CN109062029A - A kind of repetitive controller system and the control method for integrating anti-saturation - Google Patents
A kind of repetitive controller system and the control method for integrating anti-saturation Download PDFInfo
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Abstract
The invention discloses a kind of repetitive controller system and the methods for integrating anti-saturation, repetitive controller system therein includes: controller module, integrate anti-saturation module and controlled device, integrating anti-saturation module includes the first output end and second output terminal, first output terminates the input terminal of the repetitive controller system, second output terminal connects the input terminal of saturation nonlinearity function module, after the control- action compensation of second output terminal output is added the compensated control amount of composition with original control signal, connect the input terminal of saturation nonlinearity function module, the output of saturation nonlinearity function module terminates the input terminal of the controlled device, the output quantity compensation of first output end is added with original output signal constitutes the input terminal that new output signal feeds back to repetitive controller system, new output signal and reference signal form deviation as repetitive controller system Input.The present invention solves technical problem poor to the compensation effect of control amount saturation in the prior art.
Description
Technical Field
The invention belongs to the technical field of repetitive controllers, and particularly relates to a repetitive controller system and an integral anti-saturation method.
Background
Repetitive controllers are generalized integrators of periodic signals and are increasingly used in the field of industrial control. In the control process, the output quantity reaches the amplitude limit value due to the saturation of the actuator, but the deviation is not eliminated, at the moment, the operation of the controller is continuously increased or reduced due to the repeated integration action of the controller, but the actuator does not have corresponding action, so that the output of the controller is not equal to the actual input of the controlled object, and the phenomenon is called integral saturation. Integral saturation can cause system overshoot to be large, transition time to be increased, closed loop response to be poor, and control and stability of the system are not facilitated. When the controller with the integral characteristic is applied to an object with a saturated actuator, integral saturation phenomenon can be generated, an output signal cannot track a given signal, and the repetitive controller always has an input error signal, so that the control quantity is always accumulated and is difficult to restore to a linear region.
To improve system performance, a suitable integral anti-saturation algorithm needs to be added. Some scholars have studied the problem of integral anti-saturation, and Galeani generalizes the traditional integral anti-saturation method into two main categories in "a tutorial on model anti-i-windows design": direct Linear integration Anti-Windup (DLAW) and Model Recovery Anti-Windup (MRAW). In the method, the DLAW method has high solving order and is not necessarily solvable, while the MRAW method has relatively low order and is simple to solve. In addition, Ramos proposes a minimum beat MRAW design method in "Optimal anti-window synthesis for repetitive controllers", but the minimum beat estimation method adopted may not have a solution. Therefore, the existing method has poor compensation effect on the saturation of the control amount.
Disclosure of Invention
The invention provides a repetitive controller system and an integral anti-saturation method, which are used for solving or at least partially solving the technical problem of poor compensation effect on control quantity saturation in the prior art.
In order to solve the above technical problem, a first aspect of the present invention provides a repetitive controller system, including: the integral anti-saturation module comprises a saturation nonlinear function module and an integral anti-saturation compensation controller, wherein an original control signal of the controller module is obtained by an error signal according to a preset control algorithm, the error signal is obtained by subtracting an original output signal from a reference signal, the input end of the controller module is used as the input end of the repetitive controller system, the output end of the controller module is connected with the input end of the integral anti-saturation module, the integral anti-saturation module comprises a first output end and a second output end, the first output end is connected with the input end of the repetitive controller system, the second output end is connected with the input end of the saturation nonlinear function module, and after compensation of a control quantity output by the second output end of the integral anti-saturation module is added with the original control signal to form a compensated control quantity, and the output quantity compensation output by the first output end of the integral anti-saturation module is added with the original output signal to form a new output signal which is fed back to the input end of the repetitive controller system, and the new output signal and the reference signal form a deviation as the input of the repetitive controller system.
Optionally, the controller module comprises: a feed forward gain module and a repetitive controller module, wherein the feed forward gain module is connected in parallel with the repetitive controller module.
Optionally, the repetitive controller module comprises a repetitive control coefficient, a low pass filter without phase offset and a linear phase lead compensation module.
