CN115328047B - Repeated control method and device for T-S fuzzy system with separated control and learner - Google Patents
Repeated control method and device for T-S fuzzy system with separated control and learner Download PDFInfo
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Abstract
The invention provides a repeated control method and a repeated control device for a T-S fuzzy system with separated control and learner, wherein the method comprises the following steps: constructing a repeated controller structure for separating control behaviors and learning behaviors, setting corresponding fuzzy control laws aiming at a T-S fuzzy system, and converting the fuzzy control laws into fuzzy controllers directly related to the control and learning behaviors through conversion; introducing adjusting parameters related to a control and learning device into the Lyapunov functional, and realizing the separation adjustment of control and learning behaviors; acquiring an expression of a control and learner, and converting a feasible solution problem for solving the gain of the fuzzy controller into a parameter optimization problem constrained by the LMI; and evaluating the control and learning performance of the nonlinear repetitive control system, and combining a multi-objective optimization algorithm to obtain an optimal control and learner. The invention realizes the high-precision tracking control and inhibition of the periodic signal of the nonlinear system, provides technical guidance for solving the problems of the high-precision tracking control and inhibition of the actual nonlinear system, and has important theoretical and application values.
Description
Technical Field
The invention relates to the technical field of intelligent control systems, in particular to a method and a device for repeatedly controlling a T-S fuzzy system with separated control and learner.
Background
Periodic control tasks are widely present in practical industrial processes and require high precision tracking or suppression of periodic reference inputs or disturbances, and such systems are often complex nonlinear systems. The T-S fuzzy model is an effective tool for processing the complex nonlinear system, a series of linear sub-models are connected smoothly by utilizing nonlinear fuzzy weights, the complex nonlinear system is approximated infinitely, the front piece variable of the T-S fuzzy model is a fuzzy membership function, the back piece variable is a linear sub-system, and the characteristic enables the linear control theory to be directly applied to analysis and design of the nonlinear system. The nonlinear system described by the T-S fuzzy model is called as a T-S fuzzy system, the periodic signal high-precision tracking or suppressing of the system is researched, and technical guidance is provided for solving the problem of high-precision tracking or suppressing control of an actual nonlinear system.
The repetitive control can realize high-precision tracking or suppression of periodic signals, and is different from a general control strategy, the repetitive control not only has general control behaviors, but also has specific learning behaviors, the repetitive control can realize high-precision control finally by continuously learning and accumulating experiences and utilizing the information of the previous period, and the repetitive control is difficult to realize by the general control strategy, so that the repetitive control has two-dimensional characteristics: continuous control behavior and discrete learning behavior. The conventional repetitive controller has a problem of coupling of control and learning behaviors structurally, and although the two behaviors can be described separately by means of a two-dimensional continuous/discrete hybrid model and then priority adjustment is achieved, independent adjustment of the two behaviors cannot be achieved. How to separate the two behaviors from the structure is a key for realizing independent adjustment of control and learning behaviors, lays a foundation for optimal adjustment of the control and learning behaviors, and has important theoretical and application values for simultaneously optimizing the control and learning performance of a nonlinear repetitive control system and realizing high-precision tracking control of periodic signals.
Disclosure of Invention
The invention aims to solve the main technical problem that the traditional repetitive controller structurally has the coupling problem of control and learning behaviors, and the control behaviors and the learning behaviors are structurally separated to realize independent adjustment of the two behaviors.
According to one aspect of the present invention, there is provided a T-S fuzzy system repetitive control method for controlling and learner-separating, comprising the steps of:
constructing a repeated controller structure with separated control and learner, setting corresponding fuzzy control laws aiming at a T-S fuzzy system, converting the fuzzy control laws into controllers directly related to control and learning behaviors through conversion, and respectively adjusting the control and learning behaviors of a nonlinear repeated system;
Two adjusting parameters related to a control and learner are introduced into the Lyapunov functional, so that the separation adjustment of control and learning behaviors is realized;
based on the stability condition of the inequality of the linear matrix, acquiring an expression of a control and learner, and converting a feasible solution problem for solving the gain of the fuzzy controller into a parameter optimization problem constrained by the inequality of the linear matrix;
and establishing two performance indexes to evaluate the control and learning performance of the nonlinear repetitive control system respectively, and acquiring an optimal control and learning device by utilizing a multi-objective optimization algorithm.
