阅读说明：本技术 一种基于改进粒子群的电机串级自抗扰控制参数优化方法 (Motor cascade active disturbance rejection control parameter optimization method based on improved particle swarm ) 是由 石照耀 张攀 林家春 于 2020-11-06 设计创作，主要内容包括：本发明公开了一种基于改进粒子群的电机串级自抗扰控制参数优化方法,搭建永磁同步电机矢量控制系统模型,使用一阶ADRC控制器代替电流环的PI控制器,使用二阶ADRC代替速度环PI控制器,然后使用改进粒子群优化算法整定ADRC控制器的参数,通过ITAE准则与迭代次数终止寻优,最终获得串级ADRC的控制参数,加快永磁同步电机的响应速度、提高抗干扰能力、兼容快速性与超调性。本发明采用串级ADRC控制策略,使用一阶ADRC控制器代替电流环的PI控制器,使用二阶ADRC代替速度环的PI控制器用来提高系统的快速性与抗干扰能力,同时实现快速无超调的启动、调速。使用改进粒子群优化算法可以简化ADRC控制参数的整定过程,可以加快收敛速度,避免陷入局部最优,并得到最优的结果。(The invention discloses a motor cascade active disturbance rejection control parameter optimization method based on improved particle swarm, which comprises the steps of building a vector control system model of a permanent magnet synchronous motor, replacing a PI (proportional integral) controller of a current loop with a first-order ADRC (advanced digital control) controller, replacing a PI controller of a speed loop with a second-order ADRC controller, setting parameters of the ADRC controller by using an improved particle swarm optimization algorithm, terminating optimization through an ITAE (iterative analysis and optimization) criterion and iteration times, finally obtaining control parameters of the cascade ADRC, accelerating the response speed of the permanent magnet synchronous motor, improving the anti-interference capability, and being compatible with rapidity and overshoot. The invention adopts a cascade ADRC control strategy, uses a first-order ADRC controller to replace a PI controller of a current loop, uses a second-order ADRC controller to replace a PI controller of a speed loop to improve the rapidity and the anti-interference capability of a system, and simultaneously realizes the rapid start and speed regulation without overshoot. The ADRC control parameter setting process can be simplified by using an improved particle swarm optimization algorithm, the convergence speed can be accelerated, the local optimization is avoided, and the optimal result is obtained.)

1. A motor cascade active disturbance rejection control parameter optimization method based on improved particle swarm is characterized in that: the method comprises the following steps of,

step 1, building a first-order ADRC vector control model of a current loop of a permanent magnet synchronous motor;

building a first-order ADRC current loop vector control model of the permanent magnet synchronous motor, wherein the first-order ADRC current loop vector control model comprises a Clark conversion module, a Park conversion module, an Ipatch conversion module, an SVPWM module, a torque loop first-order ADRC module and a flux loop first-order ADRC module;

step 2, optimizing a first-order ADRC control parameter of a current loop by using an improved particle swarm optimization algorithm;

step 3, evaluating whether the ADRC parameters of the current loop are optimal or not by using a fitness function ITAE, and outputting the control parameters of the ADRC if the fitness value reaches a set condition within the iteration times;

step 4, building a second-order ADRC vector model of the speed loop;

and 5, optimizing a second-order ADRC parameter of the speed loop.

2. The method for optimizing the motor cascade active disturbance rejection control parameters based on the improved particle swarm according to claim 1, wherein the method comprises the following steps: in the step 1, step 1.1, a coder signal at the tail end of a rotor is collected, a sampling resistor is used for collecting a three-phase current signal, and the current signal is subjected to Clark conversion to obtain a static two-phase current I_α、I_β；I_α、I_βObtaining Id and Iq currents after Park; id corresponds to exciting current, and Iq corresponds to torque current; adopting a control mode that Id is 0;

step 1.2, adopting a first-order ADRC control mode for the magnetic chain ring and the torque ring respectively; id. Iq is respectively subjected to difference calculation with a set target value, and then output Vq and Vd are obtained after first-order ADRC conversion; obtaining two sinusoidal signals V after the inverse Park conversion of Vq and Vd_α、V_β；V_α、V_βAfter SVPWM conversion, six paths of complementary symmetrical PWM signals are output, and a control path power device drives the permanent magnet synchronous motor to work.

