Motor rotating speed ring ADRC controller parameter optimization method

Abstract

The invention discloses a parameter optimization method for an ADRC controller of a motor rotating speed loop, and relates to the field of swarm intelligence optimization algorithms, a self-adaptive genetic algorithm is applied to the rotating speed loop of the motor for a simulation experiment, a current loop of the motor adopts PI control, and the bandwidth of the current loop is adjusted by adjusting parameters so as to meet the control requirement of the rotating speed. ADRC control is adopted for control of a motor rotating speed ring, and S-function is built and written in Matlab / Simulink to achieve ADRC control simulation; the adaptive genetic algorithm comprises crossover and mutation operations, and individual fitness in the population is used as a reference index of crossover probability and mutation probability, so that excellent individuals can be screened out; according to the method, parameters in the genetic algorithm can be adaptively adjusted, and selection of the crossover probability and the mutation probability plays a great role in accurately searching global optimum by the genetic algorithm.

Description

Technical Field

[0001] The present invention relates to the field of swarm intelligence optimization algorithms, and in particular to a method for optimizing parameters of an ADRC controller for a motor speed loop. Background Art

[0002] The motion turntable is a high-precision position servo system, which is widely used in military and civilian fields. It plays an important role in aircraft design experiments, radar servo control systems, quantum communications, etc. Among them, the motor control system is an important part of the turntable system, and the motor speed control is very important. With the development of society and the advancement of science and technology, the performance requirements for the turntable servo system are getting higher and higher. It not only requires high stability accuracy and good dynamic quality, but also has a certain anti-interference ability.

[0003] The research direction of domestic and foreign scholars focuses on the innovation and improvement of control algorithms, and many control strategies have been proposed to improve the performance of motion turntables, such as sliding film control, backstepping control, neural network control, etc. Active disturbance rejection control technology (ADRC) has a certain anti-interference ability, but the controller has too many parameters and it is difficult to obtain a set of optimal solutions during tuning, so it is necessary to select a certain method for parameter optimization. Swarm intelligence optimization algorithm refers to a method of simulating some laws of nature and searching for the optimal fitness in a certain solution space to obtain the optimal solution. It simulates the behavior of biological groups and reflects the participation, aggregation and collaborative behavior of biological groups. Swarm intelligence optimization algorithms have also developed very maturely, such as simulated annealing algorithm, genetic algorithm, ant colony algorithm, particle swarm optimization algorithm, sparrow search algorithm, etc.

[0004] Genetic algorithm is a classic heuristic algorithm, which evolved from the genetic evolution process of organisms in nature. It has strong global optimization ability. It does not depend on the specific field of the problem, has strong robustness to the type of problem, and is widely used in many scientific fields. However, genetic algorithms also have the defect of falling into local optimal solutions. Traditional genetic algorithms have problems such as low optimization efficiency and premature convergence. Improving traditional genetic algorithms and improving optimization efficiency is also a problem that needs to be solved at present. Summary of the invention

[0005] In view of the above technical problems, the present invention proposes a method for optimizing the parameters of the motor speed loop ADRC controller, and applies an adaptive genetic algorithm to the motor speed loop for simulation experiments, wherein the motor current loop adopts PI control, and the bandwidth of the current loop is adjusted by adjusting parameters to meet the control requirements of the speed, while the motor speed loop is controlled by ADRC control, and S-function is built and written in Matlab / Simulink to realize ADRC control simulation;

[0006] Among them, the voltage balance equation of the permanent magnet DC torque motor under constant magnetic field excitation conditions is:

[0007]

[0008] E g =K e ω M

[0009] Where t is time, E g is the motor back electromotive force, K e is the motor back electromotive force coefficient, ω M is the motor speed, U a is the voltage on the armature winding, I a is the armature current, R a is the armature winding resistance, L a is the armature winding inductance;

[0010] The motor torque meets the following requirements:

[0011]

[0012] In the formula, the motor torque T M =K t I a , K t is the torque coefficient, T L The load torque converted to the motor shaft, J Ges is the total moment of inertia converted to the motor shaft;

[0013] As a lagging amplification link, the PWM power amplifier has a transfer function mathematical model as follows:

[0014]

[0015] In the formula, K PWM is the gain of the power amplifier, T PWM is the time constant of the power amplifier;

[0016] Connect the PWM power amplifier in series to the armature circuit, feed back the current from the armature, and add current PI control to the driver to form a current loop;

[0017] The input of the current loop is the armature current, and the output of the current loop is the rotation speed of the motor.

