A penalty function optimization method for ultrasonic motor model-free servo system based on Lagrange multipliers

Abstract

The invention discloses a method for optimizing the penalty function of an ultrasonic motor model-free servo system based on Lagrange multipliers, including controller initialization, prediction of the real-time operating state of the servo system, real-time prediction state correction of the system, construction of a Lagrange-type augmented penalty function expression about the input quantity, searching for the optimal solution of the augmented penalty function by the steepest descent Newton method, control state monitoring, and control parameter correction; the method of the invention obtains motor operation state characterization parameters by analyzing the input and output data of the servo system without relying on the physical model of the system; based on the penalty function, the constrained optimization problem about the frequency is converted into an unconstrained variant, the Newton-steepest descent method is selected as the Lagrangian-type loss function optimization, the optimal solution of the operating frequency is estimated, and the ultrasonic motor is finally driven to work. The method of the invention has the advantages of strong real-time state tracking, high input estimation accuracy, high control precision, and self-adaptability.

Description

Technical Field

[0001] The invention relates to automatic control and motor control technology, in particular to a penalty function optimization method for an ultrasonic motor model-free servo system based on Lagrange multipliers. Background Art

[0002] The excitation signal of the ultrasonic motor is limited by the operating frequency of the internal piezoelectric ceramic sheet. The excitation signal frequency of ultrasonic motors of the same model but different batches will vary due to the processing technology. At the same time, due to the loss of friction materials and temperature rise during operation, the resonant frequency point of the ultrasonic motor will shift. Therefore, the frequency range of the excitation signal changes in real time during the operation of the ultrasonic motor. This feature of the ultrasonic motor places higher requirements on the adaptability of the servo system.

[0003] In addition, there is an excitation frequency section that cannot work during the loading moment and commutation process of the ultrasonic motor, namely the dead zone. At present, the improved algorithms for the discontinuous motion state caused by the dead zone include: using sliding mode control to design a variable structure system observer to weaken the influence of the dead zone, and adjusting the state variables of the sliding mode controller in real time to achieve precise position control; further increasing the number of input parameters, designing a second-order sliding mode control method based on frequency and phase; rewriting the piecewise function expression of the output with respect to the input into a first-order relationship in the form of conditional derivatives, and then using the state observer to achieve position control of the ultrasonic motor, avoiding the situation where the implementation of the control strategy is limited because the output is not differentiable with respect to the input.

[0004] The change of the resonant frequency point and the existence of the dead zone both limit the excitation frequency of the ultrasonic motor. The current control algorithm mainly designs the control algorithm for the existing frequency limit. Considering that the excitation frequency range is difficult to express analytically, in order to further improve the control accuracy of the servo system, it is necessary to incorporate the time-varying excitation frequency range into the control strategy and use the excitation frequency as a constraint to find an input that meets the output performance. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a penalty function optimization method for ultrasonic motor model-free servo system based on Lagrange multipliers, which makes up for the defect that the model-free control method of the classical ultrasonic motor servo system cannot handle the application background of controlled input restriction.

[0006] Technical solution: A method for optimizing the penalty function of an ultrasonic motor model-free servo system based on Lagrange multipliers of the present invention comprises the following steps:

[0007] S1, initializing the servo system, including setting the initialization state estimation step factor η, the state estimation weight factor μ, the input estimation weight factor β and the servo system local characteristic parameter φ(k);

[0008] S2, predicting the real-time operating state of the servo system, and correcting the predicted real-time operating state of the servo system;

[0009] S3. Construct a Lagrangian augmented penalty function expression for the input quantity as an equivalent unconstrained variant of the restricted input estimate;

[0010] S4. Select the fastest-descent Newton method to find the optimal solution of the Lagrangian augmented penalty function. Initialize the fastest-descent Newton method, define the particle's moving direction as d and the moving step length as α; select any point in the feasible domain as the starting point x for the optimization. 0 , design the initial moving step length as α 0 =1, the optimization error ε=1×10 -2 ;