Preferably, the repetitive controller structure with separated control and learner is formed by parallel connection of a proportional controller and a modified repetitive controller.
Preferably, the improved repetitive controller is formed by a delay module e -Ts in series with a low-pass filter q(s) =ω c/(s+ωc and then subjected to unit positive feedback;
the state equation of the improved repetitive controller is as follows:
wherein x I (t) is the state of the low-pass filter, For the derivative of x I (T), e (T) is the difference between the reference input r (T) and the output y (T), e is a natural constant, T is the period of the reference input signal, s is the laplace operator, ω c represents the cut-off frequency of the low pass filter.
Preferably, the expression of the T-S blur system is:
wherein x P (t) is the state of the controlled object, For the derivative of x P (T), A i is a T-S fuzzy system state coefficient matrix; b i is a T-S fuzzy system input coefficient matrix; c is the output coefficient matrix of the T-S fuzzy system;
setting a corresponding fuzzy control law as follows:
Wherein, Is the gain of the proportional controller,Is the gain of the improved repetitive controller; i, j=1, 2,..r is the fuzzy rule number, r is the total number of fuzzy rules, Σ isOr (b)Is abbreviated as (1); h i (z (t)) or h j (z (t)) is the normalized weight of the precondition variable z (t) under r fuzzy rules;
obtaining a fuzzy controller related to control and learning through transformation:
Wherein, In order to adjust the gain of the control action,To adjust the gain of learning behavior;
And (3) bringing the state space equation and the fuzzy control law of the repetitive controller structure into a T-S fuzzy system to obtain the state space equation of the whole closed loop system:
Wherein,
I is an identity matrix of appropriate dimensions.
Preferably, the step of introducing two adjustment parameters related to the control and learner into the Lyapunov functional to realize separate adjustment of the control and learning behaviors specifically includes:
The Lyapunov functional is built with the following expression:
Wherein, A symmetric positive definite matrix, wherein the symmetric matrix is represented by x, and s is an integral variable;
After the Lyapunov functional is derived, the judgment conditions for obtaining the system stability are as follows:
For two tuning parameters α, β and the cut-off frequency ω c of the low-pass filter, if there is a positive symmetric matrix X 1、U1, an arbitrary matrix W j or W i, so that for 1.ltoreq.i.ltoreq.j.ltoreq.r, the following linear matrix inequality is given If true, the system is stable, otherwise, the system is unstable;
Wherein,
Sym represents the sum of itself and its transpose, and r is the total number of fuzzy rules.
Preferably, the expressions of the control and learner are as follows:
Wherein W j is LMI matrix, I n,Iq is identity matrix with proper dimension, and weight matrix can be influenced by adjusting the size of parameters alpha and beta Thereby adjusting the control gainAnd learning gainAnd converting a feasible solution problem for solving the gain of the fuzzy controller into a parameter optimization problem constrained by the LMI.
Preferably, the step of establishing two performance indexes to evaluate the control and learning performance of the nonlinear repetitive control system respectively and obtaining the optimal control and learning device by using a multi-objective optimization algorithm specifically includes:
the establishment control performance index J C and the learning performance index J L are respectively as follows:
wherein Q C,R,QL is a weight factor for adjusting the weight of control and learning performance, e (T) is a difference between a reference input r (T) and an output y (T), u (T) is a fuzzy control input, and T is a period of a reference input signal;
and combining the two performance indexes, searching the optimal parameter combination of alpha and beta by adopting a multi-objective optimization algorithm, so that the min { J C,JL }, and the given control and learning performance indexes are met, thereby obtaining the optimal control and learner.
Preferably, the multi-objective optimization algorithm comprises: any one of a multi-objective genetic algorithm, a multi-objective particle swarm optimization algorithm, and a multi-objective evolutionary algorithm.
According to another aspect of the present invention, there is provided a T-S fuzzy system repetitive control apparatus for controlling and learner-separating, comprising:
The controller construction module is used for constructing a repeated controller structure with separated control and learner, setting corresponding fuzzy control laws aiming at the T-S fuzzy system, converting the fuzzy control laws into controllers directly related to control and learning behaviors through conversion, and respectively adjusting the control and learning behaviors of the nonlinear repeated system;
the adjusting parameter acquisition module is used for introducing two adjusting parameters related to the control and learning device into the Lyapunov functional, so as to realize the separation adjustment of the control and learning behaviors;
the problem conversion module is used for acquiring an expression of the control and learner based on the stability condition of the linear matrix inequality and converting a feasible solution problem for solving the gain of the fuzzy controller into a parameter optimization problem constrained by the linear matrix inequality;
and the multi-objective optimization module is used for establishing two performance indexes to evaluate the control and learning performance of the nonlinear repeated control system respectively, and acquiring an optimal control and learning device by utilizing a multi-objective optimization algorithm.
