Disturbance compensation and tracking control method for variable speed rotary DC motor servo system

Abstract

The invention discloses a disturbance compensation and tracking control method for a variable speed rotary DC motor servo system, comprising the following steps: step S1: establishing a brushless DC motor state space model according to a voltage balance equation and a torque balance equation; step S2: analyzing the intrinsic connection between the system time domain and position domain, constructing a position domain internal model of a periodic signal according to the position-related periodic characteristics of a reference input signal, and establishing an improved position domain repetitive controller; step S3: constructing a disturbance observer according to the brushless DC motor state space model, performing real-time estimation on system matching and non-matching disturbances to obtain a disturbance estimation value, combining a position domain repetitive control law and a disturbance estimation value, and designing a composite repetitive control law based on active disturbance compensation; step S4: using the position information of the motor rotor to establish a digital implementation method of a position domain repetitive controller synchronized with a time domain robust stabilization controller.

Description

Technical Field

[0001] The invention relates to the technical field of motor control, and in particular to a disturbance compensation and tracking control method for a variable speed rotating DC motor servo system. Background Art

[0002] Brushless DC motors are widely used in industrial process control, aerospace, robotics and other fields due to their reliable operation, simple structure and good speed regulation performance. In practical applications, brushless DC motors need to perform high-precision tracking and control of position-related periodic reference signals. For example, in non-circular CNC turning systems, the tool driven by the motor makes a straight reciprocating motion in the vertical direction of the workpiece turntable spindle. When the turntable rotation speed is not constant, the tool feed amount relative to the turntable rotation position is a time-varying periodic signal. It is well known that repetitive control based on the internal model principle is one of the effective methods to solve the problem of periodic signal control. This method converts the internal model of the periodic signal into a periodic signal. Placed in a stable closed loop, so as to achieve a period of T r The repetitive control system has excellent control performance for periodic signals with fixed period length in the time domain, but it is very sensitive to periodic fluctuations. r Any slight change will greatly reduce the gain of the repetitive controller at the fundamental frequency and harmonics, which will seriously affect the system performance.

[0003] To solve the above problems, Nakano et al. proposed the concept of position domain based on the fact that the position-dependent periodic signal is a periodic function of the rotation angle and the period length is a constant, and designed a position domain repetitive controller to handle the position-dependent periodic disturbance in the uniform rotation system. The advantage of the position domain repetitive controller is that it can construct an accurate internal model of the position-dependent periodic signal, thus ensuring the system's high-precision control of the position-dependent periodic signal.

[0004] Existing research mainly considers the problem of tracking and / or suppressing position-related periodic signals by a linear time-invariant system, but the actual rotating system has nonlinear characteristics and is inevitably affected by external environment and internal parameter perturbations. According to the Bode integral theorem, the position domain repetitive controller achieves superior periodic performance by reducing the system's sensitivity to periodic signals at fundamental and harmonic frequencies, but at the cost of increased sensitivity in other frequency bands, which in turn makes the position domain repetitive control system more sensitive to non-periodic disturbances. The active anti-interference method currently proposed mainly converts internal and external disturbances to the system input channel through coordinate transformation, and then applies the observer method to estimate and compensate for the lumped disturbance. However, this conversion process usually requires the derivation of uncertainty terms and system input and output, resulting in noise amplification and increasing the impact of uncertainty on the system. Therefore, how to solve the tracking control of position-related periodic signals while effectively dealing with the nonlinear characteristics and uncertainties in variable speed rotating motion systems is an urgent problem to be solved. Summary of the invention

[0005] The technical problem to be solved by the present invention is: in view of the technical problems existing in the prior art, the present invention provides a disturbance compensation and tracking control method for a variable speed rotary DC motor servo system, which has high efficiency, simple controller structure, and is easy to implement, and the control system has better disturbance suppression, tracking control performance and robustness.

[0006] In order to solve the above technical problems, the technical solution proposed by the present invention is:

[0007] A disturbance compensation and tracking control method for a variable speed rotary DC motor servo system comprises the following steps:

[0008] Step S1: establishing a brushless DC motor state space model according to a voltage balance equation and a torque balance equation;

[0009] Step S2: Analyze the intrinsic connection between the time domain and the position domain of the system, construct the position domain internal model of the periodic signal according to the position-related periodic characteristics of the reference input signal, and establish an improved position domain repetitive controller;

[0010] Step S3: construct a disturbance observer according to the state space model of the brushless DC motor, estimate the system matching and non-matching disturbances in real time to obtain the disturbance estimation value, combine the position domain repetitive control law and the disturbance estimation value, and design a composite repetitive control law based on active disturbance compensation;

[0011] Step S4: Using the position information of the motor rotor, a digital implementation method of a position domain repetitive controller synchronized with the time domain robust stabilization controller is established.