3. The method for optimizing the motor cascade active disturbance rejection control parameters based on the improved particle swarm according to claim 1, wherein the method comprises the following steps: in step 2, step 2.1, designing and improving a particle swarm optimization algorithm; inertia weight omega and learning factor c in particle swarm optimization algorithm₁、c₂Is the key to influence the convergence of the PSO algorithm;

step 2.2, the inertia weight in the standard particle swarm algorithm is changed linearly, and a factor c is learned₁、c₂Is a fixed value; the reasonable searching process should have stronger global searching capability in the early stage, and gradually reduce the searching area along with the increase of the iteration times;

step 2.3, omega is in nonlinear change, and is larger first and smaller second; c. C₁、c₂In a non-linear variation, c₁Big first and small second, c₂First small and then big; if the diversity and convergence of the particle swarm are simultaneously ensured, c₁The initial decline is slow, and the later decline is rapid; c. C₂In cooperation with c₁The change is that the increase is slow at the beginning and rapid at the later stage;

step 2.4, the difference of the improved particle swarm optimization algorithm relative to the standard particle swarm optimization algorithm is that a nonlinear Sigmoid function is adopted as the variation law of omega, and the standard Sigmoid function is adjusted to a value range of 0.4, 0.95]Use of a sin-based²Learning factor algorithm of x dynamic transformation;

step 2.5, testing the optimization speed and the optimization capability of the improved particle swarm optimization algorithm by using Rastrigerin and SchaferJD functions as test objects;

step 2.6, the parameters to be optimized in the first-order ADRC of the current loop comprise six parameters, namely beta01, beta02 and beta1 in the torque control process and beta01, beta02 and beta1 in the flux linkage control process; the search space D of the particle swarm is 6, 5 particles in 6-dimensional space are initialized to form a swarm, and each particle represents a potential optimal solution in the optimization problem.

4. The method for optimizing the motor cascade active disturbance rejection control parameters based on the improved particle swarm according to claim 1, wherein the method comprises the following steps: step 4, step 4.1, adding a speed loop second-order ADRC on the basis of the current loop first-order ADRC vector control; a second-order ADRC controller is used for replacing a speed loop PI controller;

step 4.2, the encoder collects position data of the rotor, and rotation speed information is obtained through calculation; the rotation speed signal is input into a second-order ADRC, and the output of the second-order ADRC acts on the input of a first-order ADRC of the torque loop to form a cascade ADRC control mode.

5. The method for optimizing the motor cascade active disturbance rejection control parameters based on the improved particle swarm according to claim 1, wherein the method comprises the following steps: in step 5, step 5.1, the parameters to be set in the second-order ADRC include 5 parameters including beta01, beta02 and beta03 in the extended state observer and beta1 and beta2 in the nonlinear state error feedback; initializing 5 particle swarms with 5 dimensions to form a cluster, wherein each particle represents a potential optimal solution in an optimization problem;

step 5.2, using an ITAE evaluation criterion as a fitness function of the particle swarm optimization algorithm; and if the fitness value reaches a set condition within the iteration times, outputting a control parameter of the second-order ADRC.

Technical Field

The invention belongs to the field of high-precision alternating current servo control, relates to a high-precision servo control method for a permanent magnet synchronous motor, and particularly relates to an improved particle swarm optimization method for parameter optimization of an active disturbance rejection controller of a current loop and a speed loop of the permanent magnet synchronous motor.

Background

The permanent magnet synchronous motor has the advantages of simple structure, high efficiency, high power density, small torque pulsation, quick response and the like, and is widely applied to the high-precision servo control fields of household appliances, automobiles, machine tools, robots, industrial servo, aviation, aerospace and the like. Therefore, the requirement on the speed regulation performance of the permanent magnet synchronous motor is higher and higher.