The technical scheme provided by the invention has the beneficial effects that: aiming at the periodic control task of the nonlinear system widely existing in the actual industrial process, a T-S fuzzy system repeated control method for separating the control and the learner is provided, the separation adjustment of the control and the learning behavior is realized, the rapidity and the stability of the nonlinear repeated control system are improved, the high-precision tracking control and the inhibition of the periodic signal of the nonlinear system are realized, the technical guidance is provided for solving the problems of the high-precision tracking control and the inhibition of the actual nonlinear system, and the method has important theoretical and application values.
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The specific effects of the present invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of a method for repetitive control of a T-S fuzzy system with control and learner separated in an embodiment of the present invention;
FIG. 2 is a system block diagram of a method for repetitive control of a T-S fuzzy system with separate control and learner in accordance with an embodiment of the present invention;
FIG. 3 is a multi-objective parameter optimization diagram of a control and learner separated T-S fuzzy system repetitive control method in an embodiment of the present invention;
FIG. 4 is a graph of tracking error effects (optimal control performance) of a method for repetitive control of a T-S fuzzy system with control and learner separated in an embodiment of the present invention;
FIG. 5 is a graph of tracking error effects (learning performance is optimal) of a method for repetitive control of a T-S fuzzy system with control and learner separated in an embodiment of the present invention;
fig. 6 is a block diagram of a T-S fuzzy system repetitive control apparatus with a separate control and learner in an embodiment of the present invention.
Detailed Description
For a clearer understanding of technical features, objects and effects of the present invention, a detailed description of embodiments of the present invention will be made with reference to the accompanying drawings.
In order that the above-recited objects, features and advantages of the present invention will be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those described herein, and therefore the scope of the present invention is not limited to the specific embodiments disclosed below.
Embodiment one:
Referring to fig. 1, an embodiment of the present invention provides a flowchart of a method for repeatedly controlling a T-S fuzzy system with separated control and learner, the method specifically includes:
s1: constructing a repeated controller structure with separated control and learner, setting corresponding fuzzy control laws aiming at a T-S fuzzy system, converting the fuzzy control laws into controllers directly related to control and learning behaviors through conversion, and respectively adjusting the control and learning behaviors of a nonlinear repeated system;
Specifically, in step S1, a proportional controller (P) and an improved repetitive controller (MRC) are connected in parallel to obtain a repetitive controller structure (P-MRC), thereby improving the rapidity and stability of the nonlinear repetitive control system, realizing the structural separation of control and learning behaviors in the repetitive control, designing a corresponding fuzzy control law for a T-S fuzzy system, and converting the fuzzy control law into a controller directly related to the control and learning behaviors through conversion Control and learning behavior of the nonlinear repetitive system is regulated.
Referring to fig. 2, fig. 2 is a system block diagram of a T-S fuzzy system repetitive control method of a control and learner separation design according to the present invention; the system comprises a P-MRC and T-S fuzzy system; in the step S1, a P-MRC structure with a P controller and an MRC connected in parallel is adopted, so that the separation of control and learning behaviors of a nonlinear repetitive control system is facilitated, and the method specifically comprises the following steps:
S11: the improved repetitive controller (MRC) is formed by serially connecting a delay module e -Ts with a low-pass filter q(s) =omega c/(s+ωc, and then generating by unit positive feedback, wherein the MRC state equation is that Wherein x I (t) is the state of the low-pass filter,For the derivative of x I (T), e (T) is the difference between the reference input r (T) and the output y (T), e is a natural constant, T is the period of the reference input signal, s is the laplace operator, ω c represents the cut-off frequency of the low pass filter.