[0018] Furthermore, the speed of the motor is controlled by the active disturbance rejection control technology of the second-order active disturbance rejection controller; the active disturbance rejection control technology is a nonlinear control method, and the second-order active disturbance rejection controller includes a tracking differentiator (TD), an extended state observer (ESO) and a nonlinear state error feedback control law (NLSEF).

[0019] Furthermore, the differential form of the tracking differentiator is as follows:

[0020]

[0021] In the formula, k is the kth sampling, T is the sampling period, and v 1 is the tracking signal of the input signal v, v 2 is the differential signal of the input signal v, r 0 is the speed factor, h 0 is the filtering factor, the fastest control comprehensive function fst(x 1 ,x 2 ,r 0 ,h 0 ) is defined as:

[0022]

[0023] In formula (5), all parameters before fst are intermediate variables, and fst is the output value of the function.

[0024] Furthermore, the differential form of the extended state observer is as follows:

[0025]

[0026] In the formula, u is the system input, y is the system output, and z i (i=1,2,3) is the output variable of the extended state observer, α i (i=1,2) and β 0i (i=1,2,3) is the step size parameter, fal is a nonlinear function, and its expression is:

[0027]

[0028] Furthermore, the nonlinear state error feedback control law is

[0029]

[0030] In the formula, u 0 is the error feedback control quantity, β 1 and β 2 Both are adjustable gain, b 0 Control gain for the system.

[0031] Furthermore, the adaptive genetic algorithm includes crossover and mutation operations, and uses the fitness of individuals in the population as a reference indicator of crossover probability and mutation probability, so as to screen out excellent individuals.

[0032] Furthermore, the crossover probability of the adaptive genetic algorithm is:

[0033]

[0034] Where P c is the crossover probability, f c is the fitness of the two parents before crossover, f max ,f min are the maximum and minimum values ​​of fitness in the population, respectively, k 1 ,k 2 ,k 3 They are all constants between 0 and 1.

[0035] Furthermore, the mutation operation is usually used in conjunction with the crossover operation to improve the global search performance of the algorithm. When the algorithm is about to approach the optimal solution, the mutation operation effectively accelerates the convergence speed of the algorithm. The mutation probability of the adaptive genetic algorithm is:

[0036]

[0037] Where P m is the mutation probability, k 4 ,k 5 ,k 6 Is a constant between 0 and 1.

[0038] Furthermore, the steps of the adaptive genetic algorithm are:

[0039] S1. Encode the parameters to be optimized, set the number of groups and the maximum number of iterations, and generate the initial group;

[0040] S2, select a fitness function to evaluate the fitness of each individual in the group;

[0041] S3, perform selection operations on two by two, eliminate individuals with low fitness, and simultaneously copy individuals with high fitness;

[0042] S4, performing a crossover operation on the selected individuals according to the adaptive crossover probability;

[0043] S5. According to the adaptive mutation probability, the selected individuals are mutated to generate new individuals.

[0044] S6, repeat steps S2-S5 to determine whether the maximum number of iterations has been reached or the fitness has converged to the set value;

[0045] S7. Output the final result.

[0046] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention solves the defects of traditional genetic algorithms such as low optimization efficiency and premature convergence, solves the defect of traditional genetic algorithms falling into local optimal solutions, improves traditional genetic algorithms, and improves optimization efficiency; (2) The present invention uses an improved adaptive genetic algorithm and applies the algorithm to the speed loop of a motor for simulation experiments, adopts PI control for the current loop of the motor, and adjusts the current loop to a larger bandwidth by adjusting parameters to meet the control requirements of the speed; (3) The present invention solves the problem that the parameters of traditional genetic algorithms are fixed during the optimization process, which will affect the performance and efficiency of the algorithm to a certain extent; (4) The present invention can adaptively adjust the parameters in the genetic algorithm, and the selection of crossover probability and mutation probability plays a great role in the accurate search of the global optimum by the genetic algorithm. The present invention makes some optimization adjustments to the traditional genetic algorithm, and takes the individual fitness in the population as an important reference indicator for the crossover probability and mutation probability, so as to better screen out excellent individuals. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of the current loop of the present invention.

