Model reference adaptive control method and system of approximate period time-varying nonlinear circuit

Abstract

The invention relates to a model reference adaptive control method of a nonlinear circuit containing approximate period time-varying parameters. The method comprises the following steps: establishing an approximate period segmentation steady system model of a nonlinear circuit; the method comprises the following steps: determining how many sub-intervals coexist in a controlled system model through a method of identifying an approximate period segmentation steady system switching moment of unknown parameters; establishing a stable reference model according to the number of the subintervals in combination with the stability condition of the proposed approximate period segmentation steady system; establishing a linear matrix inequality constraint condition, solving a Lyapunov matrix parameter based on a Lyapunov stability theory, and designing update rates of different control gains for each state quantity of a nonlinear circuit system so as to update a real-time control quantity; and finally converging the actual control gain to the nominal control gain, so that the state of the controlled system model with unknown parameters tracks the expected state track. According to the invention, control is carried out under the condition of interference input, and the practicability is higher.

Description

Technical Field

[0001] The invention relates to a model reference adaptive control method for a nonlinear circuit containing quasi-periodic time-varying parameters, and belongs to the field of model adaptive control. Background Art

[0002] The model reference adaptive control method is a kind of parallel control concept. As a control method, it has the characteristics of adaptability and robustness. Compared with other control methods such as PID control, the model reference adaptive control method can realize the self-update of control parameters, and can better cope with external disturbances, and can adjust parameters in real time to adapt to changes. Compared with model predictive control, model reference adaptive control requires less prior knowledge of the system, and can control the system under the premise of unknown system parameters. The most important feature is that model reference adaptive control can realize the state of the controlled system to converge to the state trajectory of the expected system. Different from general stability control, it can make the state quantity of the controlled system change according to the expected value according to the designer's idea.

[0003] In order to realize model reference adaptive control, it is necessary to first establish the desired and stable reference system model, and then use the parameter relationship between the controlled system and the reference system to realize the update of the control gain. The methods include direct model reference adaptive control and indirect model reference adaptive control: direct model reference adaptive control directly updates the control gain to obtain the real-time updated control quantity, so the control process is relatively "direct"; in contrast, indirect model reference adaptive control does not make the controlled system track the desired model, because there is an observation model for connection in the middle, which makes the process more "indirect"; but whether it is direct or indirect model reference adaptive control, the state of the controlled model can track the desired state trajectory, and the convergence speed is fast and the convergence accuracy is high.

[0004] In recent years, model reference adaptive control methods have been widely used in the control of industrial systems. For example, some existing reference models based on design give the update rate of the longitudinal adaptive control parameters of vehicle-mounted variable-wingspan UAVs, and use the designed controller to make the system performance close to the reference model's performance. However, since the selected reference model is still a steady-state system, this method is not applicable when more complex state trajectories are expected in engineering. For example, some existing technologies have designed an integrated fault-tolerant control strategy based on a multi-model adaptive unknown input observer and a model reference adaptive control method for common faults of fixed-wing aircraft actuators. However, the controlled system discussed in this method, namely the lateral motion model of the fixed-wing aircraft, is a time-invariant system. For more complex controlled models, this control method will no longer be applicable. Summary of the invention

[0005] The present invention provides a model reference adaptive control method for a nonlinear circuit with quasi-periodic time-varying parameters, aiming to solve at least one of the technical problems existing in the prior art.

[0006] The technical solution of the present invention relates to a model reference adaptive control method, which is applied to a nonlinear circuit containing quasi-periodic time-varying parameters. The method according to the present invention comprises the following steps:

[0007] S100, establishing a quasi-periodic piecewise steady-state system model of a nonlinear circuit; the quasi-periodic piecewise steady-state system model does not have a fixed period, and is used as a controlled system model for approximating a nonlinear circuit;

[0008] S200, determining how many subintervals exist in the controlled system model by identifying the switching time of the quasi-periodic piecewise steady system of unknown parameters;

[0009] S300, according to the number of subintervals and in combination with the stability condition of the proposed quasi-periodic piecewise steady system, a corresponding stable reference model based on the quasi-periodic piecewise steady system is established;

[0010] S400, then using the reference model parameters to establish linear matrix inequality constraints, based on Lyapunov stability theory, solving to obtain Lyapunov matrix parameters that stabilize the system, and using the Lyapunov matrix parameters to design different control gain update rates for each state quantity of the nonlinear circuit system, so as to update the real-time control quantity;

[0011] S500 , making the actual control gain finally converge to the nominal control gain, so that the state of the controlled system model with unknown parameters tracks the expected state trajectory.

[0012] Further, in step S100:

[0013] Assume there is an interval [T min ,T max ], where T min Represents the shortest cycle time, T max Represents the longest cycle duration;

[0014] Let the duration of each cycle be T i , T i As the length of the subinterval of the quasi-periodic piecewise steady-state system, T i ∈[T min ,T max ];

[0015] The state equation of the quasi-periodic piecewise steady-state system model with disturbance input and unknown parameters is expressed as follows:

[0016]

[0017] In the formula, the time-varying parameter matrices A(t), B(t), B w (t) represent the nominal system matrix, input matrix and interference input matrix respectively, and all parameters are unknown; x(t) = [x 1 (t),x 2 (t),…,x n (t)], n is the dimension of the system, x(t) is the state quantity of the system; u(t) = [u 1 (t),u 2 (t),…,u m (t)], m is the dimension of the control input, u(t) is the control input of the system; w(t) = [w 1 (t),w 2 (t),…,w f (t)], f is the dimension of the interference input signal, w(t) is the interference input signal and its parameters are unknown.

