Model-free adaptive control method based on UKF pseudo partial derivative estimation

Abstract

The invention discloses a model-free adaptive control method based on UKF pseudo partial derivative estimation, and belongs to the technical field of automatic control. The method mainly solves the problems that an accurate mathematical model is difficult to establish in a nonlinear control system in the actual industry, and various uncertainties, complex unknown disturbances and the like influence the control accuracy. The control scheme comprises the following steps: designing a model-free adaptive controller based on input and output data; designing an unscented Kalman filter (UKF) to estimate a pseudo partial derivative; establishing a model-free adaptive control scheme based on UKF pseudo partial derivative estimation; according to the model-free adaptive control method based on UKF pseudo partial derivative estimation disclosed by the invention, better control precision and stronger anti-interference capability can be realized in an industrial nonlinear process under the influence of unknown disturbance, and the control precision requirement of industrial production is met.

Description

Technical Field

[0001] The present invention belongs to the field of automatic control technology, and more specifically, relates to a model-free adaptive control (MFAC) method based on unscented Kalman filter (UKF) pseudo partial derivative estimation. Background Art

[0002] In recent years, with the continuous improvement of industrial production levels, higher control requirements have been put forward for process control and equipment control in intelligent manufacturing. Among them, the adaptive control method based on optimization has high control accuracy and does not rely on operator experience, which will greatly reduce labor cost losses.

[0003] For the study of adaptive control of nonlinear systems, the following two issues need to be considered: 1. There are constantly changing unknown disturbances in the actual production process. The controller needs to effectively handle the dynamic changes of the system caused by the unknown disturbances to ensure the stability of the control process; 2. While maintaining stable operation, improve the accuracy of control error tracking.

[0004] At present, model-free adaptive control methods have been widely used in actual production, such as chemical reaction process control, power electronics, frequency and voltage control of power systems, etc. They have the advantages of strong robustness, high control accuracy, and only use the input and output data of the controlled object without the need for the model and structure of the controlled object. At the same time, facing more complex and more information-containing production process control and equipment control, the controller is usually required to have higher control accuracy, greater flexibility and elasticity to meet the control requirements of complex and changeable nonlinear systems. In order to improve the control effect of nonlinear systems, domestic and foreign scholars have done a lot of research, such as model-free adaptive control based on fuzzy logic and model-free adaptive control based on neural network learning. Most of these methods are based on operator experience and require a large amount of data to train the neural network, which poses challenges to the real-time and reliability requirements of the controller. Therefore, how to design a control method with strong robustness, high control accuracy, high flexibility and elasticity that does not rely on accurate models to solve the increasingly complex actual production process control for complex and strongly nonlinear system control is an urgent problem to be solved in this field. Summary of the invention

[0005] The present invention discloses a model-free adaptive control method based on UKF pseudo partial derivative estimation. The technical problem to be solved is to ensure that the actual production process control does not rely on the accurate model to achieve high-precision control while enhancing the anti-interference ability of the controller and improving the parameter selection range to make it more flexible and elastic.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] The present invention discloses a model-free adaptive control method based on UKF pseudo partial derivative estimation, which is mainly aimed at the problems such as unknown disturbance influence on nonlinear control systems in industrial production, has good control accuracy and strong anti-interference ability, and meets the control accuracy requirements in industrial production.

[0008] The present invention discloses a model-free adaptive control method based on UKF pseudo partial derivative estimation, the method comprising the following steps:

[0009] Step 1: Design a model-free adaptive controller based on input and output data, characterized in that: design a model-free adaptive control law algorithm:

[0010]

[0011] in,

[0012] λ is a positive weight coefficient; ρ is a step size factor greater than 0; y * (t+1) is the expected output of the nonlinear system at time t+1; y(t) represents the output of the nonlinear system at time t; u(t) represents the control quantity of the model-free adaptive controller at time t; u(t-1) represents the control quantity of the model-free adaptive controller at time t-1; φ(t) is the defined pseudo partial derivative.