[0011] S5. Optimal solution determination: Calculate the first-order derivative of the Lagrangian augmented penalty function with respect to the input estimate. If the calculated result does not exceed the optimization error ε, then the minimum point x is considered to be i is the approximate optimal solution x * , directly execute step S9; otherwise, execute step S6 in sequence;

[0012] S6. Calculate the moving direction of the particle: If the moving direction d of the particle in the i-th iteration i The equation G i d i +g i =0 has a solution and G i is the second-order derivative of the Lagrangian augmented penalty function with respect to the input estimate, g i is the first-order derivative of the Lagrangian augmented penalty function with respect to the independent variable, then execute S7, otherwise d i :=-g i , and then execute S7;

[0013] S7, calculate the particle moving step length: using the Armijo criterion as the criterion, set the discrimination coefficient and step length attenuation coefficient, and calculate the moving step length α of the particle in the i-th iteration i ;

[0014] S8, Update particle position: stipulate that each iteration of the particle follows a linear rule Move, x i is the position of the particle at the i-th iteration, x i+1 is the position of the particle in the i+1th iteration, α i is the moving step length of the particle in the i-th iteration, d i The moving direction of the particle for the i-th iteration is updated according to the linear rule, and the process returns to step S5 to execute until the specified number of iterations is exceeded;

[0015] S9, Lagrangian augmented penalty function optimization judgment; if the approximate optimal solution x * satisfy a=f l and b = f h are the lower and upper limits of the allowable operating frequency of the ultrasonic motor, σ j is the penalty factor when constructing the Lagrangian augmented penalty function expression for the jth time, λ j is the Lagrange multiplier when constructing the Lagrange augmented penalty function expression for the jth time, then it is considered that the approximate optimal solution x * The optimal solution u(k)=x in this round of optimization * , directly execute step S11; otherwise, execute step S10 sequentially;

[0016] S10, update loss function coefficients: update the loss function coefficients σ respectively j+1 =2σ j ,λ j+1 =λ j -σ j min{(x i -a)(bx i ), λ j / σ j},σ j+1 To find x i When the optimal solution is obtained, the penalty factor when constructing the Lagrangian augmented penalty function expression for the j+1th time, λ j To find x i When the optimal solution is obtained, the Lagrange multiplier when constructing the Lagrange augmented penalty function expression for the j+1th time, and steps S3 to S5 are repeated during iteration;

[0017] S11, control status monitoring: according to the control requirements, select all or part of the control indicators of stabilization time, average steady-state error, overshoot, rise time, and unit control time to monitor the operation status of the servo system in real time. If the control effect does not meet the standard, execute step S12, otherwise, enter the next (k+1) system time and return to step S2 until the control end instruction is received;

[0018] S12, control parameter correction: according to the influence of each control parameter on the servo system motor speed control effect, adjust the control parameter value within the allowable range defined by each control parameter; then the system enters the next (k+1) system moment and returns to step S2 until the control end instruction is received.

[0019] Furthermore, the state estimation step size factor η, the state estimation weight factor μ and the input estimation weight factor β initialized in step S1 are random numbers not greater than 1; and the initialized servo system local characteristic parameter φ(1) is a non-positive random number.

[0020] Furthermore, the prediction formula for the real-time operating state of the servo system in step S2 is:

[0021]

[0022] Among them, φ(k-1) is the local characteristic parameter of the servo system at time k-1, Δu(k-1)=u(k-1)-u(k-2) is the change of the servo system input at time k-1, y(k) is the servo system output at time k, and y(k-1) is the servo system output at time k-1.

[0023] Furthermore, the method for real-time prediction and state correction of the servo system in step S2 is:

[0024]

[0025] Among them, sign(φ(k)) is the sign function of the local characteristic parameter φ(k) of the servo system, which ensures that the local characteristic parameter of the servo system is always non-positive. is the local characteristic parameter of the servo system after correction.