[0048] Figure 2 This is a second-order ADRC control block diagram of the present invention.

[0049] Figure 3 Flowchart of the improved genetic algorithm of the present invention.

[0050] Figure 4 It is the closed-loop Bode diagram of the current loop of the present invention.

[0051] Figure 5 It is the Simulink simulation block diagram of the present invention.

[0052] Figure 6 This is a schematic diagram of the improved genetic algorithm in parameter optimization according to the present invention.

[0053] Figure 7 This is the time domain response diagram of the motor speed loop of the present invention.

[0054] Figure 8 It is the cost value convergence curve of the present invention. DETAILED DESCRIPTION

[0055] The present invention will be further described below in conjunction with specific embodiments. The illustrative embodiments and descriptions of the present invention are used to explain the present invention but are not intended to limit the present invention.

[0056] Genetic algorithm is a classic heuristic algorithm, which evolved from the genetic evolution process of organisms in nature. It has strong global optimization ability. It does not depend on the specific field of the problem, has strong robustness to the type of problem, and is widely used in many scientific fields. However, genetic algorithm also has the defect of falling into local optimal solution. Improving the traditional genetic algorithm and improving the optimization efficiency is also a problem that needs to be solved at present.

[0057] Aiming at the shortcomings of traditional genetic algorithms such as low optimization efficiency and premature convergence, the present invention proposes a method for optimizing parameters of a motor speed loop ADRC controller.

[0058] Example: Figure 1-Figure 8 A motor speed loop ADRC controller parameter optimization method is shown, and an adaptive genetic algorithm is applied to the motor speed loop for simulation experiments, wherein the motor current loop adopts PI control, and the bandwidth of the current loop is adjusted by adjusting parameters to meet the speed control requirements, while the motor speed loop is controlled by ADRC control, and S-function is built and written in Matlab / Simulink to realize ADRC control simulation;

[0059] Among them, the voltage balance equation of the permanent magnet DC torque motor under constant magnetic field excitation conditions is:

[0060]

[0061] E g =K e ω M

[0062] Where t is time, E g is the motor back electromotive force, K e is the motor back electromotive force coefficient, ω M is the motor speed, U a is the voltage on the armature winding, I a is the armature current, R a is the armature winding resistance, L a is the armature winding inductance;

[0063] The motor torque meets the following requirements:

[0064]

[0065] In the formula, the motor torque T M =K t I a , K t is the torque coefficient, T L The load torque converted to the motor shaft, J Ges is the total moment of inertia converted to the motor shaft;

[0066] As a lagging amplification link, the PWM power amplifier has a transfer function mathematical model as follows:

[0067]

[0068] In the formula, K PWM is the gain of the power amplifier, T PWM is the time constant of the power amplifier;

[0069] The PWM power amplifier is connected in series to the armature circuit, the current is fed back from the armature, and the current PI control is added to the driver to form a current loop; in order to make the speed loop as the outer loop have a certain bandwidth, the bandwidth of the current loop as the inner loop must be sufficient, that is, it can quickly respond to the expected current. It can be seen that the input of the current loop is the armature current, and the output is the motor speed. Its control block diagram is as follows Figure 1 As shown, the speed of the motor is then controlled, using the anti-disturbance control technology.

[0070] Active disturbance rejection control technology is a nonlinear control method. The advantage of this control method is that it does not require an accurate mathematical model for the controlled object. It tracks and compensates the uncertainty factors in the system modeling and the external disturbance in the system as the same disturbance in the system. This control method has strong robustness. Typical second-order active disturbance rejection controllers are as follows: Figure 2 shown.