[0013] Step 2: Design an unscented Kalman filter (UKF) to estimate the pseudo partial derivatives of the model-free adaptive controller, which mainly includes the following steps:

[0014] Based on the input and output of the controlled object, the following state space equation is designed for UKF state estimation:

[0015]

[0016] in,

[0017] y UKF (t) is the predicted output of UKF at time t; I is the identity matrix;

[0018] Generate sample points at time t:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] in,

[0025] χ t is the sample point at time t; UKF is the scaling parameter; n is the dimension; P is the covariance; W is the weight factor;

[0026] The sample points are passed through the state equation:

[0027]

[0028]

[0029] in,

[0030] v(·) is the UKF state equation designed above;

[0031] Calculate the prior covariance of the predicted state quantity at time t:

[0032]

[0033] The sample points are passed through the designed output state equation:

[0034]

[0035]

[0036] in,

[0037] z(·) is the UKF prediction output state equation designed above;

[0038] Calculate the ex ante covariance of the forecast output at time t:

[0039]

[0040]

[0041] Based on the prior covariance, calculate the UKF gain value:

[0042]

[0043] in,

[0044] σ is the system noise; g t+1 is the gain of UKF at time t+1;

[0045] Calculate and update the UKF prediction state:

[0046]

[0047] Get the UKF estimate of φ(t)

[0048] Step 3: Establish a model-free adaptive control scheme based on UKF pseudo-partial derivative estimation, which mainly includes the following steps:

[0049] Model-free adaptive control law algorithm based on UKF pseudo-partial derivative estimation;

[0050]

[0051] in,

[0052] The estimated pseudo-partial derivative of the UKF at time t.

[0053] Beneficial effects:

[0054] The present invention discloses a model-free adaptive control method based on UKF pseudo partial derivative estimation. The unscented Kalman filter is introduced into the model-free adaptive algorithm for the first time, and the real-time prediction and update of the pseudo partial derivative parameters in the model-free adaptive control algorithm are realized, thereby obtaining the optimal control quantity of the controlled object, improving the control accuracy and flexibility of the control algorithm, and having good robustness, meeting the requirements for control accuracy and robustness in industrial production.

[0055] After reading the specific embodiments of the present invention in conjunction with the accompanying drawings, other features and advantages of the present invention will become more clear. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 The flowchart of the model-free adaptive control method based on UKF pseudo partial derivative estimation proposed by the present invention;

[0057] Figure 2 This is a simplified structural diagram of the working principle of the model-free adaptive control method based on UKF pseudo partial derivative estimation proposed in the present invention;

[0058] Figure 3 The tracking performance of the model-free adaptive control method based on UKF pseudo partial derivative estimation proposed in the present invention;

[0059] Figure 4 The tracking performance of the model-free adaptive control method based on the traditional projection method pseudo-partial derivative parameter prediction;

[0060] Figure 5 is the control input of the model-free adaptive control method based on UKF pseudo partial derivative estimation proposed in the present invention;

[0061] Figure 6 It is the control input of the model-free adaptive control method based on the prediction of pseudo-partial derivative parameters using the traditional projection method; DETAILED DESCRIPTION

[0062] In order to better illustrate the purpose and advantages of the present invention, a comparison is made below with a model-free adaptive control method based on pseudo-partial derivative parameter prediction using the projection method, and the invention is further described in detail in conjunction with the corresponding drawings.

[0063] The present invention has good control accuracy and strong anti-interference ability under the control of nonlinear systems in industrial production, meeting the requirements of control accuracy in industrial production. A model-free adaptive control method based on UKF pseudo partial derivative estimation is proposed. Below, a specific implementation method of a model-free adaptive control method based on UKF pseudo partial derivative estimation is described in detail.

[0064] See also Figure 1 As shown, the present embodiment discloses a model-free adaptive control method based on UKF pseudo partial derivative estimation, comprising the following steps:

[0065] Step S1: Design a model-free adaptive controller based on input and output data.

[0066] Step S11: Establishing a nonlinear mathematical relationship between the input and output data of the controlled system.

[0067] The actual industrial production control system is a nonlinear system with time-varying parameters, multiple variables, and unknown disturbances, which can be expressed as the following general nonlinear function relationship between input and output:

[0068] y(t+1)=f(y(t),u(t));

[0069] in,

[0070] f(·) represents a nonlinear function; y(t+1) represents the output of the nonlinear system at time t+1; y(t) represents the output of the nonlinear system at time t; u(t) represents the control quantity of the model-free adaptive controller at time t;

[0071] Step S12: Convert the nonlinear system into an equivalent dynamic linearization data model.