[0026] Furthermore, the Lagrangian augmented penalty function expression in step S3 is:

[0027]

[0028] Among them, x i is the optimal solution for the i-th iteration of the estimated value of input u(k), and Characterize the operating status of the servo system, is the local characteristic parameter of the servo system after correction, w(k)=y e (k+1)-y(k)+φ(k)u(k-1),y e (k+1) is the expected output at time k+1, σ is the penalty factor of the penalty function, λ is the Lagrange multiplier, and σ and λ are updated according to step S10 in each optimization iteration. a=f l and b = f h They are respectively the lower and upper limits of the allowable operating frequency of the ultrasonic motor.

[0029] Furthermore, the first-order derivative g of the Lagrangian augmented penalty function with respect to the input estimate in step S5 is i The calculation formula is:

[0030]

[0031] Where P is the Lagrangian augmented penalty function, x i is the optimal solution for the i-th iteration of the estimated value of input u(k), and Characterize the operating status of the servo system, is the local characteristic parameter of the servo system after correction, w(k)=y e (k+1)-y(k)+φ(k)u(k-1),y e (k+1) is the expected output at time k+1, σ is the penalty factor of the penalty function, λ is the Lagrange multiplier, σ and λ are updated according to step S10 in each optimization iteration, a=f l and b = f h They are respectively the lower and upper limits of the allowable operating frequency of the ultrasonic motor.

[0032] Furthermore, the second-order derivative G of the Lagrangian augmented penalty function with respect to the input estimate in step S6 is i The calculation formula is:

[0033]

[0034] Where P is the Lagrangian augmented penalty function, x i is the optimal solution for the i-th iteration of the estimated value of input u(k), and Characterize the operating status of the servo system, is the local characteristic parameter of the servo system after correction, w(k)=y e (k+1)-y(k)+φ(k)u(k-1),y e (k+1) is the expected output at time k+1, σ is the penalty factor of the penalty function, λ is the Lagrange multiplier, σ and λ are updated according to step S10 in each optimization iteration, a=f l and b = f h They are respectively the lower and upper limits of the allowable operating frequency of the ultrasonic motor.

[0035] The present invention discloses a penalty function optimization system for an ultrasonic motor model-free servo system based on Lagrange multipliers, comprising:

[0036] A controller initialization module is used to initialize the control parameters of the controller, including the state estimation step factor η, the state estimation weight factor μ, the input estimation weight factor β and the local characteristic parameter φ(k) of the servo system;

[0037] Prediction module, used to predict the real-time operation status of the servo system;

[0038] A deviation correction module is used to correct the predicted real-time operating status of the servo system;

[0039] The augmented penalty function building block is used to construct the Lagrangian augmented penalty function with respect to the input quantity;

[0040] The augmented penalty function optimization module is used to initialize the steepest-descent Newton method optimization and select the steepest-descent Newton method to find the optimal solution of the augmented penalty function;

[0041] Monitoring module, used to select control indicators to monitor the operating status of the servo system in real time;

[0042] The control parameter correction module is used to adjust the control parameter value within the allowable range defined by each control parameter according to the influence of each control parameter on the servo system motor speed control effect.

[0043] A device of the present invention includes a memory and a processor, wherein:

[0044] A memory for storing computer programs that can be run on the processor;

[0045] The processor is used to execute the steps of the above-mentioned method for optimizing the penalty function of an ultrasonic motor model-free servo system based on Lagrange multipliers when running the computer program.

[0046] A storage medium of the present invention stores a computer program, which, when executed by at least one processor, implements the steps of the above-mentioned Lagrange multiplier-based penalty function optimization method for an ultrasonic motor model-free servo system.