The permanent magnet synchronous control system mostly adopts a cascade PI (D) control strategy. Namely, the current loop is used as the innermost loop, the speed loop is used as the second loop, and the position loop is used as the outermost loop. The cascade PI (D) control mode has the advantages of simple structure and easy realization. But also has the problems of poor dynamic performance, weak anti-interference capability, incapability of being compatible with quick and overshoot and the like. In high-precision control occasions, multiple sets of PI (D) parameters are needed to adapt to different working conditions.

Aiming at the problems of poor dynamic performance, weak anti-interference capability and incapability of being compatible with rapid and overshoot of cascade PI control, a cascade ADRC controller is used for replacing the cascade PI controller, parameters of the cascade ADRC are adjusted by using an improved particle swarm optimization algorithm, the dynamic performance and the anti-interference capability of the PMSM are finally improved, and rapid and overshoot-free starting and speed regulation are realized.

An active disturbance rejection control theory is provided on the basis of deep analysis of PID control by Mr. Hanjingqing of Chinese academy of sciences, and the essence of error elimination based on errors in PID control is fused. The active disturbance rejection control technology does not depend on a mathematical model of a controlled object, and high-performance control is realized by estimating internal and external disturbances of a system in real time and compensating a control signal.

The ADRC needs more setting parameters, and the parameters in the active disturbance rejection controller need to be finely set to obtain an accurate control effect. ADRC parameter setting is a complex adjusting process, and currently, an empirical method, a bandwidth/zero pole configuration method, a BP neural network method and the like are mainly adopted. The empirical method requires the adjustment of the debugger according to the accumulated experience, and the adjustment process is complicated, but the method is most widely used. The bandwidth method/pole-zero allocation method needs a large amount of complicated calculation according to a model of a system to obtain control parameters, and the universality is poor. Although the BP neural network method can dynamically adjust parameters, the response time of the system is sensitive to parameter changes, so that the stability of the system is reduced. The parameters needing to be set in the series ADRC are more, and for a current loop, the parameters needing to be set in the first-order ADRC of the d-axis current and the q-axis current include beta01 in ESO, beta02 and beta1 in NLSEF. For the speed ring ADRC, the parameters needing to be adjusted are beta01, beta02 and beta03 in ESO and beta1 and beta2 in NLSEF.

Aiming at the problem of complicated setting of cascade ADRC control parameters, an improved particle swarm optimization algorithm is provided, and the cascade ADRC control parameters can be conveniently and rapidly obtained. The particle swarm optimization algorithm has the advantages of simple structure, few parameters, easy realization, high convergence speed and the like. Particle swarm optimization algorithms were originally proposed by doctor Kennedy and by doctor Eberhart in 1995. The algorithm is derived from the foraging process of the bird swarm, and the optimal solution is sought through cooperation and information sharing between the swarm and the individuals. But the standard particle swarm optimization algorithm is easy to get early and fall into a local optimal solution. By improving the inertia weight omega and the learning factor c in the particle swarm optimization algorithm₁、c₂The convergence rate can be improved, and the particle swarm optimization algorithm is prevented from trapping in the local optimal solution early.

Disclosure of Invention

The method aims at the problems that the response speed is low, the anti-interference capability is weak, and the compatibility between the high speed and the overshoot is unavailable in the cascade PI control strategy of the permanent magnet synchronous motor. The invention provides a cascade ADRC control strategy for improving a particle swarm optimization algorithm. Firstly, a permanent magnet synchronous motor vector control system model is built, a first-order ADRC controller replaces a PI controller of a current loop, a second-order ADRC replaces a speed loop PI controller, parameters of the ADRC controller are set by using an improved particle swarm optimization algorithm, optimization is stopped by an ITAE criterion and iteration times, control parameters of a cascade ADRC are finally obtained, the response speed of the permanent magnet synchronous motor is accelerated, the anti-interference capability is improved, and the rapidness and the overshoot are compatible.

The technical scheme of the invention is a permanent magnet synchronous motor cascade ADRC parameter optimization method based on an improved particle swarm optimization algorithm, which comprises the following steps:

step 1, building a first-order ADRC vector control model of a current loop of the permanent magnet synchronous motor.