S12: the P-MRC is connected with the P controller in parallel by the MRC controller, so that the rapidity and the stability of the nonlinear repetitive control system are improved, and the control and the learning behaviors in the repetitive control are separated structurally;
s13: for T-S fuzzy system X P (t) is the state of the controlled object,For the derivative of x P (T), A i is a T-S fuzzy system state coefficient matrix; b i is a T-S fuzzy system input coefficient matrix; c is the output coefficient matrix of the T-S fuzzy system, and corresponding fuzzy control law is set Is the gain of the P controller and,Is the gain of the MRC; i, j=1, 2, k r is the number of fuzzy rules, r is the total number of fuzzy rules, Σ isOr (b)Is abbreviated as (1); h i (z (t)) or h j (z (t)) is normalized weight of the precondition variable z (t) under r fuzzy rules, and the normalized weight is transformed to obtain the fuzzy controller related to control and learning Is to adjust the gain of the control action,To adjust the gain of learning behavior;
s14: the state space equation and the fuzzy control law of the P-MRC are brought into a T-S fuzzy system to obtain the state space equation of the whole closed loop system:
I is an identity matrix of appropriate dimensions.
S2: two adjusting parameters related to a control and learner are introduced into the Lyapunov functional, so that the separation adjustment of control and learning behaviors is realized;
further, in step S2, a Lyapunov functional is built, and a controller and a learner are introduced The relevant adjustment parameters α, β are as follows:
S21: the constructed Lyapunov functional is A symmetric positive definite matrix, wherein the symmetric matrix is represented by x, and s is an integral variable;
S22: after the Lyapunov functional is derived, the judgment conditions for obtaining the system stability are as follows: for two tuning parameters α, β and the cut-off frequency ω c of the low-pass filter, if positive definite symmetric matrix X 1、U1 and arbitrary matrix W j are present, so that for 1.ltoreq.i.ltoreq.j.ltoreq.r, the following applies If true, the system is stable, otherwise, the system is unstable;
Wherein the method comprises the steps of
Sym represents the sum of itself and its transpose.
S3: based on the stability condition of the inequality of the linear matrix, acquiring an expression of a control and learner, and converting a feasible solution problem for solving the gain of the fuzzy controller into a parameter optimization problem constrained by the inequality of the linear matrix;
in step S3, the obtained control and learner The expression of (2) is as follows:
W j is LMI matrix, I n,Iq is identity matrix with proper dimension, so that the weight matrix can be influenced by adjusting the sizes of parameters alpha and beta Thereby adjusting the control gainAnd learning gainThe feasible solution problem of solving the fuzzy controller gain is converted into a parameter optimization problem constrained by LMI (linear matrix inequality).
S4: and establishing two performance indexes to evaluate the control and learning performance of the nonlinear repetitive control system respectively, and acquiring an optimal control and learning device by utilizing a multi-objective optimization algorithm.
In step S4, two performance indexes J C,JL are established to evaluate the control and learning performance of the nonlinear repetitive control system respectively, and an optimal control and learning device is obtained by utilizing a multi-objective optimization algorithmThe method comprises the following steps:
S41: establishing control performance index And learning performance indexQ C,R,QL is a weight factor for adjusting the weight of the control and learning performance;
s42: referring to FIG. 3, in combination with two performance metrics, a multi-objective optimization algorithm is used to find the best parameter combination of α, β such that min { J C,JL }, meets a given control and learning performance metric, and thus results in an optimal control and learner
It should be noted that the multi-objective optimization algorithm includes: multi-objective genetic algorithm, multi-objective particle swarm optimization algorithm, multi-objective evolutionary algorithm.
In this example, the NSGA-II algorithm in the multi-objective genetic algorithm is preferred.
In this embodiment, a common nonlinear system is used as a controlled object, and a control target is set to optimally adjust the control performance and learning performance of the nonlinear repetitive control system. Simulation experiments are carried out by using an optimized control and learner, the period reference input is set to r (t) =10sin pi t, the external disturbance is set to d (t) =20, and t >15s, and the experimental results are shown in fig. 4 and 5. The experimental result shows that when the control performance of the system is optimal, the tracking error of the first period is minimum, but a longer time is required to enter a steady state; while the learning performance of the system is optimal, although the tracking error of the first period is slightly larger, the system can enter a steady state through fewer learning times. Therefore, the optimization of the control performance and the learning performance of the nonlinear repetitive control system can be realized through the optimization controller and the learner, and the high-precision tracking requirement of the actual nonlinear system on the periodic signal is met.