[0018] Further, in step S200,

[0019] S210, determining the switching time by detecting whether there is a jump in the identification result within a short time segment, so as to obtain the system matrix A i Control Matrix B i The corresponding switching time set T s1 and T s2 ;

[0020] S220, the above switching time set T s1 and T s2 Taking the union can obtain all switching time points within a period of time for the quasi-periodic piecewise steady-state system with unknown parameters, as well as taking the time segments between the time points and collecting the identification quantity information Φ and Γ obtained above, comparing the identification quantities in different intervals to determine whether the system parameters of the two sub-intervals are consistent, and combining the range of each cycle duration to determine how many sub-intervals there are in each cycle.

[0021] Wherein, the step S210 includes:

[0022] S211, assume that the control input of the controlled system model satisfies u(t) = u(t-t e ), let t e is a parameter selected in the identification process, let ∈(t) = x(t)–x(t―t e ),t≥t e , let Ξ(t)=[∈(t),∈(t―t s ),…,∈(t―(N―1)ts )], where t s is the sampling interval;

[0023] S212, let Φ be the identification system matrix A i The matrix quantity, and Φ satisfies Ξ(t)=ΦΞ(t―t s ), where t∈[t 1 +Nt s +t e ,t 2 ], where N represents the sample size, Each time, a small segment of state data is taken online for calculation to collect information about Φ. When the value of Φ undergoes a certain change and the magnitude of the change exceeds a certain threshold, it is judged that a switch has occurred, and a set of switching times is generated and recorded as T s1 ;

[0024] S213, let Γ be the identification control matrix B i The matrix quantity, Each time, a small segment of state data is taken online for calculation to collect information about Γ. When the value of Γ undergoes a certain change and the magnitude of the change exceeds a certain threshold, it is judged that a switch has occurred, and a set of switching times is generated and recorded as T s2 .

[0025] Further, in step S300,

[0026] For each cycle duration T i ∈[T min ,T max ], without considering the control input and disturbance input, the state equation of the quasi-periodic piecewise steady-state system is expressed as follows:

[0027]

[0028] set up is the duration of the kth subinterval in the i-th cycle, which satisfies set up ρ(.) represents the spectral radius of the matrix, λ * is a positive number selected, representing an exponential decay rate; if and only if or And M i is a diagonalizable matrix, the quasi-periodic piecewise constant system λ * - Index stability.

[0029] Further, in step S300,

[0030] The system matrix A of all subintervals of the stable reference model ismi The Hurwitz matrix is ​​selected, and the necessary and sufficient conditions for the stability of the quasi-periodic piecewise steady system are proposed to determine whether the designed system meets the exponential stability condition;

[0031] Among them, the state equation of the stable reference model is expressed as follows:

[0032]

[0033] In the formula, A m (t), B m (t) are all quasi-periodic time-varying matrices, r(t) is the reference input signal, x m (t) is the state of the reference model; each cycle contains S subintervals. When time t is in the i-th subinterval, i = 1, 2, ..., S, there is A m (t) = A mi , B m (t) = B mi ; Wherein, when the time is in the i-th subinterval, the switching signal x i The value of (t) is 1, and the switching signal χ i The value of (t) is 0.

[0034] Further, in step S400,

[0035] According to the system matrix A of the stable reference model mi Substitute into the following linear matrix inequality system to solve the linear matrix inequality system:

[0036]

[0037] P 1,0 ≤μ 1 P S,S+1 ,

[0038] P i,i―1 ≤μ i P i―1,i ,

[0039]

[0040] In the formula, P i,i―1 and P i,i+1 are the Lyapunov matrices corresponding to the initial and final moments of the ith subinterval, respectively. The Lyapunov matrix is ​​a symmetric positive definite form and satisfies P i,i-1 ,P i,i+1 >0, i=1,2,…,S.

[0041] Further, in step S400,

[0042] Assume that the corresponding control gain of each state variable x(t), r(t), w(t) is K x (t), K r (t), K w (t), the real-time control quantity is expressed as follows:

[0043] u(t)=K x (t)x(t)+K r (t)r(t)+K w (t)w(t)

[0044] And suppose that there is a corresponding set of nominal control gains in each sub-interval (t) and the parameters satisfy the following matching relationship:

[0045]

[0046] The parameter update rate of the control gain satisfies the following relationship so that the tracking error e(t) eventually converges to 0:

[0047]

[0048] In the formula, κ xi , κ ri , κ wi represents the scaling constant corresponding to the state quantities x(t), r(t), and w(t) when the time is in the i-th subinterval, S i is a fixed matrix, is a positive definite matrix, and P(t) is the Lyapunov matrix obtained by solving the linear matrix inequality.

[0049] Further, in step S400,

[0050] The expression of the Lyapunov matrix P(t) corresponding to the kth subinterval in the i-th cycle is as follows:

[0051]

[0052] The time-varying Lyapunov matrix P(t) is substituted into the parameter update rate, and the obtained control gain update rate is used to solve the nominal control gain corresponding to each subinterval, and then the real-time control amount is obtained, so that the tracking error e(t) converges asymptotically to 0.

[0053] The technical solution of the present invention also relates to a computer-readable storage medium on which program instructions are stored, and the above-mentioned method is implemented when the program instructions are executed by a processor.

[0054] The technical solution of the present invention also relates to a model reference adaptive control system, which includes a computer device, and the computer device contains the above-mentioned computer-readable storage medium.

[0055] The beneficial effects of the present invention are as follows:

[0056] The model reference adaptive control method of the nonlinear circuit containing quasi-periodic time-varying parameters of the present invention is used to control the state tracking of the controlled system containing unknown parameters to the state trajectory of the desired reference system, realizes the asymptotic tracking of the state trajectory of the nonlinear circuit containing unknown quasi-periodic time-varying parameters to the desired quasi-periodic piecewise steady-state system reference model, and realizes the convergence of the control gain to the standard control gain value.