A vector control model of a first-order ADRC current loop of the permanent magnet synchronous motor is built and mainly comprises a Clark conversion module, a Park conversion module, an Ipatch conversion module, an SVPWM module, a moment loop first-order ADRC module and a flux loop first-order ADRC module.

Step 1.1, collecting a coder signal at the tail end of a rotor, collecting a three-phase current signal by a sampling resistor, and obtaining a static two-phase current I after the current signal is subjected to Clark conversion_α、I_β。I_α、I_βAnd obtaining Id and Iq currents after Park. Id corresponds to the field current and Iq corresponds to the torque current. The control method of Id 0 is adopted.

And 1.2, respectively adopting a first-order ADRC control mode for the magnetic chain ring and the torque ring. Id. Iq is respectively subjected to difference calculation with a set target value, and then output Vq and Vd are obtained after first-order ADRC conversion. Obtaining two sinusoidal signals V after the inverse Park conversion of Vq and Vd_α、V_β。V_α、V_βAfter SVPWM conversion, six paths of complementary symmetrical PWM signals are output, and a control path power device drives the permanent magnet synchronous motor to work.

And 2, optimizing a first-order ADRC control parameter of the current loop by using an improved particle swarm optimization algorithm. In order to simplify the adjustment process of the first-order ADRC parameters of the current loop, an improved particle swarm optimization algorithm is used for setting.

And 2.1, designing and improving a particle swarm optimization algorithm. Inertia weight omega and learning factor c in particle swarm optimization algorithm₁、c₂Is the key to influence the convergence of the PSO algorithm. When the inertia weighted value is large, the local optimum is favorably jumped out, the global optimization is carried out, but the convergence speed is slow. When the inertia weighted value is small, the local search is facilitated, and the algorithm convergence is fast. Learning factor c₁When the average particle size is relatively large, the specific gravity of the individual cognitive part of the particles is large, the dispersion phenomenon of the particles is more obvious, and the overall optimal solution has large blindness. Learning factor c₂When the concentration is relatively large, the specific gravity of the cognitive part of the population is large, the consciousness of the population of the particles is strong, the aggregation phenomenon is more obvious, and the population is easy to fall into the local optimal solution.

Step (ii) of2.2, the inertia weight in the standard particle swarm algorithm is changed linearly, and a factor c is learned₁、c₂Is a fixed value. The reasonable search process should have stronger global search capability in the early stage, gradually reduce the search area with the increase of the iteration times, and have stronger local search capability and faster convergence rate in the later stage of the iteration.

And 2.3, improving and adjusting the change process relative to a standard particle swarm optimization algorithm. Omega is in nonlinear change, large first and small second. c. C₁、c₂In a non-linear variation, c₁Should be large first and then small, c₂It should be small first and then large. If the diversity and convergence of the particle swarm are simultaneously ensured, c₁The decline should start slowly, the decline in the later period rapidly, and the early and late periods should be as long as possible. c. C₂Should cooperate with c₁The change is slow in the initial increase and rapid in the later period.

Step 2.4, the difference of the improved particle swarm optimization algorithm relative to the standard particle swarm optimization algorithm is that a nonlinear Sigmoid function is adopted as the variation law of omega, and the standard Sigmoid function is adjusted to a value range of 0.4, 0.95]Use of a sin-based²And x learning factor algorithm of dynamic transformation. +

And 2.5, testing the optimization speed and the optimization capability of the improved particle swarm optimization algorithm by using the classical Rastrigrin and Schafer J D functions as test objects.

Step 2.6, the parameters to be optimized in the first-order ADRC of the current loop include six parameters, namely beta01, beta02 and beta1 in the torque control process and beta01, beta02 and beta1 in the flux linkage control process. The search space D of the particle swarm is 6, 5 particles in 6-dimensional space are initialized to form a swarm, and each particle represents a potential optimal solution in the optimization problem.