Optionally, the repetition control coefficient is KrcSaid low-pass filter without phase offset is Q (z) ═ a0z+a1+a0Z, the linear phase lead compensation module is Gf(z)＝zpThe transfer function of the repetitive controller module is:where N is the ratio of the signal sampling frequency to the original input signal frequency, taken as an integer, 2a0+a1Advance compensation of beat number by 1
Based on the same inventive concept, a second aspect of the present invention provides a method for controlling integral anti-saturation of a repetitive controller system according to the first aspect, comprising:
after an original control signal is input into the integral anti-saturation module, a saturation control quantity is obtained through the saturation nonlinear function module, and a control quantity saturation deviation is obtained by subtracting the original control signal from the saturation control quantity, wherein the original control signal is obtained by subtracting an original output signal from a reference signal according to a preset control algorithm, and the original control signal is input into a controlled object to obtain an original output signal;
processing the control quantity saturation deviation through the integral anti-saturation compensation controller to obtain control quantity compensation and output quantity compensation;
adding the control quantity compensation and the original control signal to obtain a compensated control quantity, wherein the compensated control quantity is used for compensating the original control signal;
and the output quantity compensation and the original output signal are added to obtain a new output signal, and the new output signal is fed back to the input end of the repetitive controller system, wherein the new output signal and the reference signal form deviation and serve as the input of the repetitive controller system.
Optionally, the control quantity compensation is obtained after a feedback control coefficient is obtained based on a preset optimal state feedback control rule, wherein the preset optimal state feedback control rule is obtained by a linear quadratic regulator LQR;
the output quantity compensation is obtained from a model object, wherein the model object comprises: a continuous state space equation and a discrete state space equation, the continuous state space equation being:
wherein x is a state quantity, u is a control quantity, y is an output quantity, A is a system matrix and represents the correlation condition among the state variables in the system, and B1The input matrix is used for representing the influence of each input variable on each state variable, and the output matrix is C for reflecting the action relation between the state variables and the output variables;
the discrete state space equation is obtained by discretizing the continuous state space equation, and the discrete state space equation is as follows:
wherein x isk+1Represents the state quantity at the time k +1, xkRepresents the state quantity at time k, ukIndicating the control quantity at time k, ykAn output quantity representing time k, AdFor a matrix A discretized coefficient matrix, B1dIs a matrix B1Discretized coefficient matrix, CdIs a coefficient matrix after the matrix C is discretized.
Optionally, the saturation control amount obtained by the saturation nonlinear function module includes:
constructing a saturation nonlinear function sat (), wherein the saturation nonlinear function is as follows:
wherein,input signal being a non-linear function, uminIs the minimum value of the input, umaxIs the maximum value of the input;
and processing the input signal through the nonlinear function to obtain the saturation control quantity.
Optionally, the obtaining of the control quantity compensation and the output quantity compensation after processing the control quantity saturation deviation by the integral anti-saturation compensation controller includes:
constructing a state equation Caw (z) of the compensator, wherein the state equation Caw (z) is:
wherein x isawkCompensator state variable at time k, xaw(k+1)The compensator state at the time k +1, u' the control saturation deviation, ukThe control signal is the original control signal, and the control signal is the original control signal,for saturated control quantity, variable coefficient matrix AdFor a matrix A discretized coefficient matrix, B1dIs a matrix B1Discretized coefficient matrix, CdThe coefficient matrix after discretization of the matrix C is shown in K, L as coefficients.