[0047] Beneficial effects: Compared with the prior art, the technical effects of the present invention are as follows: (1) The present invention adopts a penalty function method to transform the frequency-constrained optimization problem into an unconstrained variant, which helps to improve the accuracy of running state tracking; (2) The present invention selects the Newton-steepest descent method as the Lagrangian loss function optimization, which simplifies the control process and is crucial to improving control operability; (3) Compared with the classical model-free control algorithm, the present invention has the advantages of strong real-time state tracking, high estimated input accuracy, high control precision, and adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a structural block diagram of the servo system of the present invention;

[0049] Figure 2 is a flow chart of the method of the present invention;

[0050] Figure 3 is a comparison diagram of experimental results of an ultrasonic motor tracking a sinusoidal signal when it is unloaded in an embodiment of the present invention;

[0051] Figure 4 It is a comparison diagram of the experimental results of the ultrasonic motor tracking the square wave signal when it is unloaded in the embodiment of the present invention. DETAILED DESCRIPTION

[0052] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0053] The present invention is a method for optimizing the penalty function of an ultrasonic motor model-free servo system based on Lagrange multipliers. The control structure of the method when implemented in an ultrasonic motor servo system is as follows: Figure 1 As shown, the servo system includes: an ultrasonic motor, a local dynamic feature adaptive identification module and a controlled input Lagrangian-penalty function optimization estimation module, wherein the controlled input Lagrangian-penalty function optimization estimation module accepts the target output as a reference value for finding an estimated input, and uses the Lagrangian penalty function optimization estimation method to estimate the input value, and the ultrasonic motor selects the estimated input value as the excitation electrical signal frequency to complete the servo system output; the local dynamic feature adaptive identification module uses the local dynamic feature adaptive identification method to analyze the numerical relationship between the estimated input and the corresponding servo system output, obtains the system local feature parameters, and together with the system historical output, guides the Lagrangian penalty function optimization estimation method to adjust the optimization parameters.

[0054] The present invention discloses a penalty function optimization method for an ultrasonic motor model-free servo system based on Lagrange multipliers. With the help of the Lagrange multiplier method, the optimization problem of the constrained working frequency is completed to realize the servo control of the ultrasonic motor. Without relying on the physical model of the system, the motor operating state characterization parameters are obtained by analyzing the input and output data of the servo system; based on the penalty function, the constrained optimization problem about the frequency is converted into an unconstrained variant, and the Newton-steepest descent method is selected as the Lagrangian augmented penalty function optimization to estimate the optimal solution of the working frequency, and finally drive the ultrasonic motor to work. The method of the present invention has the advantages of strong real-time state tracking, high input estimation accuracy, high control precision, and self-adaptability. Figure 2 The specific implementation process is as follows:

[0055] Step 1: Initialize the servo system parameters. Set the initialization control parameters: the state estimation step factor η, the state estimation weight factor μ, and the input estimation weight factor β as random numbers not greater than 1; set the servo system initialization local characteristic parameter φ(1) as a non-positive random number.

[0056] Step 2: predicting the real-time operating state of the servo system. For the servo system, at the kth (k=2, 3, 4, ...) moment, the controller calculates the local characteristic parameter φ(k) of the servo system according to the following iterative formula to characterize the real-time operating state of the servo system.

[0057]

[0058] Among them, φ(k-1) is the local characteristic parameter of the servo system at time k-1, Δu(k-1)=u(k-1)-u(k-2) is the change of the servo system input at time k-1, y(k) is the servo system output at time k, and y(k-1) is the servo system output at time k-1.

[0059] Step 3: The servo system predicts the state in real time and corrects the deviation. For the local characteristic parameter φ(k) of the servo system calculated at time k, correction is made according to the following rules:

[0060]

[0061] in, is the local characteristic parameter of the servo system after correction, sign(φ(k)) is the sign function of φ(k), which ensures that the local characteristic parameter is always non-positive, which conforms to the law of negative correlation between ultrasonic motor output and input, and can avoid the divergence of the servo system.

[0062] Step 4: construct a Lagrangian augmented penalty function expression for the input quantity. According to the following expression, an equivalent unconstrained variant of the restricted input estimation is constructed. The present invention selects the Lagrangian augmented penalty function expression.

[0063]

[0064] Among them, x i is the optimal solution for the i-th iteration of the estimated value of input u(k), and Characterizes the operating state of the servo system, w(k)=y e (k+1)-y(k)+φ(k)u(k-1),y e (k+1) is the expected output at time k+1, β is the input estimation weight factor, σ is the penalty factor of the penalty function, λ is the Lagrange multiplier, and σ and λ are updated according to step S10 in each optimization iteration, a=f l and b = f h They are respectively the lower and upper limits of the allowable operating frequency of the ultrasonic motor.