[0012] The improvement of the above technical solution is as follows:

[0013] Preferably, in step S1, a brushless DC motor state space model is established based on a voltage balance equation and a torque balance equation:

[0014]

[0015] The coefficient matrix is:

[0016]

[0017] Where u(t) is the voltage applied to the two-phase conducting winding, x(t) = [x1(t), x2(t)] T is the state variable, x1(t) is the angular velocity of the motor rotor, x2(t) is the armature current, f(x,u,M c ) is the system mismatch uncertainty, the second component f2 is the system match uncertainty, and y(t) is the system output;

[0018] R0, L0 and J0 represent the nominal values ​​of phase resistance, phase inductance and moment of inertia, respectively. R0ΔR, L0ΔL and J0ΔJ represent the perturbations of phase resistance, phase inductance and moment of inertia, respectively. i(t) is the armature current, ω(t) is the angular velocity of the motor rotor, and M c (t) is the external load torque of the motor, k e is the back electromotive force coefficient, p is the number of motor poles, R is the resistance of each phase winding, L s is the inductance of each phase winding, and J is the total moment of inertia of the motor rotor and load.

[0019] Preferably, in step S2, an improved position domain repetitive controller is constructed based on the internal model of the position-related periodic reference signal, the improved repetitive controller is provided with a low-pass filter, the improved repetitive controller is embedded in the main system, and after phase correction, an improved position domain repetitive controller based on phase compensation is obtained.

[0020] The improved position domain repetitive controller is designed as follows:

[0021]

[0022] Among them, α is the phase compensation factor, s is the Laplace operator, is a low-pass filter, and Γ is a position domain period.

[0023] Preferably, step S3 comprises the following steps:

[0024] Step S31: construct a disturbance observer according to the brushless DC motor state space model formula in step S1:

[0025]

[0026] in, is f(x,u,M c ), is the estimated value of the system mismatch disturbance, is the estimated value of the system matching disturbance, M(t) is the internal state of the observer, and L is the observer gain to be designed;

[0027] Step S32: Combining the position domain repetitive control law and the disturbance estimation value, a composite repetitive control law based on active disturbance compensation is obtained:

[0028]

[0029] Among them, K x is the state feedback gain, K d is the disturbance compensation gain, designed as

[0030] K d =-[C(A+B u K x ) -1 B u ] -1 C(A+B u K x ) -1 B d .

[0031] Preferably, in step S3, an improved repetitive controller is constructed, the improved repetitive controller is provided with a low-pass filter, the improved repetitive controller is embedded into the main system, and an improved repetitive controller based on phase compensation is obtained after phase correction.

[0032] Preferably, in step S4, the angular velocities of the position domain repetitive controller input signal and the position-related periodic reference signal are sampled for a fixed time period, and the angular position information is used to implement the function of the position domain repetitive controller, thereby obtaining the output of the position domain repetitive controller.

[0033] The disturbance compensation and tracking control method of the variable speed rotary DC motor servo system provided by the present invention has the following advantages compared with the prior art:

[0034] (1) The disturbance compensation and tracking control method of the variable speed rotary DC motor servo system of the present invention has a simple design, strong real-time control and high tracking accuracy. Under the condition that the motor output speed and armature current can be directly measured by sensors, the present invention provides a new method for position-related periodic signal control of the variable speed rotary motion system. On the one hand, various uncertainties are estimated and actively compensated in real time, and on the other hand, high-precision tracking of position-related periodic reference input signals can be achieved.

[0035] (2) The disturbance compensation and tracking control method of the variable speed rotary DC motor servo system of the present invention has a two-degree-of-freedom structure and uses a disturbance observer to estimate the system uncertainty. Compared with other active disturbance suppression methods, it reduces the phase lag caused by the observer and improves the disturbance estimation accuracy.

[0036] (3) The disturbance compensation and tracking control method of the variable speed rotary DC motor servo system of the present invention utilizes the position domain periodic characteristics of the rotary motion system to construct an improved repetitive controller including a position domain inner model of a reference input signal, and utilizes the position information of the motor rotor to establish a time domain digital implementation method of the improved repetitive controller, so that an integrated controller including a time domain disturbance observer and a position domain repetitive controller can be synchronously executed through equal-periodic sampling, thereby improving the applicability and practicality of the tracking control and disturbance suppression methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic diagram of the process of the present invention.