[0072] Specifically, the general nonlinear system in step S11 satisfies:

[0073] The input and output of the system are observable and controllable, that is, for a bounded expected value y * (t+1), in the presence of unknown disturbances, there exists a bounded control input signal u(t) such that under the action of the control input signal u(t), the output of the system is equal to the expected given signal.

[0074] The system satisfies the generalized Lipschitz condition, when Δu(t)≠0, Δy(t+1)≤bΔu(t);

[0075] in,

[0076] b is a positive constant; Δy(t+1)=y(t+1)-y(t), Δu(t)=u(t)-u(t-1);

[0077] Step S13: For the general nonlinear system in step S11, when Δu(t)≠0, there exists a pseudo partial derivative φ(t), and the system is transformed into:

[0078] Δy(t+1)=φ(t)Δu(t);

[0079] in,

[0080] φ(t) is the pseudo partial derivative defined; φ(t)≤b.

[0081] Step S14: See Figure 2 As shown, a model-free adaptive controller is designed based on input and output data.

[0082] First consider the following input estimation criteria:

[0083] J(u(t))=y * (t+1)-y(t+1) 2 +λu(t)-u(t-1) 2 ;

[0084] Solving equations The model-free adaptive control law algorithm can be obtained:

[0085]

[0086] in,

[0087] λ is a positive weight coefficient; ρ is a step size factor greater than 0, which is introduced into the control algorithm to make it more general; y * (t+1) is the expected output.

[0088] In order to make the algorithm more capable of tracking time-varying systems and better applicable to nonlinear systems in actual production processes, a reset algorithm is added:

[0089] φ(t)=φ(1),φ(t)≤ε or Δu(t-1)≤ε;

[0090] in,

[0091] ε is a small positive number; φ(1) is the initial value of the pseudo partial derivative.

[0092] Step S2: Design an unscented Kalman filter (UKF) to estimate pseudo partial derivatives.

[0093] Step S21: Design the following UKF state space equation to predict the pseudo partial derivatives in the model-free adaptive control algorithm:

[0094]

[0095] in,

[0096] y UKF (t) is the predicted output of UKF at time t; I is the identity matrix;

[0097] Step S22: Generate a sample point (χ) at time t.

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] in,

[0104] χ t is the sample point at time t; UKF is the scaling parameter; n is the dimension; P is the covariance; W is the weight factor;

[0105] Step S23: The sample points are transferred through the state equation.

[0106]

[0107]

[0108] in,

[0109] v(·) is the state equation of UKF in step S21;

[0110] Step S24: Calculate the prior covariance of the predicted state quantity at time t.

[0111]

[0112] The sample points are passed through the output state equation designed in step S21:

[0113]

[0114]

[0115] in,

[0116] z(·) is the predicted output state equation of UKF in step S4;

[0117] Step S25: Calculate the prior covariance of the predicted output at time t.

[0118]

[0119]

[0120] Step S26: Calculate the UKF gain value based on the prior covariance.

[0121]

[0122] in,

[0123] σ is the system noise; g t+1 is the UKF gain at time t+1;

[0124] Step S27: Calculate and update the UKF prediction state quantity.

[0125]

[0126] Step S3: Establish a model-free adaptive control scheme based on UKF pseudo partial derivative estimation.

[0127] The details are as follows:

[0128] The pseudo partial derivative estimate predicted by UKF in step S2 is updated to the model-free adaptive control law algorithm designed in step S1, thus obtaining a model-free adaptive control scheme based on UKF pseudo partial derivative estimation.

[0129] Step S31: The reset algorithm based on UKF pseudo partial derivative estimation also satisfies the reset algorithm described in step S1, namely:

[0130] Or Δu(t-1)≤ε;

[0131] Step S32: Update the estimated value of the UKF pseudo partial derivative to the model-free adaptive control law algorithm to obtain the optimal control quantity of the nonlinear system.

[0132]

[0133] in, is the estimated value of the pseudo partial derivative of UKF at time t.

[0134] The general nonlinear system used in the embodiment is given as follows:

[0135]

[0136] Among them, a(t)=round(t500) is a time-varying parameter. Obviously, the introduction of time-varying parameters makes the structure, parameters and order of the nonlinear system time-varying.

[0137] Consider the following desired output signal.

[0138]

[0139] In order to compare the above general nonlinear system, a model-free adaptive control method based on UKF pseudo partial derivative estimation is proposed ( Figure 3 and Figure 5 ) and the model-free adaptive control method based on pseudo-partial derivative parameter prediction using projection method ( Figure 4 and Figure 6 ) takes the same parameters.