One or more technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages:
according to the repetitive controller system provided by the embodiment of the invention, the tracking and each harmonic elimination of the reference signal can be realized through the controller module, the saturation deviation of the control quantity caused by the saturation of the actuator can be obtained through the saturation nonlinear function module, the integral anti-saturation compensation controller is used for reconstructing the saturation loss of the control quantity to respectively obtain the control quantity compensation and the output quantity compensation, and thus the saturation compensation of the control quantity and the output quantity is realized. The control quantity compensation obtained by the integral anti-saturation compensation controller is added with the original control signal to form a compensated control quantity, the output quantity compensation is added with the original output signal to form a new output signal which is fed back to the input end, and the new output signal and the reference signal form deviation to be used as the input of the repetitive controller system. An integral anti-saturation module can be constructed according to a controlled object, so that a system added with the integral anti-saturation compensation controller and the saturation nonlinear function module is a linear time-invariant system which is not affected by saturation of an actuator from input to output, the saturation compensation of the controlled variable is more direct, and the compensation effect of the saturation of the controlled variable is improved. The technical problem that the existing method has poor compensation effect on the saturation of the control quantity is solved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a block diagram of an integral anti-saturation strategy for a repetitive controller system in an embodiment of the present invention;
FIG. 2 is a flow chart of an integral anti-saturation method according to an embodiment of the present invention;
FIG. 3 is a block diagram of a repetitive controller module in an embodiment of the present invention;
FIG. 4 is a block diagram of a proportional repetitive controller in an embodiment of the invention.
Detailed Description
The invention provides a repetitive controller system and an integral anti-saturation method, which are used for solving the technical problem of poor compensation effect on control quantity saturation in the prior art.
The technical scheme in the embodiment of the application has the following general idea:
the repetitive controller system comprises a controller module, an integral anti-saturation module and a controlled object, wherein the integral anti-saturation module comprises a saturation nonlinear function module and an integral anti-saturation compensation controller, an original control signal of the controller module is obtained by an error signal according to a preset control algorithm, the error signal is obtained by subtracting an original output signal from a reference signal, an input end of the controller module is used as an input end of the repetitive controller system, an output end of the controller module is connected with an input end of the integral anti-saturation module, the integral anti-saturation module comprises a first output end and a second output end, the first output end is connected with the input end of the repetitive controller system, the second output end is connected with an input end of the saturation nonlinear function module, and a control quantity output by the second end of the integral anti-saturation module is compensated and added with the original control signal to form a compensated control quantity And the output quantity compensation output by the first end of the integral anti-saturation module is added with the original output signal to form a new output signal which is fed back to the input end of the repetitive controller system, and the new output signal and the reference signal form a deviation as the input of the repetitive controller system.
The repetitive controller system provided by the invention can construct the integral anti-saturation module according to the controlled object, so that the system added with the integral anti-saturation compensation controller and the saturation nonlinear function module is a linear time-invariant system which is not influenced by the saturation of the actuator from input to output, the compensation for the saturation of the controlled variable is more direct, and the compensation effect for the saturation of the controlled variable is improved. The technical problem that the existing method has poor compensation effect on the saturation of the control quantity is solved.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, the repetitive controller system of the present embodiment includes:
a controller module 100, an integral anti-saturation module 200 and a controlled object 300, wherein the integral anti-saturation module 200 comprises a saturation nonlinear function module sat () and an integral anti-saturation compensation controller Caw(z), original control signal u of the controller modulekIs obtained from an error signal obtained from a reference signal r according to a predetermined control algorithmkSubtracting the original output signal ykObtaining the controlled object 300 as Gp (z), dkIs a perturbation signal.
The input end of the controller module is used as the input end of the repetitive controller system, the output end of the controller module is connected with the input end of the integral anti-saturation module, the integral anti-saturation module comprises a first output end and a second output end, the first output end is connected with the input end of the repetitive controller system, the second output end is connected with the input end of the saturation nonlinear function module, and the control quantity compensation v output by the integral anti-saturation module1kWith the original control signal ukAdding up to form compensated control quantitiesThe input end of a saturation nonlinear function module sat () is connected, the output end of the saturation nonlinear function module is connected with the input end of a controlled object, and the output quantity output by the integral anti-saturation module is compensated by v2kWith the original output signal ykAdding up to form a new output signal ylkIs fed back to the weightInput of complex controller system, new output signal ylkAnd a reference signal rkForming a deviation ekAs an input to the repetitive controller system.
Specifically, in the prior art, the repetitive controller includes a controller module without an integral anti-saturation module, and then the output of the controller module is the original control signal ukCan be derived from the error signal derived from the reference signal rkSubtracting the original output signal ykAnd (4) obtaining. That is, the output of the controller is typically calculated based on the error, and a negative feedback is constructed such that the output can always keep up with the input signal (also referred to as the given signal, the reference signal).