[0038] Figure 2 It is the equivalent circuit diagram of brushless DC motor.

[0039] Figure 3 It is the structural block diagram of the brushless DC motor servo system experimental platform.

[0040] Figure 4 It is a structural block diagram of the control system of the present invention.

[0041] Figure 5 It is a hardware connection diagram of the experimental platform when the present invention is applied.

[0042] Figure 6 It is a graph of a position-dependent periodic reference signal in an application example of the present invention.

[0043] Figure 7 It is the position-dependent periodic reference signal and system output curve during the experimental verification of the present invention.

[0044] Figure 8 It is the system tracking error curve during the experimental verification of the present invention.

[0045] Fig. 9 This is the system control input curve during the experimental verification of the present invention.

[0046] Fig.10 It is the system non-matching uncertainty estimation curve during the experimental verification of the present invention.

[0047] Fig.11 It is the system matching uncertainty estimation curve when the present invention is experimentally verified.

[0048] Fig.12 It is a comparison curve of the speed tracking errors of the embodiment of the present invention (position domain repetitive control method based on disturbance observer (DO)) and the position domain repetitive control method based on state feedback and the state feedback control method based on generalized extended state observer (GESO) during the experimental verification of the present invention.

[0049] Fig.13 It is a comparison curve of the rotation speed tracking error between the embodiment of the present invention and the DO-based state feedback control method and the GESO-based position domain repetitive control method during the experimental verification of the present invention. DETAILED DESCRIPTION

[0050] The specific embodiments of the present invention are described in detail below. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0051] like Figures 1 to 13 As shown, the present invention provides a disturbance compensation and tracking control method for a variable speed rotating DC motor servo system, which specifically includes the following steps:

[0052] Step S1: Establish a brushless DC motor state space model based on the voltage balance equation and the torque balance equation.

[0053] It is divided into the following steps:

[0054] Step S11: Based on the voltage balance equation and the torque balance equation, the brushless DC motor servo system state equation formula (1) is established:

[0055]

[0056] Among them, ω(t) is the angular velocity of the motor rotor, i(t) is the armature current, u(t) is the voltage applied to the two-phase conducting winding, M c (t) is the external load torque on the motor, J is the moment of inertia, k e is the back electromotive force coefficient, p is the number of motor poles, R is the resistance of each phase winding, L s is the inductance of each phase winding, and J is the total moment of inertia of the motor rotor and load.

[0057] During the actual operation of the motor, the internal temperature will change due to the influence of friction and eddy current, which will cause the resistance R and inductance L of the armature winding to change. s This will cause parameter perturbation. On the other hand, changes in external loads will cause perturbations in the moment of inertia J. Assume that there is a parameter perturbation of the following form:

[0058]

[0059] Among them, R0, L0 and J0 represent the nominal values ​​of phase resistance, phase inductance and moment of inertia, respectively, and R0ΔR, L0ΔL and J0ΔJ represent the perturbations of phase resistance, phase inductance and moment of inertia, respectively.

[0060] Step S12: define the state variable as x(t)=[x1(t),x2(t)] T , where x1(t) = ω(t), x2(t) = i(t), the control input is u(t), and the system output is y(t) = ω(t). The state space model of the brushless DC motor is established:

[0061]

[0062] The coefficient matrix is:

[0063]

[0064] From formulas (3) and (4), we can see that (A, B u ) is controllable, and f(x,u,M c ) is the system mismatch uncertainty, and the second component f2 is the system match uncertainty.

[0065] Step S2: Analyze the intrinsic connection between the time domain and the position domain of the system, construct the position domain internal model of the periodic signal according to the position-related periodic characteristics of the reference input signal, and establish an improved position domain repetitive controller.

[0066] The inherent connection between the system time domain and location domain and the design steps of the location domain repetitive control law are as follows:

[0067] Step S21: The position-dependent periodic reference signal refers to a reference input signal which is a periodic function with respect to the angular position θ. The position-dependent periodic reference signal is defined as It is a periodic function of the rotational angular displacement θ, with a period of Γ.

[0068] Assuming the motor only rotates in one direction, the angular position θ can be defined as:

[0069]

[0070] Where v(t) is the angular velocity. Therefore, the relationship between the variables θ(t) and v(t) is:

[0071]

[0072] Then t = φ -1 (θ) exists.

[0073] Step S22: Let L 2 (0,t f) is represented as a Lebesgue square integrable function space:

[0074]

[0075] Formula (7) is a norm Hilbert space.

[0076] Define a weighted function space:

[0077]

[0078] Formula (8) is a norm Hilbert space.

