Self-correction control method and device based on discount least square parameter identification and storage medium

Abstract

The invention discloses a self-correction control method and device based on discount least square parameter identification and a storage medium, and belongs to the field of target tracking control of a photoelectric tracking system. According to the method, parameter identification is carried out on a second-order system of the fast reflector by using a least square method, and PID parameters of the system are designed by using the identified parameters according to a pole assignment method, so that self-correction PID control is realized. The discount least square method can identify the model of the system more quickly and stably, so that a better control effect can be achieved. According to the method, a control structure is optimized, model information is fully applied under the condition that the system hardware cost is not increased, the system control performance is improved, and the service life of the fast reflector is prolonged.

Description

Technical Field

[0001] The present invention belongs to the field of target tracking control of an optoelectronic tracking system, and in particular relates to a self-correction control method, a device and a storage medium based on discounted least squares parameter identification. Background Art

[0002] As a common optical system, the fast mirror system plays an important role in various application fields, such as astronomical observation, laser communication, target tracking, etc. However, in actual applications, the fast mirror system is often affected by many interferences and disturbances, including environmental vibration, mechanical structure performance degradation, and controller electromagnetic interference. These factors will affect the performance and stability of the system. Some scholars have designed an online estimator to identify the modal dynamics of the system, and designed an adaptive notch filter to track the changing mode, which significantly reduced the system tracking error; some scholars have proposed to design a full tracking controller and a discrete sliding mode variable structure controller for long and short periods respectively to ensure the stability of the system. However, the problems solved by the above studies are all to improve the system's ability to resist external interference under the premise that the system model parameters do not change. In the actual fast mirror system, the system not only has external interference, but also the interference of the fast mirror itself cannot be ignored. For example, the mechanical structure performance of the fast mirror changes due to temperature changes, the fatigue of the mechanical structure under long-term operation, and the heating of the voice coil motor cause its performance to change. Therefore, how to improve the stability of the system under the condition of comprehensive various interference factors is an urgent problem to be solved. Summary of the invention

[0003] In order to solve the above technical problems, the present invention proposes a self-correcting control method, device and storage medium based on discounted least squares parameter identification. The method first uses the discounted least squares method to utilize the input and output information of the fast reflection mirror to identify the discrete transfer function of the system, and then uses the pole configuration method to calculate the control law of PID control in real time according to the identified discrete transfer function. Finally, the PID controller is corrected in real time to realize self-correcting PID control and improve the control performance of the system.

[0004] To achieve the purpose of the present invention, the technical solution adopted by the present invention is as follows:

[0005] The self-correcting control method based on discounted least squares parameter identification includes the following steps:

[0006] Step (1): Establish a mathematical model of the system using the characteristics of the fast reflector, obtain the discrete transfer function of the system, and determine the number of unknown parameters of the discrete system that need to be identified;

[0007] Step (2): Establish a parameter identification model based on the discounted least squares method by collecting the input and output information of the system in real time and the number of unknown parameters of the discrete system in step 1;

[0008] Step (3): Establish the denominator polynomial of the closed-loop expected transfer function ;

[0009] Step (4): Based on the closed-loop expected transfer function denominator polynomial , and parameter identification model, the Diophantine equation is established and solved using the pole placement method to obtain the control law of the self-correcting PID controller.

[0010] In a second aspect, the present invention also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned self-correction control method based on discounted least squares parameter identification.

[0011] In a third aspect, the present invention further provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enables the processor to implement the aforementioned self-correcting control method based on discounted least squares parameter identification.

[0012] The beneficial effects of the present invention are:

[0013] The present invention only relies on the input and output of the controlled object to identify the transfer function of the controlled object in real time, thereby designing a self-correcting controller, avoiding the traditional PID control trial and error method, and saving time; no additional sensors are required, reducing system complexity and hardware costs; since the transfer function of the system is identified in real time, it still has excellent performance when the system fatigues and structural characteristics change. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a control block diagram of the self-correcting control method based on discounted least squares parameter identification of the present invention;

[0015] Figure 2 It is a schematic diagram of the actual optical path of the present invention;

[0016] Figure 3 The control effect comparison curves of the present invention and the prior art method under parameter perturbation are shown in FIG. 1 , wherein (a) is the effect diagram of the present invention, (b) is the effect diagram of the self-correcting PID control based on the least squares parameter identification of the forgetting factor, and (c) is the effect diagram of the pole configuration PID control. DETAILED DESCRIPTION

[0017] The specific implementation modes of the present invention are described in detail below with reference to the accompanying drawings.