[0065] Step 5, the steepest-descent Newton method is used to find the optimal solution of the augmented penalty function in step 4. The moving direction of particle x is defined as d, the moving step length is α, and the particle is required to move according to the linear rule in each iteration, that is, x i is the position of the particle at the i-th iteration, x i+1 is the position of the particle in the i+1th iteration, αi is the moving step length of the particle in the i-th iteration, d i is the moving direction of the particle in the i-th iteration. Select any point in the feasible domain as the starting point for optimization. 0 , design the initial moving step length as α 0 =1, the optimization error ε=1×10 -2 .

[0066] Step 6: Optimal solution determination. Calculate the first-order derivative g of the augmented function with respect to the input estimate according to the following formula: i If the calculated result does not exceed the optimization error ε, then it is considered that the approximate minimum point x * For x i , directly execute step 10, otherwise execute step 7 sequentially.

[0067]

[0068] Step 7, calculate the direction of particle movement. Calculate the second-order derivative G of the augmented function with respect to the independent variable according to the following formula: i .

[0069]

[0070] If the solution is about d i The equation G i d i +g i =0 has a solution and Then execute step 8, otherwise d i ∶=-g i , and then proceed to step 8.

[0071] Step 8: Calculate the particle moving step length. Using the Armijo criterion as the criterion, calculate α i The discriminant coefficient is set to 0.55 and the step attenuation coefficient is set to 0.4.

[0072] Step 9: Update the particle value. According to the rules Update the particle value and repeat step 6 until the specified number of iterations is exceeded.

[0073] Step 10: Augment the function to find the optimal solution. * satisfy Then we think x * The optimal solution u(k)=x in this round of optimization * , directly execute step 12; otherwise, execute step 11 sequentially.

[0074] Step 11: Update the loss function coefficients. Update the loss function coefficients σ respectively j+1 =2σj ,λ j+1 =λ j -σ j min{(x i -a)(bx i ), λ j / σ j},σ j To find x i When the optimal solution is obtained, the penalty factor when constructing the Lagrangian augmented penalty function expression for the jth time, λ j To find x i At the optimal solution, the Lagrange multiplier when constructing the Lagrange augmented penalty function expression for the jth time, σ j+1 To find x i When the optimal solution is obtained, the penalty factor when constructing the Lagrangian augmented penalty function expression for the j+1th time, λ j To find x i When the optimal solution is obtained, the Lagrange multiplier when constructing the Lagrange augmented penalty function expression for the j+1th time is repeated from step 4 to step 6.

[0075] Step 12, control status monitoring. According to the control requirements, select all or part of the control indicators of stabilization time, average steady-state error, overshoot, rise time, and unit control time to monitor the servo system operation status in real time. If the control effect does not meet the standard, execute step 13, otherwise, enter the next (k+1) system time, and repeat steps 2 to 6 until the control end instruction is received.

[0076] Step 13, control parameter correction. According to the influence of each control parameter on the motor speed control effect summarized in Table 1 below, adjust the control parameter value within the allowable range of each control parameter definition. Then the system enters the next (k+1) system moment and repeats steps 2 to 6 until the control end instruction is received.

[0077] Table 1 The influence of various control parameters on the motor speed control effect

[0078]

[0079] The present invention discloses a penalty function optimization system for an ultrasonic motor model-free servo system based on Lagrange multipliers, comprising:

[0080] A controller initialization module is used to initialize the control parameters of the controller, including the state estimation step factor η, the state estimation weight factor μ, the input estimation weight factor β and the local characteristic parameter φ(k) of the servo system;

[0081] Prediction module, used to predict the real-time operation status of the servo system;

[0082] A deviation correction module is used to correct the predicted real-time operating status of the servo system;

[0083] The augmented penalty function building block is used to construct the Lagrangian augmented penalty function with respect to the input quantity;

[0084] The augmented penalty function optimization module is used to initialize the steepest-descent Newton method optimization and select the steepest-descent Newton method to find the optimal solution of the augmented penalty function;

[0085] Monitoring module, used to select control indicators to monitor the operating status of the servo system in real time;

[0086] The control parameter correction module is used to adjust the control parameter value within the allowable range defined by each control parameter according to the influence of each control parameter on the servo system motor speed control effect.