The repetitive controller system and the integral anti-saturation method provided by the embodiment of the invention are additionally provided with the integral anti-saturation module on the basis of the existing repetitive controller structure (the controller module of the invention), wherein the integral anti-saturation module comprises a saturation nonlinear function module sat () and an integral anti-saturation compensation controller Caw() The saturation nonlinear function module may obtain a control quantity saturation deviation due to actuator saturation.
In a specific implementation process, the saturation control quantity can be obtained through a saturation nonlinear function moduleAnd subtracting the original control signal from the saturation control to obtain a control saturation deviation u'k. The integral anti-saturation compensation controller is used for reconstructing saturation loss of the control quantity to respectively obtain control quantity compensation and output quantity compensation, and therefore saturation compensation of the control quantity and the output quantity is achieved. Specifically, the compensated control quantity can be formed by adding the control quantity compensation obtained by the integral anti-saturation compensation controller and the original control signalThe output quantity compensation is added with the original output signal to form a new output signal which is fed back to the input end and is compared with the reference signal rkForm deviationekAs an input to the repetitive controller system.
According to the embodiment of the invention, the introduced integral anti-saturation module is inserted into the traditional controller module, so that integral saturation can be effectively inhibited, the reference signal can be quickly and accurately tracked when the controller is out of saturation, and the technical effect of improving the dynamic response performance of the whole repetitive controller system is achieved.
As an alternative implementation manner, in the repetitive controller system provided in the embodiment of the present invention, the controller module includes: the system comprises a feedforward gain module and a repetition controller module, wherein the feedforward gain module is connected with the repetition controller module in parallel.
Specifically, referring to fig. 4, r (z) is a reference signal (input signal) of the control bit module, e (z) is e (z) r (z) -y (z) is a tracking error, u (z) is a control signal of the control bit module, d (z) is a disturbance signal of the control bit module, y (z) is an output signal of the controller module, G (z) is an output signal of the controller module, andp(z) is a control target, KpIn a proportional segment, y (z) is represented by formula (8):
wherein G iso(z)＝Gp(z).[1+Kp·Gp(z)]-1The system stability needs to satisfy the following two conditions:
1) closed loop systems being stable without adding complex controllers, i.e. G0(z) all poles are within the unit circle;
2)1-{[1-krczpGo(z)]Q(z)}z-Nthe characteristic root of 0 is within the unit circle. This gives a sufficient condition for the system to be stable, namely:
|A(z)|＝|[1-krczpGo(z)]Q(z)|＜1
wherein,
when the repetitive controller is designed, the appropriate krc, Q (z) and p are selected to meet the two conditions, so that the whole control system can be ensured to be stable.
Because the single repetitive controller module acts with a delay of one fundamental wave period, the transfer function of the repetitive controller module and the forward gain module are connected in parallel to form a proportional repetitive controller (namely, a feed-forward gain module in the invention), thereby further improving the response performance of the system.
As an alternative implementation, referring to fig. 3, in the repetitive controller system provided in the embodiment of the present invention, the repetitive controller module includes: repetition control coefficient KrcLow pass filter Q (z) without phase shift and linear phase lead compensation module Gf(z)。
Specifically, e (z) is the error signal of the repetitive control bit module, u (rc) is the output signal of the repetitive control bit module, the repetitive control can suppress the periodic interference, and the low-pass filter can improve the performance of the repetitive controller system.
Specifically, in the repetitive controller system provided by the embodiment of the present invention, the repetitive control coefficient is KrcThe low-pass filter without phase shift is Q (z) ═ a0z+a1+a0Z, linear phase lead compensation module is Gf(z)＝zpThe transfer function of the repetitive controller module is:where N is the ratio of the signal sampling frequency to the original input signal frequency, taken as an integer, 2a0+a1Advance compensation of beat number by 1Taking a positive integer.
Based on the same inventive concept as the embodiment, the invention also provides a control method for integral anti-saturation of the repetitive controller system based on the embodiment, which is specifically referred to as embodiment two.