[0057] After constructing the mathematical model of the quasi-periodic piecewise steady system, the present invention first identifies the switching moment of the controlled system, determines how many sub-intervals there are in the controlled system and the switching order of the sub-intervals through data processing, and then designs the desired reference model by using the stability condition of the quasi-periodic piecewise steady system after obtaining this information, then uses the parameter data in the designed reference model to solve the Lyapunov matrix that makes the system stable, designs the Lyapunov function and designs the update rate of the control gain by the asymptotic convergence condition, thereby obtaining the constantly changing control gain and the real-time control quantity, and finally can realize that the tracking error gradually converges to 0, and when the reference input signal is introduced to meet the continuous excitation condition, the asymptotic convergence of the control gain can also be guaranteed.

[0058] The present invention aims at a nonlinear circuit system with quasi-periodic time-varying parameters, introduces an interference input signal to represent the uncertainty factors that often exist in actual circuit systems, and performs control under the condition of interference input, making the control method more practical. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a nonlinear circuit structure diagram and parameter corresponding information according to the present invention.

[0060] Figure 2 The present invention is a flowchart for gradually analyzing and controlling a quasi-periodic piecewise steady-state system with unknown parameters according to the method of the present invention.

[0061] Figure 3 It is an information diagram of the identification quantities Φ, Γ corresponding to the system parameters in each subinterval of the quasi-periodic piecewise steady system according to the method of the present invention.

[0062] Figure 4 It is a trajectory diagram of three actual state quantities and a reference state quantity in a corresponding nonlinear circuit system according to the method of the present invention.

[0063] Figure 5It is a graph showing the changing trajectories of the tracking errors of three state quantities in the corresponding nonlinear circuit system according to the method of the present invention.

[0064] Figure 6 It is the convergence status of each parameter in the actual control gain matrix according to the method of the present invention. DETAILED DESCRIPTION

[0065] The concept, specific structure and technical effects of the present invention will be clearly and completely described below in combination with the embodiments and drawings to fully understand the purpose, scheme and effect of the present invention.

[0066] It should be noted that, unless otherwise specified, when a feature is referred to as being "fixed" or "connected" to another feature, it may be directly fixed or connected to another feature, or it may be indirectly fixed or connected to another feature. The singular forms "a", "said" and "the" used herein are also intended to include the plural forms, unless the context clearly indicates otherwise. In addition, unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art. The terms used in this specification are intended only to describe specific embodiments and are not intended to limit the invention. The term "and / or" used herein includes any combination of one or more of the related listed items.

[0067] It should be understood that, although the term first, second, third etc. may be adopted to describe various elements in the present disclosure, these elements should not be limited to these terms. These terms are only used to distinguish the same type of elements from each other. For example, without departing from the scope of the present disclosure, the first element may also be referred to as the second element, and similarly, the second element may also be referred to as the first element. The use of any and all examples or exemplary language ("for example", "such as" etc.) provided herein is only intended to better illustrate embodiments of the present invention, and unless otherwise required, the scope of the present invention will not be limited.

[0068] Reference Figures 1 to 6 In some embodiments, a model reference adaptive control method according to the present invention is applied to a nonlinear circuit with quasi-periodic time-varying parameters, and the method comprises at least the following steps:

[0069] S100, establishing a quasi-periodic piecewise steady-state system model of a nonlinear circuit; the quasi-periodic piecewise steady-state system model does not have a fixed period, and is used as a controlled system model for approximating the nonlinear circuit;

[0070] S200, determining how many sub-intervals exist in the controlled system model by identifying the switching time of the quasi-periodic piecewise steady system of unknown parameters;

[0071] S300, according to the number of subintervals and in combination with the stability condition of the proposed quasi-periodic piecewise steady system, a corresponding stable reference model based on the quasi-periodic piecewise steady system is established;

[0072] S400, then using the reference model parameters to establish linear matrix inequality constraints, based on the Lyapunov stability theory, solving the Lyapunov matrix parameters that stabilize the system, and using the Lyapunov matrix parameters to design different control gain update rates for each state quantity of the nonlinear circuit system to update the real-time control quantity;

[0073] S500 , making the actual control gain finally converge to the nominal control gain, so that the state of the controlled system model with unknown parameters tracks the expected state trajectory.

[0074] The quasi-periodic time-varying system of the embodiment of the present invention originates from the phenomenon that the system dynamically presents non-strict periodic cyclic changes, which is widely present in actual engineering. It is common in aerospace systems, medical systems, power systems, etc. Among them, because each cycle of parameters in actual engineering applications is not strictly in accordance with a fixed periodic cycle, the duration of each cycle will change more or less, and this change is unpredictable and belongs to an unknown quantity. The quasi-periodic time-varying system of the present invention is more in line with the requirements of actual engineering applications. Further, because the quasi-periodic time-varying characteristics are difficult to accurately model, there must be unknown parameters and interference inputs in actual quasi-periodic time-varying systems such as nonlinear circuits. The embodiment of the present invention uses a quasi-periodic piecewise steady-state system as a reference model, which is a model reference adaptive control method for unknown quasi-periodic time-varying controlled systems, and is suitable for solving nonlinear circuit control problems containing quasi-periodic parameters and interference inputs. The present invention uses a quasi-periodic piecewise steady-state system as a reference model, which not only effectively increases the degree of freedom of design, but also takes into account the situation of interference input, making the control method more practical in actual applications. Furthermore, the switching moment identification method for the quasi-periodic piecewise steady-state system of the present invention can make the identification more accurate by adjusting the parameters of the identification process, further increasing the flexibility of the identification method, and can use data for identification online instead of offline, which is more suitable for actual engineering applications.

[0075] The present invention also analyzes the conditions for the stability of a quasi-periodic piecewise steady system and provides a number of sufficient or necessary conditions. On the one hand, it can more intuitively determine whether a quasi-periodic piecewise steady system satisfies exponential stability, which helps to ensure its stability as a reference system; on the other hand, it can more quickly solve the Lyapunov matrix that makes the system stable, which can be used to design the update rate of the parameters, laying the foundation for the design of a model reference adaptive control method based on a quasi-periodic piecewise steady system.