[0087] A device of the present invention includes a memory and a processor, wherein:

[0088] A memory for storing computer programs that can be run on the processor;

[0089] The processor is used to execute the steps of the above-mentioned method for optimizing the penalty function of an ultrasonic motor model-free servo system based on Lagrange multipliers when running the computer program, and can achieve the same technical effect as the above-mentioned method.

[0090] A storage medium of the present invention stores a computer program, which, when executed by at least one processor, implements the steps of the above-mentioned method for optimizing the penalty function of an ultrasonic motor model-free servo system based on Lagrange multipliers, and can achieve the same technical effect as the above-mentioned method.

[0091] The following describes in detail the experimental results of the Lagrange multiplier-based ultrasonic motor model-free servo system penalty function optimization method when it is implemented in an ultrasonic motor servo system through embodiments.

[0092] Figure 3 and Figure 4The characteristics of the external constraint control method for no-load tracking of sinusoidal signals and square wave signals and the model-free penalty function scheme based on Lagrange multipliers of the present invention are compared. The external constraint control method uses the input constraint as a threshold and directly acts on the estimated input value, while the present invention integrates the constraint condition into the algorithm optimization process. Both control schemes set the same expected input signal, with a frequency of 0.5Hz, a valley value of 5r / min, a peak value of 85r / min, and a sampling period of 10ms. The parameters of the classic model-free control algorithm are set as η=1, μ=0.01, ρ=0.8, β=100, and the parameters of the model-free penalty function control algorithm based on Lagrange multipliers are set as η=1, μ=0.01, ρ=0.8, β=100, α=2.

[0093] By comparing the real-time errors under the two algorithms, it can be found that: to achieve the same control target, the overshoot of the algorithm of the present invention is significantly lower than that of the external constraint control method. When the speed is high, the average steady-state error curves of the two algorithms overlap more, and the error deviation between them is not large; when the speed is low, the error increases accordingly, among which the external constraint control algorithm is more sensitive to the increase of the target speed, especially for the part of the square wave where the speed suddenly decreases, the error increases significantly, while the error of the model-free penalty function scheme based on Lagrange multipliers of the present invention does not change much, and the performance is more stable.

[0094] In summary, the model-free penalty function control method of an ultrasonic motor servo system based on Lagrange multipliers of the present invention is an improved algorithm proposed on the basis of the classical model-free control algorithm, which takes into account the characteristics of the ultrasonic motor system and the input constraint requirements, constructs a Lagrange-type augmented penalty function by integrating the control input estimation algorithm and the constraint conditions of the model-free adaptive control, applies the Lagrange multiplier method to construct the Lagrange-type augmented penalty function, and solves the equivalent unconstrained problem by the Newton method-steepest descent method, and finally directly obtains the control input estimation that meets the constraint conditions. The improved method of the present invention includes the constraint conditions of the input estimation value in the optimization process, and the input estimation result can be directly used as the working frequency of the motor excitation signal, and is no longer constrained by the input threshold constraint, which can effectively avoid the distortion of the state estimation result. The simulation verification based on the present invention shows that compared with the classical model-free adaptive control method, the overshoot of the improved algorithm introducing the penalty function method is greatly reduced, and the control effect is expected to be improved.