Embodiment two:
Referring to fig. 6, the present embodiment provides a T-S fuzzy system repetitive control apparatus with separated control and learner, comprising the following modules:
The controller construction module 1 is used for constructing a repeated controller structure with separated control and learner, setting corresponding fuzzy control laws aiming at the T-S fuzzy system, converting the fuzzy control laws into controllers directly related to control and learning behaviors through transformation, and respectively adjusting the control and learning behaviors of the nonlinear repeated system;
The adjusting parameter obtaining module 2 is used for introducing two adjusting parameters related to the control and learning device into the Lyapunov functional, so as to realize the separation adjustment of the control and learning behaviors;
The problem conversion module 3 is used for acquiring an expression of the control and learner based on the stability condition of the linear matrix inequality and converting a feasible solution problem for solving the gain of the fuzzy controller into a parameter optimization problem constrained by the linear matrix inequality;
and the multi-objective optimization module 4 is used for establishing two performance indexes to evaluate the control and learning performance of the nonlinear repetitive control system respectively, and acquiring an optimal control and learning device by utilizing a multi-objective optimization algorithm.
The embodiment of the invention provides a repeated control method and device for a T-S fuzzy system with separated control and learner, aiming at improving the rapidity and stability of a nonlinear repeated control system. Firstly, providing a repeated controller structure for separating control behaviors and learning behaviors, designing corresponding fuzzy control laws aiming at a T-S fuzzy system, and converting the fuzzy control laws into a fuzzy controller directly related to the control and learning behaviors through conversion; then, introducing adjusting parameters related to a control and learning device into the Lyapunov functional, and realizing the separation adjustment of control and learning behaviors; next, deriving a control and learner expression, converting a feasible solution problem for solving the gain of the fuzzy controller into a parameter optimization problem constrained by the LMI; and finally, establishing two performance indexes to evaluate the control and learning performance of the nonlinear repetitive control system respectively, and combining a multi-objective optimization algorithm to obtain an optimal control and learning device. The beneficial effects of the invention are as follows: aiming at the periodic control task of the nonlinear system widely existing in the actual industrial process, a repeated control method of a T-S fuzzy system with a control and learner separated design is provided, high-precision tracking control and suppression of periodic signals of the nonlinear system are realized, technical guidance is provided for solving the problems of high-precision tracking control and suppression of the actual nonlinear system, and important theory and application value are provided.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or system. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or system that comprises the element.
The foregoing embodiment numbers of the present invention are merely for the purpose of description, and do not represent the advantages or disadvantages of the embodiments. In the unit claims enumerating several means, several of these means may be embodied by one and the same item of hardware. The use of the terms first, second, third, etc. do not denote any order, but rather the terms first, second, third, etc. are used to interpret the terms as labels.
The foregoing description is only of the preferred embodiments of the present invention, and is not intended to limit the scope of the invention, but rather is intended to cover any equivalents of the structures or equivalent processes disclosed herein or in the alternative, which may be employed directly or indirectly in other related arts.
Claims (5)
1. A repeated control method of a T-S fuzzy system with separated control and learner is characterized by comprising the following steps:
constructing a repeated controller structure with separated control and learner, setting corresponding fuzzy control laws aiming at a T-S fuzzy system, converting the fuzzy control laws into controllers directly related to control and learning behaviors through conversion, and respectively adjusting the control and learning behaviors of a nonlinear repeated system;
Two adjusting parameters related to a control and learner are introduced into the Lyapunov functional, so that the separation adjustment of control and learning behaviors is realized;
based on the stability condition of the inequality of the linear matrix, acquiring an expression of a control and learner, and converting a feasible solution problem for solving the gain of the fuzzy controller into a parameter optimization problem constrained by the inequality of the linear matrix;
Establishing two performance indexes to evaluate the control and learning performance of the nonlinear repetitive control system respectively, and acquiring an optimal control and learning device by utilizing a multi-objective optimization algorithm;
The repeated controller structure with separated control and learner is formed by parallelly connecting a proportional controller and an improved repeated controller;
The improved repetitive controller is formed by connecting a delay module e -Ts with a low-pass filter q(s) =omega c/(s+ωc in series and then performing unit positive feedback;
the state equation of the improved repetitive controller is as follows:
wherein x I (t) is the state of the low-pass filter, For the derivative of x I (T), e (T) is the difference between the reference input r (T) and the output y (T), e is a natural constant, T is the period of the reference input signal, s is the laplace operator, ω c represents the cut-off frequency of the low pass filter;
The expression of the T-S fuzzy system is as follows:
wherein x P (t) is the state of the controlled object, For the derivative of x P (T), A i is a T-S fuzzy system state coefficient matrix; b i is a T-S fuzzy system input coefficient matrix; c is the output coefficient matrix of the T-S fuzzy system;
setting a corresponding fuzzy control law as follows:
Wherein, Is the gain of the proportional controller,Is the gain of the improved repetitive controller; i, j=1, 2,..r is the fuzzy rule number, r is the total number of fuzzy rules, Σ isOr (b)Is abbreviated as (1); h i (z (t)) or h j (z (t)) is the normalized weight of the precondition variable z (t) under r fuzzy rules;
obtaining a fuzzy controller related to control and learning through transformation:
Wherein, In order to adjust the gain of the control action,To adjust the gain of learning behavior;
And (3) bringing the state space equation and the fuzzy control law of the repetitive controller structure into a T-S fuzzy system to obtain the state space equation of the whole closed loop system:
Wherein,
I is an identity matrix with proper dimension;
The step of introducing two adjusting parameters related to a control and learner into the Lyapunov functional to realize the separation adjustment of the control and learning behaviors specifically comprises the following steps:
The Lyapunov functional is built with the following expression:
Wherein, A symmetric positive definite matrix, wherein the symmetric matrix is represented by x, and s is an integral variable;
After the Lyapunov functional is derived, the judgment conditions for obtaining the system stability are as follows:
For two tuning parameters α, β and the cut-off frequency ω c of the low-pass filter, if there is a positive symmetric matrix X 1、U1, an arbitrary matrix W j or W i, so that for 1.ltoreq.i.ltoreq.j.ltoreq.r, the following linear matrix inequality is given If true, the system is stable, otherwise, the system is unstable;
Wherein,
Sym represents the sum of itself and its transpose, and r is the total number of fuzzy rules.
2. The T-S fuzzy system repetitive control method of claim 1, wherein the expressions of the control and learner are respectively as follows:
Wherein W j is LMI matrix, I n,Iq is identity matrix with proper dimension, and weight matrix can be influenced by adjusting the size of parameters alpha and beta Thereby adjusting the control gainAnd learning gainThe feasible solution problem of solving the gain of the fuzzy controller is converted into a parameter optimization problem constrained by the inequality of the linear matrix.
3. The method for repeatedly controlling a T-S fuzzy system with separated control and learner as claimed in claim 1, wherein the step of establishing two performance indexes to evaluate the control and learning performance of the nonlinear repetitive control system respectively and obtain the optimal control and learner by using a multi-objective optimization algorithm comprises the following steps:
the establishment control performance index J C and the learning performance index J L are respectively as follows:
wherein Q C,R,QL is a weight factor for adjusting the weight of control and learning performance, e (T) is a difference between a reference input r (T) and an output y (T), u (T) is a fuzzy control input, and T is a period of a reference input signal;
and combining the two performance indexes, searching the optimal parameter combination of alpha and beta by adopting a multi-objective optimization algorithm, so that the min { J C,JL }, and the given control and learning performance indexes are met, thereby obtaining the optimal control and learner.
4. The method for repetitive control of a T-S fuzzy system with control and learner separation of claim 1, the multi-objective optimization algorithm comprising: any one of a multi-objective genetic algorithm, a multi-objective particle swarm optimization algorithm, and a multi-objective evolutionary algorithm.
5. An apparatus for applying the T-S fuzzy system repetitive control method of claim 1, comprising the following modules:
The controller construction module is used for constructing a repeated controller structure with separated control and learner, setting corresponding fuzzy control laws aiming at the T-S fuzzy system, converting the fuzzy control laws into controllers directly related to control and learning behaviors through conversion, and respectively adjusting the control and learning behaviors of the nonlinear repeated system;
the adjusting parameter acquisition module is used for introducing two adjusting parameters related to the control and learning device into the Lyapunov functional, so as to realize the separation adjustment of the control and learning behaviors;
the problem conversion module is used for acquiring an expression of the control and learner based on the stability condition of the linear matrix inequality and converting a feasible solution problem for solving the gain of the fuzzy controller into a parameter optimization problem constrained by the linear matrix inequality;
and the multi-objective optimization module is used for establishing two performance indexes to evaluate the control and learning performance of the nonlinear repeated control system respectively, and acquiring an optimal control and learning device by utilizing a multi-objective optimization algorithm.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
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