[0076] Specific implementation of step S100

[0077] The modeling method of the quasi-periodic piecewise steady-state system with interference input and unknown parameters of the present invention obtains a quasi-periodic piecewise steady-state system model. Among them, the quasi-periodic time-varying system refers to a type of system with properties similar to periodicity. Unlike general periodic systems, this system does not show strict periodicity, and the dynamics of the system show a certain cyclical law, but there is no fixed period. Although the system parameters will change over time, there is no fixed duration for each cycle, and the duration of each new cycle cannot be accurately determined. The present invention is aimed at the modeling problem of the quasi-periodic time-varying system with the above characteristics, and proposes a quasi-periodic piecewise steady-state system model.

[0078] Specifically, the method of the present invention adopts the state space method to construct the model of the quasi-periodic piecewise steady system. First, it is assumed that there is an interval of cycle duration variation, and it is set as [T min ,T max ], where T min Represents the shortest cycle time, T max Represents the longest cycle duration. It should be noted that the above two values ​​do not need to be very accurate. Assume that the duration of each cycle is T i , T i As the length of the subinterval of the quasi-periodic piecewise steady system, and satisfying T i ∈[T min ,T max ], the state equation of the quasi-periodic piecewise steady-state system model with disturbance input and unknown parameters can be expressed as follows:

[0079]

[0080] Where, the time-varying parameter matrices A(t), B(t), B w (t) represent the nominal system matrix, input matrix and interference input matrix respectively, and all parameters are unknown; x(t) = [x 1 (t),x 2 (t),…,x n (t)], n is the dimension of the system, x(t) is the state quantity of the system, x(t)∈R n ; u(t)=[u 1 (t),u 2 (t),…,u m (t)], m is the dimension of the control input, u(t) is the control input of the system, u(t)∈R m ; w(t) = [w 1 (t),w 2 (t),…,w f(t)], f is the dimension of the interference input signal, w(t) is the interference input signal and its parameters are unknown, w(t)∈R f .

[0081] The method of the present invention considers an approximate piecewise steady-state system as the actual control object in each subinterval. Specifically, assuming that there are S subintervals in total, the system matrix, control matrix and interference input matrix in the i-th subinterval are A and i ,B i ,B wi , i = 1, 2, ..., S, and let the percentage of each sub-interval in a cycle be η i , assuming that in the process of quasi-periodic time-varying, the percentage of each sub-interval in each cycle remains unchanged, and in each new cycle, the overall cycle duration changes indefinitely, and accordingly, the duration of each sub-interval in the new cycle will also change indefinitely. Then, when the quasi-periodic piecewise steady-state system model is in the i-th sub-interval, the state equation is as follows:

[0082]

[0083] It should be noted that the above-mentioned modeling method based on quasi-periodic piecewise steady-state system of the present invention has a certain universality in practice. For quasi-periodic time-varying systems that are commonly found in nonlinear circuits, contain interference inputs and have unknown parameters, this modeling method is more convenient and intuitive.

[0084] In an application embodiment, see Figure 1 and Figure 2 In the model reference adaptive control method of the nonlinear circuit containing quasi-periodic time-varying parameters of the present invention, a nonlinear circuit system containing quasi-periodic time-varying parameters is modeled, a state space model of the system is determined, and a state space model of the system is determined based on the selected parameters. 1 ,v 2 ,i L ] as a state variable (see Figure 2 The corresponding voltage v 1 ,v 2 and current i L ), with U(t) current source as the real-time control quantity, U w (t) The current source is used as the interference input, and the corresponding nonlinear circuit model can be written as the following expression:

[0085]

[0086] Accordingly, the state equation of the nonlinear circuit system can be expressed as:

[0087]

[0088] The quasi-periodic parameter in this system is the nonlinear resistance R v The change of parameters over time can be approximated as a quasi-periodic piecewise constant form. Considering the quasi-periodic time-varying parameters of the system, each cycle time T i ∈[T min ,T max ], and there is no relationship between the current cycle duration and the previous cycle duration. Each cycle contains a total of S sub-intervals, i = 1, 2, ..., S, and the percentage of the duration of each sub-interval in each cycle remains unchanged.

[0089] Specific implementation of step S200

[0090] See also Figure 3 The method of the present invention determines the number of subintervals of a quasi-periodic piecewise steady-state system with unknown parameters based on the method of identifying the switching moment. In practical applications, there are often situations where system parameters are unknown, including the unknown number of subintervals, which makes it impossible to design the desired reference model accordingly. In the existing applications of reference adaptive control of switching system models, in most cases it is assumed that the total number of seed system modes in the system is known, and the exact moment of mode switching is known. However, in practice, the parameters of the system may be unknown, and it is difficult to directly measure the accurate switching moment. The method of the present invention adopts a method for identifying the number of subintervals and the switching order to deal with the situation where parameters are unknown.

[0091] The method of the present invention determines how many sub-intervals there are in an unknown controlled system and the switching order between sub-intervals by collecting data. Specifically, the actual controlled system is operated in a relatively ideal environment, and the parameter information of the sub-intervals of the continuous time-varying system is obtained by collecting data and performing calculation processing.