Example two
Referring to fig. 2, the present embodiment provides a method for controlling integral anti-saturation based on the controller according to the first embodiment, the method includes:
step S101: after an original control signal is input into the integral anti-saturation module, a saturation control quantity is obtained through the saturation nonlinear function module, and a control quantity saturation deviation is obtained by subtracting the original control signal from the saturation control quantity, wherein the original control signal is obtained by subtracting an original output signal from a reference signal according to a preset control algorithm, and the original control signal is input into a controlled object to obtain an original output signal;
step S102: processing the control quantity saturation deviation through the integral anti-saturation compensation controller to obtain control quantity compensation and output quantity compensation;
step S103: adding the control quantity compensation and the original control signal to obtain a compensated control quantity, wherein the compensated control quantity is used for compensating the original control signal;
step S104: and the output quantity compensation and the original output signal are added to obtain a new output signal, and the new output signal is fed back to the input end of the repetitive controller system, wherein the new output signal and the reference signal form deviation and serve as the input of the repetitive controller system.
Specifically, the control quantity compensation and the output quantity compensation can be obtained after the control quantity saturation deviation is processed by constructing a state equation of the integral anti-saturation compensation controller. The saturation control amount can be obtained by constructing a saturation nonlinear function.
As an optional implementation manner, in the method provided in this embodiment, the control quantity compensation is obtained after obtaining the feedback control coefficient based on a preset optimal state feedback control rule, where the preset optimal state feedback control rule is obtained by a linear quadratic regulator LQR;
the output quantity compensation is obtained from a model object, wherein the model object comprises: a continuous state space equation and a discrete state space equation, the continuous state space equation being:
wherein x is a state quantity, u is a control quantity, y is an output quantity, A is a system matrix and represents the correlation condition among the state variables in the system, and B1The input matrix is used for representing the influence of each input variable on each state variable, and the output matrix is C for reflecting the action relation between the state variables and the output variables;
the discrete state space equation is obtained by discretizing the continuous state space equation, and the discrete state space equation is as follows:
wherein x isk+1Represents the state quantity at the time k +1, xkRepresents the state quantity at time k, ukIndicating the control quantity at time k, ykAn output quantity representing time k, AdFor a matrix A discretized coefficient matrix, B1dIs a matrix B1Discretized coefficient matrix, CdIs a coefficient matrix after the matrix C is discretized.
As an optional implementation manner, in the method provided in this embodiment, the saturation control amount obtained by the saturation nonlinear function module includes:
constructing a saturation nonlinear function sat (), wherein the saturation nonlinear function is as follows:
wherein,input signal being a non-linear function, uminIs the minimum value of the input, umaxIs the maximum value of the input;
and processing the input signal through the nonlinear function to obtain the saturation control quantity.
As an alternative implementation, in the method provided in this embodiment, the obtaining of the control quantity compensation and the output quantity compensation after processing the control quantity saturation deviation by the integral anti-saturation compensation controller includes:
constructing a state equation Caw (z) of the integral anti-saturation compensation controller, wherein the state equation Caw (z) is as follows:
wherein x isawkCompensator state variable at time k, xaw(k+1)The compensator state at the time k +1, u' the control saturation deviation, ukThe control signal is the original control signal, and the control signal is the original control signal,for saturated control quantity, variable coefficient matrix AdFor a matrix A discretized coefficient matrix, B1dIs a matrix B1Discretized coefficient matrix, CdThe coefficient matrix after discretization of the matrix C is shown in K, L as coefficients.
In order to more clearly illustrate the inventionThe beneficial effect of the method for integral anti-saturation provided by the invention is described by a specific example, and the saturation nonlinear function module is used for limiting the output of the controlled variable to obtain the saturation deviation of the controlled variable. Control quantity compensation v1kThe saturation deviation of the control quantity can be introduced to compensate the control quantity, and the compensation quantity v of the output quantity2kFor measuring the deviation of ideal output from actual output without actuator saturation, the output quantity compensation quantity v2kAnd adding the new output signal and the original output signal to form a new output signal, and feeding the new output signal and the reference signal back to the input end of the repetitive controller system, wherein the new output signal and the reference signal form a deviation as the input of the repetitive controller system.