Claims

1. A penalty function optimization method for ultrasonic motor model-free servo system based on Lagrange multipliers, characterized in that: The following steps are involved: S1, initializing the servo system, including setting the initialization state estimation step factor η, the state estimation weight factor μ, the input estimation weight factor β and the servo system local characteristic parameter φ(k); S2. Predict the real-time operating state of the servo system and correct the predicted real-time operating state of the servo system; the prediction formula of the real-time operating state of the servo system is: Among them, φ(k-1) is the local characteristic parameter of the servo system at time k-1, Δu(k-1)=u(k-1)-u(k-2) is the change of the servo system input at time k-1, y(k) is the servo system output at time k, and y(k-1) is the servo system output at time k-1; S3. Construct a Lagrangian augmented penalty function expression for the input as an equivalent unconstrained variant of the restricted input estimate; the Lagrangian augmented penalty function expression is: Among them, x i is the optimal solution for the i-th iteration of the estimated value of input u(k), and Characterize the operating status of the servo system, is the local characteristic parameter of the servo system after correction, w(k)=y e (k+1)-y(k)+φ(k)u(k-1),y e (k+1) is the expected output at time k+1, σ is the penalty factor of the penalty function, λ is the Lagrange multiplier, and σ and λ are updated according to step S10 in each optimization iteration. a=f l and b = f h They are the lower and upper limits of the permissible operating frequency of the ultrasonic motor respectively; S4. Select the steepest-descent Newton method to find the optimal solution of the Lagrangian augmented penalty function. Initialize the optimization of the steepest-descent Newton method, define the moving direction of the particle as d and the moving step as α; select any point in the feasible domain as the starting point x0 of the optimization, design the initial moving step as α0=1, and set the optimization error ε=1×10 -2 ; S5. Optimal solution determination: Calculate the first-order derivative of the Lagrangian augmented penalty function with respect to the input estimate. If the calculated result does not exceed the optimization error ε, then the minimum point x is considered to be i is the approximate optimal solution x * , directly execute step S9; otherwise, execute step S6 in sequence; S6. Calculate the moving direction of the particle: If the moving direction d of the particle in the i-th iteration i The equation G i d i +g i =0 has a solution and G i is the second-order derivative of the Lagrangian augmented penalty function with respect to the input estimate, g i is the first-order derivative of the Lagrangian augmented penalty function with respect to the independent variable, then execute S7, otherwise d i ∶=-g i , and then execute S7; S7, calculate the particle moving step length: using the Armijo criterion as the criterion, set the discrimination coefficient and step length attenuation coefficient, and calculate the moving step length α of the particle in the i-th iteration i ; S8, Update particle position: stipulate that each iteration of the particle follows a linear rule Move, x i is the position of the particle at the i-th iteration, x i+1 is the position of the particle in the i+1th iteration, α i is the moving step length of the particle in the i-th iteration, d i The moving direction of the particle for the i-th iteration is updated according to the linear rule, and the process returns to step S5 to execute until the specified number of iterations is exceeded; S9, Lagrangian augmented penalty function optimization judgment; if the approximate optimal solution x * satisfy a=f l and b = f h are the lower and upper limits of the allowable operating frequency of the ultrasonic motor, σ j is the penalty factor when constructing the Lagrangian augmented penalty function expression for the jth time, λ j is the Lagrange multiplier when constructing the Lagrange augmented penalty function expression for the jth time, then it is considered that the approximate optimal solution x * The optimal solution u(k)=x in this round of optimization * , directly execute step S11; otherwise, execute step S10 sequentially; S10, update loss function coefficients: update the loss function coefficients σ respectively j+1 =2σ j ,λ j+1 =λ j -σ j minQ(x i -a)(bx i ),λ j / σ j },σ j+1 To find x i When the optimal solution is obtained, the penalty factor when constructing the Lagrangian augmented penalty function expression for the j+1th time, λ j+1 To find x i When the optimal solution is obtained, the Lagrange multiplier when constructing the Lagrange augmented penalty function expression for the j+1th time, and steps S3 to S5 are repeated during iteration; S11, control status monitoring: according to the control requirements, select all or part of the control indicators of stabilization time, average steady-state error, overshoot, rise time, and unit control time to monitor the operation status of the servo system in real time. If the control effect does not meet the standard, execute step S12, otherwise, enter the next (k+1) system time and return to step S2 until the control end instruction is received; S12, control parameter correction: according to the influence of each control parameter on the servo system motor speed control effect, adjust the control parameter value within the allowable range defined by each control parameter; then the system enters the next (k+1) system moment and returns to step S2 until the control end instruction is received.