And 3, evaluating whether the current loop ADRC parameter is optimal or not by using a fitness function ITAE. And within the iteration times, if the fitness value reaches the set condition, outputting the control parameter of the ADRC.

And 4, building a second-order ADRC vector model of the speed loop.

And 4.1, adding a speed loop second-order ADRC on the basis of the current loop first-order ADRC vector control. A second order ADRC controller is used instead of the speed loop PI controller.

And 4.2, acquiring position data of the rotor by the encoder, and calculating to obtain rotating speed information. The rotation speed signal is input into a second-order ADRC, and the output of the second-order ADRC acts on the input of a first-order ADRC of the torque loop to form a cascade ADRC control mode.

And 5, optimizing a second-order ADRC parameter of the speed loop.

And 5.1, the parameters to be set in the second-order ADRC comprise 5 parameters including beta01, beta02 and beta03 in the extended state observer and beta1 and beta2 in nonlinear state error feedback. And initializing 5 particle groups with 5 dimensions to form a group, wherein each particle represents a potential optimal solution in the optimization problem.

And 5.2, using an ITAE evaluation criterion as a fitness function of the particle swarm optimization algorithm. And if the fitness value reaches a set condition within the iteration times, outputting a control parameter of the second-order ADRC.

Compared with the prior art, the invention has the following advantages:

(1) in the existing speed regulation control strategy of the permanent magnet synchronous motor, a cascade PI control mode is often used, and the control strategy has weak anti-interference capability, poor dynamic performance, starting and overshoot in the speed regulation process. In order to solve the problem, the invention adopts a cascade ADRC control strategy, uses a first-order ADRC controller to replace a PI controller of a current loop, uses a second-order ADRC controller to replace the PI controller of a speed loop to improve the rapidity and the anti-interference capability of a system, and simultaneously realizes the rapid start and speed regulation without overshoot.

(2) The empirical method and the bandwidth/zero pole configuration method have certain limitations on setting the ADRC parameters, and the setting process is complicated and complicated. The ADRC control parameter setting process can be simplified by using an improved particle swarm optimization algorithm, the convergence speed can be accelerated, the local optimization is avoided, and the optimal result is obtained.

Drawings

FIG. 1 is a structural block diagram of a permanent magnet synchronous motor cascade ADRC vector control system based on an improved particle swarm optimization algorithm;

FIG. 2 is a comparison graph of results of testing an improved particle swarm algorithm, a Sigmoid inertial weight particle swarm algorithm, and a standard particle swarm algorithm using Rastrigrin and Schafer J D as test functions; (a) testing and comparing Rastrigrin functions; (b) comparison of Schafer J D function tests

FIG. 3 is a flow chart of an algorithm for improving a particle swarm optimization algorithm to set a current loop and a speed loop;

FIG. 4 is a comparison of speed simulation results of a cascade ADRC control strategy and a cascade PI control strategy set by an improved particle swarm optimization algorithm.

Fig. 5 is a comparison of current simulation results of the cascade ADRC control strategy and the cascade PI control strategy set by the improved particle swarm optimization algorithm.

FIG. 6 is a comparison of torque simulation results of the cascade ADRC control strategy and the cascade PI control strategy after being set by the improved particle swarm optimization algorithm.

Detailed Description

The method is described in detail with reference to the accompanying figures 1-6 and the specific embodiments.

Provided is an implementation mode.

Fig. 1 is a structural block diagram of a permanent magnet synchronous motor cascade active disturbance rejection system based on an improved particle swarm optimization algorithm, and the specific implementation manner is as follows:

step S10, a first-order ADRC current loop vector control system of the permanent magnet synchronous motor is built, and the system mainly comprises a Clark conversion module, a Park conversion module, an Ipark conversion module, an SVPWM module, a torque loop first-order ADRC module and a flux loop first-order ADRC module.

Step S11, collecting encoder signals at the tail end of the rotor, collecting three-phase current signals by a sampling resistor, and obtaining static two-phase current I after Clark conversion of the current signals_α、I_β。I_α、I_βAfter being subjected to Park conversion, the current is converted into rotating Id and Iq currents, and the Id and the Iq currents are static relative to a rotor. Id corresponds to exciting current, Iq corresponds to torque current, Id and Iq are not sinusoidal signals any more, but direct current signals, and the excitation and the torque of the motor can be controlled by controlling the two variables.

