mathematical model of the technical system (1) of the form

as a state model (ZM), with currents i _L and a voltage v as

State variables Xj, a load voltage v ₂ as disturbance variable wi, a product of an intermediate circuit voltage v ₀ and a duty cycle d as input variable (u), the load voltage V2 as output variable (y), and with resistances Rj and R _o , inductances Lj and L and a capacitance C2.

13. Control circuit (100) according to claim 10 to 12, characterized in that in the

Control unit (2) a linear mathematical model of the form AM-, ^v ₂ = q - v ₂ +

AMI y( ₀ ■ d) + wi is provided as the output model AM, with given constants q and y.

14. Control circuit (100) according to claim 13, characterized in that in the

Control unit (2) the state model ZM and the output variable model AM to form an output state model AZM of the form

be combined.