[0018] like Figure 1The figure shows the control block diagram of the self-correction control method based on the least squares parameter identification of the present invention, which includes a controller module, a PID parameter design module, a system parameter identification module, and a physical optical path diagram as shown in FIG. Figure 2 As shown; by collecting the real-time input and output signals of the controlled object, the discounted least square method is used for parameter identification, and the PID control law is designed by the pole configuration method using the identified system discrete transfer function and the expected characteristic equation. The specific implementation steps of the composite compensation time lag using the device are as follows:

[0019] Step (1): The transfer function of the fast mirror is:

[0020] ,

[0021] in, is the moment of inertia of the reflector and the flexible support, is the deflection angle of the fast mirror, U is the input voltage of the fast mirror, is the torsional stiffness of the flexible support, c is the equivalent damping coefficient of the flexible support, is the mass of the voice coil motor, l is the distance between the action point of the voice coil motor and the rotation axis of the reflector, L is the total inductance of the loop, is the back electromotive force coefficient, is the motor torque coefficient, s is the Laplace operator, and R is the total loop resistance.

[0022] According to the polynomial decomposition theory, the denominator of the transfer function of the system always contains a real root. The transfer function can be written as a series connection of an oscillation link and an inertia link, as shown below:

[0023] ,

[0024] in, is the output of the transfer function, K is the gain of the transfer function, , is the oscillation frequency, is the damping ratio, is the electrical time constant;

[0025] in, The parameter value of is small and can be ignored in the control system. Therefore, the third-order fast mirror system is equivalent to a second-order oscillation system, and its equivalent second-order system is analyzed:

[0026] ,

[0027] Therefore, the fast mirror transfer function is bilinearly discretized and written in the form of a difference equation:

[0028] ,

[0029] Where:

[0030] ,

[0031] Among them, y(k) represents the system output, is the input and output data of the current time and the past time, k represents the time, represents the vector to be identified, is the noise of the system, u(k) represents the input of the system, T represents the transposition operation, , , , , Represents the estimated value of each element of the vector to be identified.

[0032] Step (2): The discounted least squares method (RDM) introduces the forgetting factor and the weighting factor on the basis of the least squares method. When the weighting factor is introduced, the identification model obtained represents the average characteristics of the system in the data interval; when the forgetting factor is introduced, the identification model obtained can represent the dynamic characteristics of the system. The discounted least squares method considers the characteristics of the weighting factor and the forgetting factor at the same time, and combines the weighting factor and the forgetting factor in the time interval. The identification model obtained takes into account both the average characteristics and dynamic characteristics of the system.

[0033] Discount Factor in Discount Least Squares Method The relationship between the weighting factor and the forgetting factor is:

[0034] , In the formula, i,j represents the time index different from time k;

[0035] Select the criterion function:

[0036] ,

[0037] The estimated values ​​of the model parameters at the kth moment can be written as:

[0038] ,

[0039] make:

[0040] ,

[0041] ,

[0042] The last time for The estimated value plus the correction term can get the new estimated value, and its recursive formula is:

[0043] ,

[0044] In the formula, represents the estimated value of the vector to be identified of the fast mirror system at the kth moment, and the vector to be identified The initial estimate of is a sufficiently small real vector, , weighting factor , forgetting factor , is the covariance matrix, the initial value , I represents the identity matrix, is a sufficiently large positive integer, , is the recursion matrix in the identification process;

[0045] The identified fast mirror transfer function is: ,

[0046] Among them, the estimated parameters , is the estimated output, , ,as well as , , are the characteristic polynomial coefficients of the fast mirror system , , and the fast mirror system input polynomial coefficients , The estimated value of .

[0047] Step (3): The denominator polynomial of the closed-loop expected transfer function selected according to the simulation is: , z represents the complex variable of z-transform, and the superscript -1 represents the unit time delay.

[0048] Step (4): The discrete form of the controlled object is:

[0049] ,

[0050] In the formula, represents the input of the system, Represents the system output, Represents noise:

[0051] ,

[0052] The incremental PID control algorithm is shown in the following formula:

[0053] ,

[0054] In the formula, , , is the PID adjustment parameter, and:

[0055] ,

[0056] in, is the control quantity, is the expected output, is the actual output, rewriting the above formula as:

[0057] ,

[0058] In the formula, is an adjustable parameter, so the discrete-time transfer function of the controller can be obtained as:

[0059] ,

[0060] The above formula can also be expressed as:

[0061] ,

[0062] In the formula , represents the difference operator,

[0063] ,

[0064] ,

[0065] Therefore, the discrete time transfer function of the controller is substituted into the controlled object The output of the closed-loop system can be obtained as:

[0066] ,

[0067] Let the closed-loop characteristic polynomial be the denominator polynomial of the desired transfer function, that is, the Diophantine equation:

[0068] ,

[0069] in, is the denominator polynomial of the desired transfer function, determined by simulation and experiment , where A, B, F1, G, and R are all parameters of the controller.

[0070] Finally, solving the Diophantine equation can obtain the controller parameters F1, G, R and the self-correcting PID control law.

[0071] Example

[0072] The design process and experimental results of the present invention are described in detail below using a photoelectric tracking platform system as an example:

[0073] (1) Obtain the desired closed-loop characteristic polynomial of the system through computer simulation , mathematical modeling is used to equate the transfer function of the fast reflector system to a second-order model.

[0074] (2) Setting the initial value of the discounted least squares method , and the forgetting factor , weighting factor .