[0092] First, by identifying the system matrix A in different subintervals i It should be noted that in this process, the system matrix A is not identified. i The specific value of is not used, but the switching time is determined by detecting whether there is a jump in the identification result within a short time segment. In which, it is assumed that the system operates under the condition of no interference input. When the control input of the controlled system model satisfies u(t)=u(t―t e ), t e is a parameter selected in the identification process, let ∈(t) = x(t)–x(t―t e ),t≥t e , let Ξ(t)=[∈(t),∈(t―t s ),…,∈(t―(N―1)t s )], where t s is the sampling interval, and Φ is the identification system matrix Ai The matrix quantity, and Φ satisfies Ξ(t)=ΦΞ(t―t s ), where t∈[t 1 +Nt s +t e ,t 2 ], where N represents the sample size, and its specific expression is In this way, a small segment of state data is taken online each time for calculation to collect information about Φ. When the value of Φ undergoes a certain change and the magnitude of the change exceeds a certain threshold, it is considered that a switch has occurred. This ensures that the error caused by the calculation is not affected. The set of switching moments is recorded as T s1 In this process, by reducing t s ,t e These two parameters are used to reduce the time period of each identification, thereby improving the accuracy of identification.

[0093] Next, the control input signal is changed to a ramp signal. Specifically, let Γ be the identification control matrix B i Similarly, each time the same time segment as the previous step is taken to collect the corresponding data information online, and the solution is obtained through calculation It is understandable that in this process, the control matrix B is not obtained. i The specific value of is not the identification quantity related to it, and the relationship it satisfies is By observing the formula, we can know that based on the result of the previous step identification, that is, the system matrix A is judged to be i In the constant sub-interval, when the control input is a ramp signal and t e When it is a fixed quantity, the identification quantity Γ only has the control matrix B i It will affect the value, so the identification quantity Γ can identify the control matrix B in different sub-intervals. i , and similarly, a small segment of state quantity data is taken online each time for calculation, and the information of Γ is collected. When the identification quantity Γ undergoes a certain switch, and the size of the switch exceeds a certain threshold, it can be judged that a switch has occurred. All the switching moments obtained are collected, and the set of corresponding switching moments is recorded as T s2 .

[0094] The above two switching time sets T s1 and T s2 Taking the union, we can get all the switching time points of the quasi-periodic piecewise steady system with unknown parameters within a period of time. These switching time points represent A i or B iAll the moments when switching occurs, as well as, taking the time segments between the time points and collecting the identification quantity information Φ,Γ obtained above, comparing the identification quantities in different intervals to determine whether the system parameters of the two sub-intervals are consistent, combined with the approximate range of each cycle duration, to determine how many sub-intervals exist in each cycle.

[0095] In an application embodiment, by max , n≥2 collects state quantity information, and based on the above data processing method, continuously calculates the size of the identification quantity Φ,Γ online. Since the time period selected each time is short, the size of the time period is related to t s ,t e The parameters are related. By comparing the size of the identification quantity in adjacent time periods, when its value changes by more than a certain threshold, it is considered that switching has occurred. Among them, Φ and Γ correspond to the system matrix A respectively. i and control matrix B i First, the control input is selected as a step signal, which also satisfies the period condition u(t)=u(t―t e ), identify the system matrix A i The switching time T s1 , and retain the parameter information of the identified quantity in each sub-interval. Since there may be system matrices A between different sub-intervals i The same control matrix B i Different situations, so based on this step, further identify the control matrix B i Get the switching time set T s2 , and also retain the identification information of different sub-intervals collected, and finally combine the identification results of these two steps to obtain all the switching moments T in this short period of time s =T s1 ∪T s2 .

[0096] Next, the identification information in all sub-intervals is listed. By comparing the size of the identification of different sub-intervals, it can be determined how many sub-intervals there are in total and the switching order of the sub-intervals. By observing the changes in the sub-intervals, the sub-interval sequence that changes cyclically is found, and the approximate time range of the cycle duration is used for comparison. If there are multiple sub-interval sequences that meet the conditions, then observe whether the percentage of each sub-interval in each sub-interval sequence remains unchanged. Since the percentage of sub-intervals is unknown, it is necessary to observe whether the percentage of the duration occupied by each sub-interval in each new cycle has changed. If there are still several sub-interval sequences that meet the above conditions, the smallest cyclic sequence is taken as the actual sub-interval switching sequence.

[0097] The method of the present invention identifies the switching moment of the completed mathematical model. This process helps to update and control the parameters of the controlled system under the condition of unknown parameters in the subsequent model reference adaptive control. Therefore, the identification result in this step does not need to be the precise value of the parameter, but rather determines the total number of sub-intervals in the unknown controlled system through information such as the switching moment and the identification amount. This step is performed under the premise that the designer has little prior knowledge of the system.

[0098] Specific implementation of step S300

[0099] The method of the present invention constructs the exponential stability condition of the quasi-periodic piecewise steady system based on the Lyapunov method, so as to establish the corresponding desired stable reference model based on the quasi-periodic piecewise steady system. According to the properties of the quasi-periodic piecewise steady system, a stability condition is proposed to satisfy the exponential stability, which includes sufficient conditions and necessary conditions, and a stable reference model of the quasi-periodic piecewise steady system corresponding to the number of subintervals of the controlled system is established.

[0100] Among them, for each cycle duration T i ∈[T min ,T max ], without considering the control input and disturbance input, the state equation of the quasi-periodic piecewise steady-state system is expressed as follows:

[0101]

[0102] set up is the duration of the kth subinterval in the i-th cycle, which satisfies set up If and only if or And M i When the matrix is ​​diagonalizable, the quasi-periodic piecewise constant system λ can be derived * -Exponential stability; where λ * is a positive number selected, representing the exponential decay rate; ρ(.) represents the spectral radius of the matrix. Conversely, when the system satisfies λ * -When the index is stable, we can get It can be understood that the above sufficient and necessary conditions can more intuitively determine whether a quasi-periodic piecewise steady system satisfies exponential stability.