[0071] The second-order active disturbance rejection controller includes a tracking differentiator (TD), an extended state observer (ESO) and a nonlinear state error feedback control law (NLSEF).

[0072] The differential form of the tracking differentiator is as follows:

[0073]

[0074] In the formula, k is the kth sampling, T is the sampling period, and v 1 is the tracking signal of the input signal v, v 2 is the differential signal of the input signal v, r 0 is the speed factor, h 0 is the filtering factor, the fastest control comprehensive function fst(x 1 ,x 2 ,r 0 ,h 0 ) is defined as:

[0075]

[0076] In formula (5), all parameters before fst are intermediate variables, and fst is the output value of the function.

[0077] Furthermore, the differential form of the extended state observer is as follows:

[0078]

[0079] In the formula, u is the system input, y is the system output, and z i (i=1,2,3) is the output variable of the extended state observer, α i (i=1,2) and β 0i (i=1,2,3) is the step size parameter, fal is a nonlinear function, and its expression is:

[0080]

[0081] The nonlinear state error feedback control law is:

[0082]

[0083] In the formula, u 0 is the error feedback control quantity, β 1 and β 2 Both are adjustable gain, b 0 Control gain for the system.

[0084] From the discrete implementation of the three parts of the ADRC, TD, ESO and NLSEF, there are many parameters that need to be adjusted, such as (T, r 0 ,h 0 ,β 01 ,β 02 ,β 03 ,β 1 ,β 2 ,b,δ 1 ,δ 2 ,a 1 ,a 2 ,a 3 ,a 4 ) and other parameters. There are many control parameters of ADRC, but some of them can be estimated in advance based on experience and are generally not changed. There are also six or seven parameters that are frequently debugged, and the remaining parameters need to be optimized.

[0085] Genetic algorithm is a random optimization algorithm. It does not have too many mathematical requirements for the optimization problem to be solved, and its application scenarios and scope are relatively wide. Genetic algorithm simulates the evolution of organisms in the natural environment, and has operations such as selection, crossover, and mutation. Although it can obtain the global optimum to a certain extent, it still has limitations when facing some complex problems. In the optimization process of traditional genetic algorithms, the parameters are fixed, which will affect the algorithm performance and efficiency to a certain extent. For this reason, we can adaptively adjust the parameters in the genetic algorithm. The selection of crossover probability and mutation probability plays a great role in accurately searching for the global optimum by the genetic algorithm. The present invention makes some optimization adjustments to the traditional genetic algorithm, and uses the individual fitness in the population as an important reference indicator of the crossover probability and mutation probability, so as to better screen out excellent individuals.

[0086] Adaptive crossover probability: As the only indicator of the strength of the crossover operation, the choice of its value is crucial. If the crossover probability is too large, although the search intensity of the algorithm will be further increased, the overall efficiency of the algorithm will be affected; if the crossover probability is too small, the algorithm is likely to become slow and inefficient.

[0087] To this end, the crossover probability is continuously adjusted according to the fitness value of the individual. The crossover probability of the adaptive genetic algorithm is:

[0088]

[0089] Where P c is the crossover probability, f c is the fitness of the two parents with higher fitness before crossover, f max ,f min are the maximum and minimum values ​​of fitness in the population, respectively, k 1 ,k 2 ,k 3 They are all constants between 0 and 1.

[0090] Adaptive mutation probability: The mutation operation is usually used in conjunction with the crossover operation to improve the global search performance of the algorithm. When the algorithm is about to approach the optimal solution, the appropriate mutation operation can be used to effectively speed up the convergence of the algorithm. Similarly to the adaptive crossover probability, the mutation probability of the adaptive genetic algorithm is:

[0091]

[0092] Where P m is the mutation probability, k 4 ,k 5 ,k 6 Is a constant between 0 and 1.