In step S12, a control method is adopted in which Id is 0. The magnetic chain ring and the moment ring respectively adopt a first-order ADRC control mode. Id. Iq is respectively subjected to error calculation along with a set target value, and then output Vq and Vd are obtained after first-order ADRC conversion. Obtaining two sinusoidal signals V after the inverse Park conversion of Vq and Vd_α、V_βThe phases are 90 degrees apart. V_α、V_βAfter SVPWM conversion, six paths of complementary symmetrical PWM signals control 6 paths of power devices to drive the permanent magnet synchronous motor to work.

In step S20, the parameters to be adjusted for the first-order ADRC of the current loop include: six parameters including beta01, beta02 and beta1 in the first-order ADRC of the control moment and beta01, beta02 and beta1 in the first-order ADRC of the control flux chain.

And step S30, optimizing six parameters in the first-order ADRC of the current loop by using an improved particle swarm optimization algorithm. The method is improved on the basis of a standard particle swarm optimization algorithm, adopts a nonlinear Sigmoid function as a variation law of omega, and adjusts the standard Sigmoid function to a value range of 0.4 to 0.95]Use of a sin-based²x dynamically changing the learning factor c₁、c₂。

Step S40, initializing 5 particles in 6-dimensional space to form a population, setting the number of iterations to 20, where each particle represents a potentially optimal solution in the optimization parameters, and the search space D of the particle population is 6. And obtaining a control parameter of the first-order ADRC of the current loop through iterative optimization.

Step S50, adding a speed loop second order ADRC on the basis of the current loop first order ADRC. The encoder acquires angle data, and the actual rotating speed is obtained through calculation. And inputting the target rotating speed and the actual rotating speed into a second-order ADRC of the speed loop, and taking the output of the second-order ADRC of the speed loop as the input of a first-order ADRC of the torque loop to form a cascade ADRC control mode.

And step S60, setting a second-order ADRC control parameter of the speed loop by using an improved particle swarm optimization algorithm. The parameters to be set in the second-order ADRC of the speed ring comprise 5 parameters including beta01, beta02 and beta03 in the extended state observer and beta1 and beta2 in nonlinear state error feedback. And (3) initializing 5 particle swarms with 5 dimensions to form a cluster, setting the iteration number to be 20, and performing iterative optimization. And obtaining the control parameter of the first-order ADRC of the speed loop through iterative optimization.

Fig. 2 shows the test results of the improved particle swarm algorithm, Sigmoid inertial weight particle swarm algorithm and standard particle swarm algorithm using rastigrin and schafer J D as test functions. The figure shows that the improved particle swarm optimization algorithm has the advantages of less iteration times and high convergence speed, the Sigmoid inertial weight algorithm is adopted, and the linear weight algorithm has the slowest convergence.

Each particle in the particle swarm optimization algorithm represents a potential optimal solution in the optimization problem, and the characteristics of the particle are represented by speed, position and fitness. Position is shown as X_i＝(x_i1,x_i2,...,x_iD) The velocity is represented as V_i＝(v_i1,v_i2,...,v_iD) The particle updates the iteration by tracking individual extremum (pbest) and group extremum (gbest), and after the particle obtains the two extremums, the particle updates its speed and position by equation (14), that is:

wherein the content of the first and second substances,represents the D-dimension component of the location vector of the particle i at the k-th iteration, D ∈ [1, D]The range of variation of position is limited to [ X ]_min,X_max]In the meantime.D-dimension component representing flight velocity vector of k-th iteration particle i, and velocity variation range limited to [ V_min,V_max]In the meantime.Representing the individual extrema of the component in d-dimension for the k-th iteration particle i,and representing the extreme value of the population of the k-th iteration population in the d-dimensional component. c1 and c2 are learning factors and mainly affect the target recognition capability of the particles. rand is [0,1 ]]A random number in between.