[0103] Among them, the system matrix A of all subintervals of the stable reference model is mi All are selected as Hurwitz matrices. The sufficient conditions for the stability of the quasi-periodic piecewise steady system can be used to determine whether the designed system meets the exponential stability conditions. The state equation of the stable reference model is expressed as follows:

[0104]

[0105] In the formula, A m (t), B m (t) are all periodic time-varying matrices, r(t) is the reference input signal, x m (t) is the state of the reference model. In the stable reference model, the length of each cycle may vary but contains S subintervals. When time t is in the i-th subinterval, i = 1, 2, ..., S, there is A m (t) = A mi , B m (t) = B mi ; Assume that there is a switching signal χ corresponding to the i-th subinterval i (t), when the time is in this subinterval, its value is 1, and otherwise it is 0. Assume that in each subinterval there is a set of nominal control gains (t) The following parameter matching conditions are met:

[0106]

[0107] It can be understood that the method of the present invention designs the reference model accordingly after determining the number of sub-intervals of the unknown controlled system and the switching order. According to the stability conditions of the quasi-periodic piecewise steady-state system mentioned above, the same or different reference models are designed for each sub-interval to achieve the desired state trajectory. Therefore, when it is confirmed that the designed reference model meets the stability conditions and has the desired state trajectory, it can be inferred that the designed reference model is reasonable.

[0108] Specific implementation of step S400

[0109] The method of the present invention realizes the asymptotic convergence of the state tracking error of the controlled system through a direct model reference adaptive control method. The direct model reference adaptive control method uses the data of each state quantity to obtain the real-time updated control gain update rate, and then solves to obtain the real-time updated control gain, and uses the state feedback control method to obtain the updated real-time control quantity.

[0110] First, a stable reference model is established, which is a stable reference model of a quasi-periodic piecewise steady system. The update rate of the control gain can be solved by the relationship between the state quantities of the controlled system model and the stable reference model. According to the above step S300, the state equation of the stable reference model is expressed as follows:

[0111]

[0112] In the formula, x m(t) is the expected state trajectory of the reference model, r(t) is the input signal of the reference model; when the time is in the i-th subinterval, A m (t) = A mi , B m (t) = B mi , assuming there is a switching signal χ i (t), when the time is in the i-th subinterval, its value is 1, and otherwise it is 0.

[0113] Among them, the tracking error e(t) can converge to 0 asymptotically when time approaches ∞. Since state feedback is used, each state quantity x(t), r(t), w(t) has a corresponding control gain K x (t), K r (t), K w (t), the real-time control quantity is expressed as follows:

[0114] u(t)=K x (t)x(t)+K r (t)r(t)+K w (t)w(t)

[0115] And assume that there is a corresponding set of nominal control gains in each subinterval Make sure that the parameters meet the following matching relationship:

[0116]

[0117] When the update rate of the control gain satisfies the following relationship, the tracking error e(t) can finally converge to 0:

[0118]

[0119] In the formula, κ xi , κ ri , κ wi Represents the scaling constant corresponding to the state quantities x(t), r(t), and w(t) when the time is in the i-th subinterval. It can be set by yourself, i=1, 2, …, S; S i is a fixed matrix that needs to satisfy is a positive definite matrix, and P(t) is the Lyapunov matrix obtained by solving the linear matrix inequality. Under such an update rate condition, it can be achieved that when time t tends to ∞, e(t) can eventually converge to 0, and the convergence speed is fast.

[0120] Among them, in order to solve the Lyapunov matrix that makes the system stable, another sufficient condition is needed. Specifically, the model reference adaptive control method is designed according to the established reference system model, and the system matrix A of the designed stable reference model is mi Substitute into the following linear matrix inequality system to solve the linear matrix inequality system:

[0121]

[0122] P 1,0 ≤μ 1 P S,S+1 ,

[0123] P i,i―1 ≤μ i P i―1,i ,

[0124]

[0125] In the formula, P i,i―1 and P i,i+1 are the Lyapunov matrices corresponding to the initial and final moments of the ith subinterval, respectively. Furthermore, the Lyapunov matrix is ​​in symmetric positive definite form and satisfies P i,i-1 ,P i,i+1 >0, i=1,2,…,S. It can be understood that when λ i ◇ When it is a positive number, it corresponds to A i is the Hurwitz matrix, and vice versa, corresponding to A i is a non-Hurwitz matrix. Assume that when all subintervals are switched during the solution process, μ i ≥1,i=1,2,…,S, when A mi Choose the Hurwitz matrix, corresponding to λ i ◇ is a positive number, and the expression of the Lyapunov matrix P(t) corresponding to the kth subinterval in the i-th cycle is as follows:

[0126]

[0127] Solve to obtain the Lyapunov matrix P corresponding to each sub-interval switching time i,i―1 , P i,i+1 , but since the duration of each cycle will change, the duration of the subinterval will also change accordingly, so the time-varying Lyapunov matrix P(t) can be obtained, and then substituted into the following parameter update rate:

[0128]

[0129] The control gain update rate can be used to solve the nominal control gain corresponding to each subinterval, and then the real-time control quantity can be obtained to achieve the asymptotic convergence of the tracking error e(t) to 0. In order to facilitate the solution of the actual nonlinear circuit and obtain a better asymptotic convergence effect, the parameter μ can be taken as i =1,i=1,2,…,S.

[0130] The method of the present invention combines the Lyapunov matrix expression, and solves the above-established linear matrix inequality to obtain the Lyapunov matrix that makes the system stable. If the solution can obtain the result, it can be obtained that the quasi-periodic piecewise constant system satisfies λ * -Exponential stability. Compared with the above stability conditions, the method of the present invention is not so intuitive in judging the stability of the system, but it can more clearly obtain the Lyapunov matrix that makes the system stable.