[0093] After the above improvements, the steps of improving the adaptive genetic algorithm in the present invention are:

[0094] S1. Encode the parameters to be optimized, set the number of groups and the maximum number of iterations, and generate the initial group;

[0095] S2, select a fitness function to evaluate the fitness of each individual in the group;

[0096] S3, perform selection operations on two by two, eliminate individuals with low fitness, and simultaneously copy individuals with high fitness;

[0097] S4, performing a crossover operation on the selected individuals according to the adaptive crossover probability;

[0098] S5. According to the adaptive mutation probability, the selected individuals are mutated to generate new individuals.

[0099] S6, repeat steps S2-S5 to determine whether the maximum number of iterations has been reached or the fitness has converged to the set value;

[0100] S7. Output the final result.

[0101] The following is an example to illustrate that in the system simulation model, Figure 1 The DC motor torque and current loop model shown in the figure has the following specific parameters:

[0102]

[0103] Adjust the proportional and integral gains of the current loop, and then use the Simulink Control Design module to measure that the bandwidth of the adjusted current loop is 130Hz, as shown in Figure 4 As shown, at this time, the input of the control system composed of the current loop and the motor model is the current, and the output is the motor speed.

[0104] Next, we will build the ADRC controller. Each S-function needs to define the number of input and output variables and the number of state variables. According to formulas (4) to (8), we will write the initialization subfunction, state update subfunction and output subfunction of each S-function one by one. It should be noted that the step size in the discrete state update subfunction must be consistent with the step size in Simulink, otherwise the simulation result will be wrong. After writing each S-function module, we can follow Figure 2 Connect the input and output of each module, and finally connect the ADRC controller to the motor control system containing the current loop, and take the speed as feedback. In this way, the Simulink model of motor speed loop control based on ADRC controller is built.

[0105] Since there are too many parameters in the ADRC, it is difficult to adjust them, so it is necessary to find a better set of control parameters. Some of these parameters can be estimated based on experience, so there is no need to optimize them in the algorithm to reduce the computational complexity.

[0106] Here we set T = 0.0001, a 1 =0.5,a 2 =0.25,a 3 =0.75,a 4 =1.5,δ 1 =0.02,δ 2 =0.0025, and the remaining parameters are optimized according to the improved adaptive genetic algorithm mentioned above. The cost function has a similar effect to the fitness function, but the value is opposite. The higher the cost, the lower the fitness, and vice versa. The lower the cost, the higher the fitness. Here, the cost function is used to replace the fitness function.

[0107] The expression of the cost function is:

[0108] J=∫t|e(t)|dt (11)

[0109] In the formula, e(t) represents the error between the expected value of the system at time t and the actual value of the system output, and the cost function represents the cumulative error during this period.

[0110] Programming is performed in Matlab to initialize a population Chrom[num, size], where num represents the population size and size represents the number of genes. A row of the matrix Chrom[num, size] is used as a set of parameters to be optimized (an individual), and each column of an individual represents a gene position. The improved genetic algorithm proposed in the present invention is iterated for 150 generations, and the final optimization results of the parameters are as follows:

[0111]

[0112] The optimized parameters are brought into the simulation model of the motor speed loop for simulation. The step response is as follows: Figure 7 As shown in the figure, it can be seen that the step response time and overshoot are smaller than those of the traditional genetic algorithm. This shows that the optimization parameters of the improved algorithm are better than those optimized by the traditional algorithm. In addition, the cost function J changes with the number of iterations. Figure 8 As shown in the figure, it can also be seen that the parameters optimized by the improved genetic algorithm can make the cost function smaller, making it easier to search for the global optimal solution and find a better solution than the traditional algorithm.