Kmax is the maximum number of iterations and k is the current number of iterations.

Improved algorithm of the present invention c₁、c₂Instead of being constant, a sin-based approach is used²x algorithm for dynamically changing learning factor, c₁、c₂Transformation law is shown in formula (31)

FIG. 3 is a flow chart of an improved particle swarm optimization algorithm optimization model. The realization of stable and reliable current loop control is the premise of outer loop control, the parameters of the current loop are firstly set during parameter setting, and after the current loop parameters are set, the particle swarm optimization space and the optimization range are modified to carry out position loop iteration optimization. And (3) programming the improved particle swarm optimization algorithm through m in matlab, and assigning the optimized parameters to the working space through operating the m file.

And (3) running a model in Simulink by calling a sim function to obtain a corresponding ITAE value, and judging whether to finish iterative updating or not by limiting the iteration times and the ITAE value. If the conditions are not met, the population is continuously updated iteratively according to the updating formula, and if the conditions are met, a global optimal solution is obtained.

Fig. 4 shows the model operation result after the cascade ADRC parameter and the cascade PI parameter are set by the improved particle swarm optimization algorithm.

Selecting a permanent magnet synchronous motor with the rated power of 1.5 KW; rated torque Tn 8 Nm; the stator resistance R is 0.6 Ω; the stator inductance L is 0.75 mH; the number of pole pairs p is 4; moment of inertia J10 kg²。

The target speed was set at 500rpm at start-up, a load of 1N × m was applied at 0.1s, a speed of 1000rpm at 0.2s, and a load of 4N × m was applied at 0.3 s. The control parameters are adjusted to make the time of the two reach the steady state basically the same, the simulation result is shown in fig. 6, it can be seen from the figure that the cascade PI control mode has obvious overshoot and oscillation before reaching the steady state, and the overshoot amount in the two times of debugging is very different, which shows that a group of PI control parameters can not adapt to the speed regulation in a larger range well. And the overshoot and oscillation do not exist in the starting and speed regulating process of the cascade ADRC. At 0.1s with 1Nm load applied, neither speed varied significantly, but after 0.3s with 4Nm load, it can be seen from the close up that the PI control mode dropped to 990rpm, while the ADRC control mode dropped to 997rpm, and the recovery time for cascaded ADRC was shorter than for PI control. The anti-interference capability and stability of the control mode of the cascade ADRC are superior to those of the PI control mode.

Fig. 5 shows the current simulation results, where the change in current corresponds to the change in speed. The rotation speed of 0.2s was changed from 500rpm to 1000rpm, and the frequency of change of the current was changed to 2 times before. The load is changed from 1Nm to 3Nm before and after 0.3s, and the current amplitude of the corresponding three-phase current is also changed to 3 times, namely, the current amplitude is changed from about 1.4 to about 4.2. The current controlled by the cascade ADRC is more stable, and the amplitude of current fluctuation and the oscillation frequency of the cascade ADRC control mode at the starting stage and the speed regulation stage in 0.2s are smaller than those of the PI control mode. The current fluctuation amplitude of the cascade ADRC control mode at the starting stage is about-3A-8A, and the current fluctuation amplitude of the PI control mode is about-13A-21A. After the load is applied at 0.3s, the fluctuation amplitude of the cascade ADRC control current is smaller than that of the PID control mode current.

Fig. 6 shows the results of a torque simulation, in which the change in torque corresponds to the change in speed and current. The torque variation of the cascade ADRC control system is more stable than that of the cascade PI control system. In a starting stage and a 0.2s speed regulation stage, the fluctuation amplitude of the torque of the PI control mode is obviously larger than that of the cascade ADRC control mode, the torque of the PI control mode oscillates for many times, and the cascade ADRC control mode does not oscillate. When loads are applied for 0.1s and 0.3s, the overshoot of the torque of the cascade ADRC mode is smaller than that of the cascade PI control mode, and after the load is stabilized, the torque fluctuation amplitude of the cascade ADRC control mode is smaller than that of the PI control mode.