[0131] Specific implementation of step S500

[0132] The method of the present invention achieves the asymptotic convergence of the actual control gain to the nominal control gain by introducing the continuous excitation condition of the reference input signal. When the input signal of the stable parameter model meets the continuous excitation condition and other conditions remain unchanged, or when the frequency component is sufficiently rich, other conditions, including the parameter update rate and the designed reference model, can be kept unchanged, that is, when time tends to infinity, not only the tracking error e(t) can converge to 0, but also the actual control gain K can be achieved. x (t), K r (t), K w (t) Converges to the nominal control gain

[0133] Specifically, when the reference input signal introduces a continuous excitation condition, the control gain K(t) can be further realized to converge asymptotically to the nominal control gain K based on the previous step. * (t), this step can increase the robustness of the control process. When the number of bilateral spectrum components of the reference input signal is greater than or equal to n+1, where n is the dimension of the state quantity, when this condition is met, the matrix composed of the state quantity and the control input interference input will satisfy the row full rank, and the control gain K(t) will eventually converge to the unique solution K * (t).

[0134] The present invention realizes the state tracking of a nonlinear circuit system containing unknown quasi-periodic time-varying parameters to the state trajectory of a desired quasi-periodic piecewise constant reference model system. At the same time, when the condition of continuous excitation of the reference input signal is introduced, the control gain can also converge to the nominal control gain, thereby increasing the system's anti-interference ability and robustness.

[0135] Model Reference Adaptive Control Method and System Simulation Example

[0136] See also Figure 4 , Figure 5 and Figure 6 The model reference adaptive control method and system of the nonlinear circuit with quasi-periodic time-varying parameters of the present invention are actually tested, wherein a nonlinear circuit system with quasi-periodic time-varying characteristics is considered, the time unit is second (s), and the parameter of each cycle duration is set to T i ∈[10s,15s],C 1 =1 / 9F, C 2 =1 / 24F, R =3Ω, R 0 =1Ω, L = 1 / 7H, the circuit system has 3 sub-intervals in total, and the duration percentage of each sub-interval is η 1 =0.3,η 2 =0.2,η 3 =0.5, where the values ​​of nonlinear conductivity in the three sub-intervals are G 1 = -0.8S, G 2 =0.5S,G 3 =1S. Among them, from Figure 5 It can be seen that the tracking errors corresponding to each state quantity first converge quickly to a smaller range, and when the time is large, the tracking error is close to 0. And, see Figure 6 The actual control gain matrix of each parameter convergence situation, taking the control gain matrix of each parameter in sub-interval 3 as an actual example, from Figure 6 It can be seen that when the time is large, the control gain has almost completed convergence.

[0137] It should be appreciated that the method steps in the embodiments of the present invention can be implemented or implemented by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer readable memory. The method can use standard programming techniques. Each program can be implemented in a high-level process or object-oriented programming language to communicate with a computer system. However, if necessary, the program can be implemented in an assembly or machine language. In any case, the language can be a compiled or interpreted language. In addition, the program can be run on a programmed ASIC for this purpose.

[0138] Furthermore, the operations of the processes described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes described herein (or variations and / or combinations thereof) may be performed under the control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) that is executed collectively on one or more processors, by hardware, or a combination thereof. The computer program includes a plurality of instructions that may be executed by one or more processors.

[0139] Further, the method can be implemented in any type of computing platform that is operably connected to a suitable computer, including but not limited to a personal computer, a minicomputer, a mainframe, a workstation, a network or distributed computing environment, a separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, etc. Various aspects of the present invention can be implemented in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, an optical read and / or write storage medium, an RSM, a ROM, etc., so that it can be read by a programmable computer, and when the storage medium or device is read by the computer, it can be used to configure and operate the computer to perform the process described herein. In addition, the machine-readable code, or portions thereof, can be transmitted via a wired or wireless network. When such media includes instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor, the invention described herein includes these and other different types of non-transitory computer-readable storage media. When programmed according to the methods and techniques of the present invention, the present invention can also include the computer itself.

[0140] The computer program can be applied to input data to perform the functions described herein, thereby converting the input data to generate output data stored in a non-volatile memory. The output information can also be applied to one or more output devices such as a display. In a preferred embodiment of the present invention, the converted data represents physical and tangible objects, including specific visual depictions of physical and tangible objects produced on the display.

[0141] The above is only a preferred embodiment of the present invention. The present invention is not limited to the above implementation. As long as the technical effect of the present invention is achieved by the same means, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of protection of the present invention. Within the scope of protection of the present invention, its technical scheme and / or implementation method may have various modifications and changes.

Claims

1. A model reference adaptive control method, applied to a nonlinear circuit with quasi-periodic time-varying parameters, characterized in that: The method comprises the following steps: S100, establishing a quasi-periodic piecewise steady-state system model of a nonlinear circuit; the quasi-periodic piecewise steady-state system model does not have a fixed period, and is used as a controlled system model for approximating a nonlinear circuit; S200, determining how many subintervals exist in the controlled system model by identifying the switching time of the quasi-periodic piecewise steady system of unknown parameters; S300, according to the number of subintervals and in combination with the stability condition of the proposed quasi-periodic piecewise steady system, a corresponding stable reference model based on the quasi-periodic piecewise steady system is established; S400, then using the reference model parameters to establish linear matrix inequality constraints, based on Lyapunov stability theory, solving to obtain Lyapunov matrix parameters that stabilize the system, and using the Lyapunov matrix parameters to design different control gain update rates for each state quantity of the nonlinear circuit system, so as to update the real-time control quantity; S500 , making the actual control gain finally converge to the nominal control gain, so that the state of the controlled system model with unknown parameters tracks the expected state trajectory.