Claims

1. A method for optimizing parameters of a motor speed loop ADRC controller, characterized in that: The adaptive genetic algorithm is applied to the motor speed loop for simulation experiments. The motor current loop adopts PI control. The bandwidth of the current loop is adjusted by adjusting parameters to meet the speed control requirements. The motor speed loop is controlled by ADRC control. S-function is built and written in Matlab / Simulink to realize ADRC control simulation. Among them, the voltage balance equation of the permanent magnet DC torque motor under constant magnetic field excitation conditions is: Where t is time, E g is the motor back electromotive force, K e is the motor back electromotive force coefficient, ω M is the motor speed, U a is the voltage on the armature winding, I a is the armature current, R a is the armature winding resistance, L a is the armature winding inductance; The motor torque meets the following requirements: In the formula, the motor torque T M =K t I a , K t is the torque coefficient, T L The load torque converted to the motor shaft, J Ges is the total moment of inertia converted to the motor shaft; As a lagging amplification link, the PWM power amplifier has a transfer function mathematical model as follows: In the formula, K PWM is the gain of the power amplifier, T PWM is the time constant of the power amplifier; Connect the PWM power amplifier in series to the armature circuit, feed back the current from the armature, and add current PI control to the driver to form a current loop; The input of the current loop is the armature current, and the output of the current loop is the rotation speed of the motor.

2. A method for optimizing parameters of a motor speed loop ADRC controller as claimed in claim 1, characterized in that: The speed of the motor is controlled by the active disturbance rejection control technology of a second-order active disturbance rejection controller; the active disturbance rejection control technology is a nonlinear control method, and the second-order active disturbance rejection controller includes a tracking differentiator (TD), an extended state observer (ESO) and a nonlinear state error feedback control law (NLSEF).

3. A method for optimizing parameters of a motor speed loop ADRC controller as claimed in claim 2, characterized in that: The differential form of the tracking differentiator is as follows: Where k is the kth sampling, T is the sampling period, v1 is the tracking signal of the input signal v, v2 is the differential signal of the input signal v, r0 is the speed factor, h0 is the filter factor, and the fastest control comprehensive function fst(x1,x2,r0,h0) is defined as: In formula (5), all parameters before fst are intermediate variables, and fst is the output value of the function.

4. A method for optimizing parameters of a motor speed loop ADRC controller as claimed in claim 3, characterized in that: The differential form of the extended state observer is as follows: In the formula, u is the system input, y is the system output, and z i (i=1,2,3) is the output variable of the extended state observer, α i (i=1,2) and β 0i (i=1,2,3) is the step size parameter, fal is a nonlinear function, and its expression is:

5. A method for optimizing parameters of a motor speed loop ADRC controller as claimed in claim 4, characterized in that: The nonlinear state error feedback control law is: Where u0 is the error feedback control quantity, β1 and β2 are both adjustable gains, and b0 is the system control gain.

6. A method for optimizing parameters of a motor speed loop ADRC controller as claimed in claim 5, characterized in that: The adaptive genetic algorithm includes crossover and mutation operations, and uses the fitness of individuals in the population as a reference indicator of crossover probability and mutation probability, so as to screen out excellent individuals.

7. A method for optimizing parameters of a motor speed loop ADRC controller as claimed in claim 6, characterized in that: The crossover probability of the adaptive genetic algorithm is: Where P c is the crossover probability, f c is the fitness of the two parents before crossover, f max ,f min are the maximum and minimum values ​​of fitness in the population respectively, and k1, k2, and k3 are all constants between 0 and 1.

8. A method for optimizing parameters of a motor speed loop ADRC controller as claimed in claim 7, characterized in that: The mutation operation is usually used in conjunction with the crossover operation to improve the global search performance of the algorithm. When the algorithm is about to approach the optimal solution, the mutation operation can effectively speed up the convergence of the algorithm. The mutation probability of the adaptive genetic algorithm is: Where P m is the mutation probability, k4, k5, k6 are constants between 0 and 1.

9. A method for optimizing parameters of a motor speed loop ADRC controller as claimed in claim 8, characterized in that: The steps of the adaptive genetic algorithm are: S1. Encode the parameters to be optimized, set the number of groups and the maximum number of iterations, and generate the initial group; S2, select a fitness function to evaluate the fitness of each individual in the group; S3, perform selection operations on two by two, eliminate individuals with low fitness, and simultaneously copy individuals with high fitness; S4, performing a crossover operation on the selected individuals according to the adaptive crossover probability; S5. According to the adaptive mutation probability, the selected individuals are mutated to generate new individuals. S6, repeat steps S2-S5 to determine whether the maximum number of iterations has been reached or the fitness has converged to the set value; S7. Output the final result.

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