[0079] Let θ f =θ(t f ), and define the domain conversion operator as:

[0080]

[0081] Step S23: Similar to the time domain Laplace transform, define the signal The position domain Laplace transform is:

[0082]

[0083] Substituting formula (6) into (10), the Laplace integral transform in the time domain is obtained as follows:

[0084]

[0085] Position-dependent periodic reference signal The following conditions are met:

[0086]

[0087] The position domain Laplace transform of the position-dependent periodic reference signal:

[0088]

[0089] Among them, 1 / (1-e -sΓ ) is regarded as a position-dependent periodic reference signal Internal model.

[0090] Step S24: construct an improved position domain repetitive controller:

[0091]

[0092] Where α is the phase compensation factor and s is the Laplace operator. The improved position domain repetitive controller is essentially an approximate internal model of a position-dependent periodic reference signal. According to the internal model principle, by introducing the internal model of the reference signal into the stable closed loop, the position domain repetitive control system has satisfactory steady-state tracking performance for the position-dependent periodic reference signal.

[0093] First-order low-pass filter The relationship between input and output signals is selected as:

[0094]

[0095] in, is the filter output signal, u q (θ) is the filter input signal, ω f is the filter cutoff frequency.

[0096] because According to formula (11), we can get:

[0097]

[0098] because Combining formula (6) and (14), we get:

[0099]

[0100] Then the transfer function of the low-pass filter is obtained as:

[0101]

[0102] The phase compensation factor e in formula (13) αs Used to compensate for the phase lag caused by the low-pass filter.

[0103] The designed position domain repetitive control law is:

[0104]

[0105] Where K(s) is a controller used to enhance the dynamic response characteristics of the system, which is generally selected as a PID controller or a lead-lag compensator; U r (s) is the output signal u of the improved position domain repetitive controller r E(s) is the Laplace transform of the tracking error of the motor output speed e(t)=r(t)-y(t) in time domain.

[0106] Step S3: construct a disturbance observer according to the state space model of the brushless DC motor, estimate the system matching and non-matching disturbances in real time, and use the disturbance estimation value to design a composite repetitive control law based on active disturbance compensation.

[0107] The following steps are involved:

[0108] Step S31: construct a disturbance observer according to the brushless DC motor state space model formula (3):

[0109]

[0110] in, is f(x,u,M c ), is the estimated value of the system mismatch disturbance, is the estimated value of the system matching disturbance, M(t) is the internal state of the observer, and L is the observer gain to be designed.

[0111] Step S32: Combining the position domain repetitive control law and the disturbance estimation value, a composite repetitive control law based on active disturbance compensation is obtained:

[0112]

[0113] Among them, K x is the state feedback gain, K d is the disturbance compensation gain, which is designed as:

[0114] K d =-[C(A+B u K x ) -1 B u ] -1 C(A+B u K x ) -1 B d (20)

[0115] The composite repetitive control law u(t) is used to ensure that the system can track and control the position-related periodic reference signal with high precision while effectively suppressing the influence of disturbances on the system output.

[0116] Step S4: Using the position information of the motor rotor, establish a digital implementation method of the position domain repetitive controller synchronized with the time domain robust stabilization controller. The specific program implementation steps are as follows:

[0117] The position domain repetitive controller input signal e(t) and the angular velocity v(t) of the position-related periodic reference signal are sampled at a fixed step length T0, and the angular position information is used to implement the function of the position domain repetitive controller, thereby obtaining the output u of the position domain repetitive controller.r (t).

[0118] The relevant variables used in the digital implementation of the position domain repetitive controller are defined as follows:

[0119] Until the current time t i [=iT0], the motor rotation angle displacement is

[0120]

[0121] Formula (21) is used to determine the number of position domain cycles at the current moment, and to determine whether a learning mechanism needs to be introduced into the output of the position domain repetitive controller.

[0122] At the current time t i , the number of sampling points k corresponding to the relative position of the previous position domain period Γ It can be obtained by the following formula

[0123]

[0124] The number of sampling points k corresponding to the phase compensation factor α α for

[0125] k α =[α*k Γ / Γ] (23)

[0126] Formula (23) means that it is less than α*k Γ / The largest non-negative integer.

[0127] Delay Link The number of sampling points corresponding to the hysteresis time can be expressed as

[0128] k v =k Γ -k α (twenty four)

[0129] Combining formulas (13-14) and (22-24), the position domain repetitive controller outputs u r (t i ) can be calculated by the following formula

[0130]

[0131] Step S41: Select the sampling period T0 and the low-pass filter cutoff frequency ω f , and initialize m = 0 and s r =0.