Specifically, the compensated control amount isAnd the compensated output is ylk(i.e., the new output signal) by constructing the equation of state for the integral anti-saturation compensator, caw (z):
wherein x isawkFor the compensator state variables, the coefficient matrix Ad、B1d、CdLike the formula (2), K, L is a parameter to be designed. To facilitate the comprehensive analysis of the system after the compensator is added, a state variable x is definedlk＝xk+xawkOutput ylk＝yk+v2kThe overall state equation is obtained by adding equations (2) and (4):
equation (5) is the same type as the continuous state space equation (1) for the control object, from input ukTo the output ylkCan be viewed as a linear time-invariant system that is not affected by actuator saturation,i.e. ukAnd ylkIs an ideal linear variable. In order to make the designed closed loop system without actuator saturation stable, it is necessary to ensure that the connection part of the saturation nonlinear function module and the integral anti-saturation compensation controller, i.e. the integral anti-saturation module, in fig. 1 is stable, so as to ensure the stability of the whole system. In a specific implementation, the following theorem can be derived:
if K, L and the positive definite symmetric matrix P, W are present such that the matrix inequality 6 holds, the integral anti-saturation closed loop system is stable.
Then the variables in the integral anti-saturation compensation controller can be selected for performance optimization:
the linear quadratic performance index is selected as shown in the following formula:
wherein J is used for optimizing the recovery performance when the system is desaturated. Q is a positive state weighting coefficient matrix, and R is a positive control weighting coefficient matrix. Expression J the first term to the right represents the state xawkThe smaller the term is, the faster the state is attenuated to zero, the smaller the oscillation is, and the better the control performance is; the second term is the limit on the control energy, the faster the state decays, the greater the control energy that needs to be consumed, there is a set of contradictions between the two, and the index J is used for equilibrium optimization. And designing and solving K according to an optimal state feedback control law, so that the J value can be ensured to be minimum after Q and R are selected. When K is solved and Z is WL, (equation 6) can be regarded as a line having P, W, Z as a matrix variableThe inequality of the sexual matrix can be solved conveniently by MATLAB to obtain L ═ W- 1And Z. From the above description, the integral anti-saturation method provided in the embodiment of the present invention can achieve the effect of improving integral anti-saturation
One or more technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages:
according to the repetitive controller system provided by the embodiment of the invention, the tracking and each harmonic elimination of the reference signal can be realized through the controller module, the saturation nonlinear function module can obtain the saturation deviation of the control quantity caused by the saturation of the actuator, the integral anti-saturation compensation controller is used for reconstructing the saturation loss of the control quantity to respectively obtain the control quantity compensation and the output quantity compensation, and thus the saturation compensation of the control quantity and the output quantity is realized. The control quantity compensation obtained by the integral anti-saturation compensation controller is added with the original control signal to form a compensated control quantity, the output quantity compensation is added with the original output signal to form a new output signal which is fed back to the input end, and the new output signal and the reference signal form deviation to be used as the input of the repetitive controller system. An integral anti-saturation module can be constructed according to a controlled object, so that a system added with the integral anti-saturation compensation controller and the saturation nonlinear function module is a linear time-invariant system which is not affected by saturation of an actuator from input to output, the saturation compensation of the controlled variable is more direct, and the compensation effect of the saturation of the controlled variable is improved. The technical problem that the existing method has poor compensation effect on the saturation of the control quantity is solved.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made in the embodiments of the present invention without departing from the spirit or scope of the embodiments of the invention. Thus, if such modifications and variations of the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to encompass such modifications and variations.
Claims (8)
1. A repetitive controller system, comprising: the integral anti-saturation module comprises a saturation nonlinear function module and an integral anti-saturation compensation controller, an original control signal of the controller module is obtained by an error signal according to a preset control algorithm, the error signal is obtained by subtracting an original output signal from a reference signal, the input end of the controller module is used as the input end of the repetitive controller system, the output end of the controller module is connected with the input end of the integral anti-saturation module, the integral anti-saturation module comprises a first output end and a second output end, the first output end is connected with the input end of the repetitive controller system, the second output end is connected with the input end of the saturation nonlinear function module, wherein after compensation of a control quantity output by the second output end of the integral anti-saturation module is added with the original control signal to form a compensated control quantity, and the output quantity compensation output by the first output end of the integral anti-saturation module is added with the original output signal to form a new output signal which is fed back to the input end of the repetitive controller system, and the new output signal and the reference signal form a deviation as the input of the repetitive controller system.