[0140] Depend on Figure 3 and Figure 4 It can be seen that: in terms of tracking performance, the control method proposed by the present invention is compared with the model-free adaptive control method based on the prediction of pseudo-partial derivative parameters by the projection method. At 50 seconds, the overshoot of the control method proposed by the present invention is -0.764, and the overshoot of the model-free adaptive control method based on the prediction of pseudo-partial derivative parameters by the projection method is -1.339. Compared with the model-free adaptive control method based on the prediction of pseudo-partial derivative parameters by the projection method, the overshoot performance is improved by about 75.3%. Similarly, at 150 seconds, the overshoot performance of the method proposed by the present invention is improved by about 24.9%. Comparison shows that the tracking performance under the control algorithm proposed by the present invention is significantly improved compared with the model-free adaptive control method based on the prediction of pseudo-partial derivative parameters by the projection method.

[0141] Depend on Figure 5 and Figure 6 It can be seen that: in terms of control input performance, the control method proposed by the present invention can also significantly reduce overshoot and oscillation amplitude compared with the model-free adaptive control method based on the projection method pseudo-partial derivative parameter prediction. From the perspective of control cost, the control method proposed by the present invention can significantly reduce control cost compared with the model-free adaptive control method based on the projection method pseudo-partial derivative parameter prediction.

[0142] This embodiment mainly uses system output and tracking effect as performance parameters. Figure 4 and Figure 5 The tracking effect curves of the model-free adaptive control based on UKF pseudo partial derivative estimation and the model-free adaptive control based on projection method pseudo partial derivative parameter prediction are respectively given. It can be seen from the figure that compared with the model-free adaptive control method based on projection method pseudo partial derivative parameter prediction, the control method given by the present invention has better tracking accuracy and smaller overshoot in nonlinear time-varying systems.

[0143] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the embodiments are only used to explain the invention and are not used to limit the scope of protection of the invention. Any modifications, equivalent replacements, improvements, etc. under the same principles and concepts as the invention should be included in the scope of protection of the invention.

Claims

1. A model-free adaptive control method based on UKF pseudo partial derivative estimation, characterized in that: The method comprises the following steps: Step 1: Design a model-free adaptive controller based on input and output data; Step 2: Design an unscented Kalman filter (UKF) to estimate pseudo partial derivatives; Step 3: Establish a model-free adaptive control scheme based on UKF pseudo-partial derivative estimation.

2. According to the method of claim 1, in step 1, a model-free adaptive controller is designed based on input and output data, characterized in that: Design a model-free adaptive control law algorithm: in, λ is a positive weight coefficient; ρ is a step size factor greater than 0; y * (t+1) is the expected output of the nonlinear system at time t+1; y(t) represents the output of the nonlinear system at time t; u(t) represents the control quantity of the model-free adaptive controller at time t; u(t-1) represents the control quantity of the model-free adaptive controller at time t-1; φ(t) is the defined pseudo partial derivative.

3. The method according to claim 1, characterized in that: The design of the unscented Kalman filter (UKF) in step 2 estimates the pseudo partial derivatives of the model-free adaptive controller, which mainly includes the following steps: Based on the input and output of the controlled object, the following state space equation is designed for UKF state estimation: in, y UKF (t) is the predicted output of UKF at time t; I is the identity matrix; Generate sample points at time t: in, χ t is the sample point at time t; UKF is the scaling parameter; n is the dimension; P is the covariance; W is the weight factor; The sample points are passed through the state equation: in, v(·) is the UKF state equation designed above; Calculate the prior covariance of the predicted state quantity at time t: The sample points are passed through the designed output state equation: in, z(·) is the UKF prediction output state equation designed above; Calculate the ex ante covariance of the forecast output at time t: Based on the prior covariance, calculate the UKF gain value: in, σ is the system noise; g t+1 is the gain of UKF at time t+1; Calculate and update the UKF prediction state: Get the UKF estimate of φ(t) 4. The method according to claim 1, characterized in that: The model-free adaptive control scheme based on UKF pseudo-partial derivative estimation is established, which mainly includes the following steps: Model-free adaptive control law algorithm based on UKF pseudo-partial derivative estimation; in, The estimated pseudo-partial derivative of the UKF at time t.

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