2. The method according to claim 1, characterized in that In step S100: Assume there is an interval [T min ,T max ], where T min Represents the shortest cycle time, T max Represents the longest cycle duration; Let the duration of each cycle be T i , T i As the length of the subinterval of the quasi-periodic piecewise steady-state system, T i ∈[T min ,T max ]; The state equation of the quasi-periodic piecewise steady-state system model with disturbance input and unknown parameters is expressed as follows: In the formula, the time-varying parameter matrices A(t), B(t), B w (t) represent the nominal system matrix, input matrix and interference input matrix respectively, and all parameters are unknown; x(t) = [x1(t), x2(t), …, x n (t)], n is the dimension of the system, x(t) is the state quantity of the system; u(t)=[u1(t),u2(t),…,u m (t)], m is the dimension of the control input, u(t) is the control input of the system; w(t) = [w1(t), w2(t), …, w f (t)], f is the dimension of the interference input signal, w(t) is the interference input signal and its parameters are unknown.

3. The method according to claim 2, characterized in that In step S200, S210, determining the switching time by detecting whether there is a jump in the identification result within a short time segment, so as to obtain the system matrix A i Control Matrix B i The corresponding switching time set T s1 and T s2 ; S220, the above switching time set T s1 and T s2 Taking the union can obtain all the switching time points of the quasi-periodic piecewise steady-state system with unknown parameters within a period of time, and taking the time segments between the time points and collecting the identification information Φ and Γ obtained above, comparing the identification quantities in different intervals to determine whether the system parameters of the two sub-intervals are consistent, and combining the range of each cycle duration to determine how many sub-intervals there are in each cycle; Wherein, the step S210 includes: S211, assume that the control input of the controlled system model satisfies u(t) = u(tt e ), let t e is a parameter selected in the identification process, let ε(t) = x(t) – x(tt e ),t≥t e , let Ξ(t)=[ε(t),ε(tt s ),…,ε(t-(N-1)t s )], where t s is the sampling interval; S212, let Φ be the identification system matrix A i The matrix quantity, and Φ satisfies Ξ(t)=ΦΞ(tt s ), where t∈[t1+Nt s +t e ,t2], where N represents the sample size, Each time, a small segment of state data is taken online for calculation to collect information about Φ. When the value of Φ undergoes a certain change and the magnitude of the change exceeds a certain threshold, it is judged that a switch has occurred, and a set of switching times is generated and recorded as T s1 ; S213, let Γ be the identification control matrix B i The matrix quantity, Each time, a small segment of state data is taken online for calculation to collect information about Γ. When the value of Γ undergoes a certain change and the magnitude of the change exceeds a certain threshold, it is judged that a switch has occurred, and a set of switching times is generated and recorded as T s2 .

4. The method according to claim 3, characterized in that In step S300, For each cycle duration T i ∈[T min ,T max ], without considering the control input and disturbance input, the state equation of the quasi-periodic piecewise steady-state system is expressed as follows: set up is the duration of the kth subinterval in the i-th cycle, which satisfies set up ρ(.) represents the spectral radius of the matrix, λ * is a positive number selected, representing an exponential decay rate; if and only if or And M i is a diagonalizable matrix, the quasi-periodic piecewise constant system λ * - Index stability.

5. The method according to claim 4, characterized in that In step S300, The system matrix A of all subintervals of the stable reference model is mi The Hurwitz matrix is ​​selected to determine whether the designed system meets the exponential stability condition through the proposed necessary and sufficient conditions for the stability of the quasi-periodic piecewise-steady system, so as to ensure the stability of the quasi-periodic piecewise-steady reference system model. Among them, the state equation of the stable reference model is expressed as follows: In the formula, A m (t), B m (t) are all quasi-periodic time-varying matrices, r(t) is the reference input signal, x m (t) is the state of the reference model; each cycle contains S subintervals. When time t is in the i-th subinterval, i = 1, 2, ..., S, there is A m (t) = A mi , B m (t) = B mi ; Wherein, when the time is in the i-th subinterval, the switching signal x i The value of (t) is 1, and the switching signal χ i The value of (t) is 0.

6. The method according to claim 5, characterized in that In the step S400, According to the system matrix A of the stable reference model mi Substitute into the following linear matrix inequality system to solve the linear matrix inequality system: P 1,0 ≤μ1P S,S+1 , P i,i-1 ≤μ i P i-1,i , In the formula, P i,i-1 and P i,i+1 are the Lyapunov matrices corresponding to the initial and final moments of the ith subinterval, respectively. The Lyapunov matrix is ​​a symmetric positive definite form and satisfies P i,i-1 ,P i,i+1 >0, i=1,2,...,S.

7. The method according to claim 6, characterized in that In the step S400, Assume that the corresponding control gain of each state variable x(t), r(t), w(t) is K x (t), K r (t), K w (t), the real-time control quantity is expressed as follows: u(t)=K x (t)x(t)+K r (t)r(t)+K w (t)w(t) And suppose that there is a corresponding set of nominal control gains in each sub-interval And the parameters satisfy the following matching relationship: The parameter update rate of the control gain satisfies the following relationship so that the tracking error e(t) eventually converges to 0: In the formula, κ xi , κ ri , κ wi represents the scaling constant corresponding to the state quantities x(t), r(t), and w(t) when the time is in the i-th subinterval, S i is a fixed matrix, S i is a positive definite matrix, i = 1, 2, ..., S, and P(t) is the Lyapunov matrix obtained by solving the linear matrix inequality.

8. The method according to claim 7, characterized in that In the step S400, The expression of the Lyapunov matrix P(t) corresponding to the kth subinterval in the i-th cycle is as follows: The time-varying Lyapunov matrix P(t) is substituted into the parameter update rate, and the obtained control gain update rate is used to solve the nominal control gain corresponding to each subinterval, and then the real-time control amount is obtained, so that the tracking error e(t) converges asymptotically to 0. 9 . A computer-readable storage medium having program instructions stored thereon, wherein the program instructions, when executed by a processor, implement the method according to any one of claims 1 to 8.

10. A model reference adaptive control system, characterized in that: include: A computer device comprising a computer readable storage medium according to claim 9.

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