2. The repetitive controller system of claim 1, wherein the controller module comprises: a feed forward gain module and a repetitive controller module, wherein the feed forward gain module is connected in parallel with the repetitive controller module.
3. The repetitive controller system of claim 2, wherein the repetitive controller module comprises a repetitive control coefficient, a low pass filter without phase offset, and a linear phase lead compensation module.
4. The repetitive controller system of claim 3, wherein the coefficient of the repetitive controller module is KrcSaid low-pass filter without phase offset is Q (z) ═ a0z+a1+a0Z, the linear phase lead compensation module is Gf(z)＝zpThe transfer function of the repetitive controller module is:where N is the ratio of the signal sampling frequency to the original input signal frequency, taken as an integer, 2a0+a1Advance compensation of beat number by 1
5. A control method of integral anti-saturation based on the controller of any one of claims 1-4, comprising:
after an original control signal is input into the integral anti-saturation module, a saturation control quantity is obtained through the saturation nonlinear function module, and a control quantity saturation deviation is obtained by subtracting the original control signal from the saturation control quantity, wherein the original control signal is obtained by subtracting an original output signal from a reference signal according to a preset control algorithm, and the original control signal is input into a controlled object to obtain an original output signal;
processing the control quantity saturation deviation through the integral anti-saturation compensation controller to obtain control quantity compensation and output quantity compensation;
adding the control quantity compensation and the original control signal to obtain a compensated control quantity, wherein the compensated control quantity is used for compensating the original control signal;
and after the output quantity compensation and the original output signal are added, a new output signal is obtained and then fed back to the input end of the repetitive controller system, wherein the new output signal and the reference signal form deviation and serve as the input of the repetitive controller system.
6. The method according to claim 5, wherein the control amount compensation is obtained after obtaining the feedback control coefficient based on a preset optimal state feedback control law obtained by a linear quadratic regulator LQR;
the output quantity compensation is obtained from a model object, wherein the model object comprises: a continuous state space equation and a discrete state space equation, the continuous state space equation being:
wherein x is a state quantity, u is a control quantity, y is an output quantity, A is a system matrix and represents the correlation condition among the state variables in the system, and B1The input matrix is used for representing the influence of each input variable on each state variable, and the output matrix is C for reflecting the action relation between the state variables and the output variables;
the discrete state space equation is obtained by discretizing the continuous state space equation, and the discrete state space equation is as follows:
wherein x isk+1Represents the state quantity at the time k +1, xkRepresents the state quantity at time k, ukIndicating the control quantity at time k, ykAn output quantity representing time k, AdFor a matrix A discretized coefficient matrix, B1dIs a matrix B1Discretized coefficient matrix, CdIs a coefficient matrix after the matrix C is discretized.
7. The method of claim 5, wherein the saturation control amount obtained by the saturation nonlinear function module comprises:
constructing a saturation nonlinear function sat (), wherein the saturation nonlinear function is as follows:
wherein,input signal being a non-linear function, uminIs the minimum value of the input, umaxIs the maximum value of the input;
and processing the input signal through the nonlinear function to obtain the saturation control quantity.
8. The method of claim 6, wherein obtaining a control quantity compensation and an output quantity compensation after processing the control quantity saturation deviation by the integral anti-saturation compensation controller comprises:
constructing a state equation Caw (z) of the compensator, wherein the state equation Caw (z) is:
wherein x isawkCompensator state variable at time k, xaw(k+1)The compensator state at the time k +1, u' the control saturation deviation, ukThe control signal is the original control signal, and the control signal is the original control signal,for saturated control quantity, variable coefficient matrix AdFor a matrix A discretized coefficient matrix, B1dIs a matrix B1Discretized coefficient matrix, CdThe coefficient matrix after discretization of the matrix C is shown in K, L as coefficients.
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