[0075] (3) The actual input and output of the sampling system are used to identify the transfer function of the controlled object online in real time using the discounted least squares method.

[0076] (4) Then, the control law of the controller is obtained by solving the Diophantine equation using the identified transfer function and the desired characteristic polynomial using the pole placement method.

[0077] Figure 3 The present invention (RDM-STC-PID) (ie Figure 3 (a) in the figure and the self-tuning PID control based on the forgetting factor least squares parameter identification (RFF-STC-PID) (i.e. Figure 3 (b) in), Pole Configuration PID Control (PPC-PID) (i.e. Figure 3 Compared with (c) in the figure, the system equivalent transfer function is changed by artificially setting the time at 3.5s. The method of the present invention can respond quickly after the system parameters are perturbed, and the steady-state error still maintains the level before the parameter perturbation, with excellent performance. This method only relies on the input and output of the controlled object to identify the transfer function of the controlled object in real time, thereby designing a self-correcting controller, avoiding the traditional PID control trial and error method, and saving time. In addition, there is no need to add additional sensors, which reduces the complexity of the system and the hardware cost. Finally, the invention can identify the transfer function of the system in real time. Therefore, when the system fatigue and structural characteristics change, the parameters controlling it will change, so that the system maintains excellent performance.

[0078] In a second aspect, the present invention also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned self-correction control method based on discounted least squares parameter identification.

[0079] In a third aspect, the present invention further provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enables the processor to implement the aforementioned self-correcting control method based on discounted least squares parameter identification.

[0080] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A self-tuning control method based on discounted least squares parameter identification, characterized in that: The steps include: Step (1): Establish a mathematical model of the system using the characteristics of the fast reflector, obtain the discrete transfer function of the system, and determine the number of unknown parameters of the discrete system that need to be identified; Step (2): Establish a parameter identification model based on the discounted least squares method by collecting the input and output information of the system in real time and the number of unknown parameters of the discrete system in step (1); Step (3): Establish the denominator polynomial of the closed-loop expected transfer function ; Step (4): Based on the closed-loop expected transfer function denominator polynomial , and parameter identification model, the Diophantine equation is established and solved using the pole placement method to obtain the control law of the self-correcting PID controller.

2. The self-tuning control method based on discounted least squares parameter identification according to claim 1 is characterized in that: The system mathematical model established in step (1) is a second-order model, and the transfer function of the fast reflector is discretized and written in the form of a differential equation: ， In the formula, y(k) represents the system output, is the input and output data of the current time and the past time, k represents the time, represents the vector to be identified, is the noise of the system, and T represents the transpose operation.

3. The self-tuning control method based on discounted least squares parameter identification according to claim 2 is characterized in that: and The expression is: ， Where u(k) represents the input of the system, , , , , Represents the estimated value of each element of the vector to be identified.

4. The self-tuning control method based on discounted least squares parameter identification according to claim 3 is characterized in that: The step (2) of establishing a parameter identification model based on the least squares method includes: The recursive formula of the discounted least squares method is: ， in, represents the estimated value of the vector to be identified of the fast reflector system at the kth moment, the vector to be identified The initial estimate of is a sufficiently small real vector, , weighting factor , forgetting factor , is the covariance matrix, the initial value , I represents the identity matrix, is a sufficiently large positive integer, , is the recursion matrix in the identification process.

5. The self-tuning control method based on discounted least squares parameter identification according to claim 4 is characterized in that: The identified fast mirror transfer function is: , Among them, the estimated parameters , is the estimated output, , ,as well as , , are the characteristic polynomial coefficients of the fast mirror system , , and the fast mirror system input characteristic polynomial coefficients , , The estimated value of .

6. The self-tuning control method based on discounted least squares parameter identification according to claim 5 is characterized in that: In step (3), the denominator polynomial of the closed-loop desired transfer function established is: , z represents the complex variable of z-transform.

7. The self-tuning control method based on discounted least squares parameter identification according to claim 6 is characterized in that: In step (4), the discrete form of the controlled object is: ， Wherein, A(z) represents the characteristic polynomial of the fast mirror system, B(z) represents the input characteristic polynomial of the fast mirror system, and the superscript -1 of the parameter z represents the inversion operation.

8. The self-tuning control method based on discounted least squares parameter identification according to claim 7 is characterized in that: The discrete-time transfer function of the controller is: ， In the formula, Indicates adjustable parameters; The discrete-time transfer function of the controller is converted into the discrete form of the controlled object. The output of the closed-loop system is: + ， in, represents the expected output, A, B, F1, G, R are all parameters of the controller, let , solve the equation to obtain the controller parameters G, R, F1, and obtain the self-correcting PID control law.

9. An electronic device, characterized in that: include: one or more processors; A memory for storing one or more programs; Wherein, when one or more programs are executed by the one or more processors, the one or more processors implement the self-correcting control method based on discounted least squares parameter identification as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that: Executable instructions are stored thereon, which, when executed by a processor, enable the processor to implement the self-correcting control method based on discounted least squares parameter identification as described in any one of claims 1-8.

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