2. The method for optimizing the penalty function of an ultrasonic motor model-free servo system based on Lagrange multipliers according to claim 1, characterized in that: The state estimation step size factor η, the state estimation weight factor μ and the input estimation weight factor β initialized in step S1 are random numbers not greater than 1; the initialized servo system local characteristic parameter φ(1) is a non-positive random number.

3. The method for optimizing the penalty function of an ultrasonic motor model-free servo system based on Lagrange multipliers according to claim 1, characterized in that: The method for real-time prediction and state correction of the servo system in step S2 is: Among them, sign(φ(k)) is the sign function of the local characteristic parameter φ(k) of the servo system, which ensures that the local characteristic parameter of the servo system is always non-positive. is the local characteristic parameter of the servo system after correction.

4. The method for optimizing the penalty function of an ultrasonic motor model-free servo system based on Lagrange multipliers according to claim 1, characterized in that: The first-order derivative g of the Lagrangian augmented penalty function with respect to the input estimate in step S5 is i The calculation formula is: Where P is the Lagrangian augmented penalty function, x i is the optimal solution for the i-th iteration of the estimated value of input u(k), and Characterize the operating status of the servo system, is the local characteristic parameter of the servo system after correction, w(k)=y e (k+1)-y(k)+φ(k)u(k-1),y e (k+1) is the expected output at time k+1, σ is the penalty factor of the penalty function, λ is the Lagrange multiplier, σ and λ are updated according to step S10 in each optimization iteration, a=f l and b = f h They are respectively the lower and upper limits of the allowable operating frequency of the ultrasonic motor.

5. The method for optimizing the penalty function of an ultrasonic motor model-free servo system based on Lagrange multipliers according to claim 1, characterized in that: The second-order derivative G of the Lagrangian augmented penalty function with respect to the input estimate in step S6 is i The calculation formula is: Where P is the Lagrangian augmented penalty function, x i is the optimal solution for the i-th iteration of the estimated value of input u(k), and Characterize the operating status of the servo system, is the local characteristic parameter of the servo system after correction, w(k)=y e (k+1)-y(k)+φ(k)u(k-1),y e (k+1) is the expected output at time k+1, σ is the penalty factor of the penalty function, λ is the Lagrange multiplier, σ and λ are updated according to step S10 in each optimization iteration, a=f l and b = f h They are respectively the lower and upper limits of the allowable operating frequency of the ultrasonic motor.

6. A system for the Lagrange multiplier-based penalty function optimization method for ultrasonic motor model-free servo system according to claim 1, characterized in that: include: A controller initialization module is used to initialize the control parameters of the controller, including the state estimation step factor η, the state estimation weight factor μ, the input estimation weight factor β and the local characteristic parameter φ(k) of the servo system; Prediction module, used to predict the real-time operation status of the servo system; A deviation correction module is used to correct the predicted real-time operating status of the servo system; The augmented penalty function building block is used to construct the Lagrangian augmented penalty function with respect to the input quantity; The augmented penalty function optimization module is used to initialize the steepest-descent Newton method optimization and select the steepest-descent Newton method to find the optimal solution of the augmented penalty function; Monitoring module, used to select control indicators to monitor the operating status of the servo system in real time; The control parameter correction module is used to adjust the control parameter value within the allowable range defined by each control parameter according to the influence of each control parameter on the servo system motor speed control effect.

7. A device, characterized in that: comprising a memory and a processor, wherein: A memory for storing computer programs that can be run on the processor; A processor is used to execute the steps of a penalty function optimization method for an ultrasonic motor model-free servo system based on Lagrange multipliers as described in any one of claims 1 to 5 when running the computer program.

8. A storage medium, characterized in that: The storage medium stores a computer program, which, when executed by at least one processor, implements the steps of a penalty function optimization method for an ultrasonic motor model-free servo system based on Lagrange multipliers as described in any one of claims 1 to 5.

Images