[0132] Step S42: The position domain repetitive controller has a self-learning function, which adds the control effect of the previous rotation cycle to the control amount of the current rotation cycle, gradually eliminates the tracking deviation, and realizes high-precision tracking of the position-related periodic reference input.

[0133] Step S43: If condition η Γ ≤Γ holds, then assign u r (t i )=e(t i ) and proceed to step S47; otherwise, proceed to step S44.

[0134] Step S44: assign m=m+1 and s r =s r +v(t i-m+1 )T0;

[0135] Step S45: If condition s r If ≤Γ holds, return to step S44; otherwise, proceed to step S46.

[0136] Step S46: assign k Γ =m, and calculate u according to formula (25) r (t i );

[0137] Step S47: Output u r (t i ).

[0138] The control method of the present invention is further described by using a brushless DC motor speed control experiment.

[0139] In order to verify the feasibility and superiority of the method proposed in the present invention under actual working conditions, this example builds a tracking control experimental platform for the output speed of a brushless DC motor to a position-related periodic reference signal, and compares it with other control methods. The experimental platform has seven parts: a brushless DC motor (rated voltage of 48V, rated speed of 3000r / min, rated power of 200W), a motor driver board (which can drive a motor with a rated voltage of 24-48V), a 5V DC power supply (to power the motor driver board), an RTLAB OP5600 real-time digital simulator (including CPU and FPGA board, digital and analog signal I / O board), a host computer, a magnetic powder brake, and a tension controller (to provide external load torque for the motor).

[0140] This example uses a brushless DC motor of model S60BL-430 for experimental verification. The specific motor parameters are listed in Table 1. The brushless DC motor equivalent circuit is shown in Figure 2 shown.

[0141] Table 1 S60BL-430 brushless DC motor parameter table

[0142]

[0143] The internal signal direction of the motor experimental platform is as follows Figure 3 The system structure block diagram of the control method designed by the present invention is shown in Figure 4 As shown. The present invention uses four groups of digital-analog signal I / O ports of the RTLAB OP5600 real-time digital simulator, which are analog output port (OP5330 AO), digital output port (OP5354 DO), analog input port (OP5340AI) and digital input port (OP5353 DI). Among them, OP5330 AO outputs a voltage signal, which is converted into a current signal by a tension controller, and then controls the magnetic powder brake to generate a corresponding external load torque; OP5354 DO is used as an output port for controlling the input voltage of the motor system, and outputs a PWM control signal generated after the execution of the host computer control program. The motor drive board receives the PWM control signal and adjusts the motor speed by controlling the on and off of the power device in the drive circuit; OP5340AI is used as an input port for motor phase current detection to realize real-time measurement of armature current; OP5353 DI receives the position information of the Hall sensor inside the motor to realize real-time measurement of electronic commutation and motor speed.

[0144] Experimental verification: Position-dependent periodic reference speed tracking control experiment under different external load disturbances.

[0145] Figure 5 The hardware connection diagram of the experimental platform in a specific application example of the present invention is shown in FIG. In this experiment, the position-dependent periodic reference speed is set to The position variables are:

[0146]

[0147] The curves of the position-related periodic reference speed signal in the time domain and position domain are as follows: Figure 6 As shown. The external load torque of the motor is set as:

[0148]

[0149] The system sampling step is set to 0.00002s. When the control method proposed by the present invention is used for experiments, the bandwidth of the state feedback controller is selected as 30, and the state feedback gain is calculated to be K x =[-0.06,115.15], the disturbance observer gain is selected as L=diag[35,36], and then the disturbance compensation gain is calculated by formula (20) as K d=[364.65,-1.95]. In the position domain repetitive controller, the low-pass filter cutoff frequency ω f =50, stabilization compensator K(s)=0.08+0.022s / (s+150).

[0150] Figure 7-11 It is the system output response curve of the control method proposed in the present invention. It can be seen from the figure that when the position domain repetitive control method based on the disturbance observer proposed in the present invention is adopted, the brushless DC motor servo system can effectively suppress the motor matching and non-matching uncertainties, and at the same time ensure that the motor speed can quickly and accurately track the given position-related periodic reference speed signal.

[0151] Fig.12 The speed tracking error of the proposed method (DO-based position domain repetitive control method) is compared with that of the state feedback-based position domain repetitive control method (for example, the literature Accurate cycle aligned repetitive control for the rejection of spatially cyclic disturbances, IEEE Transactions on Industrial Electronics, 2021, 69(6): 6173-6181) and the GESO-based state feedback control method (for example, the literature Generalized extended state observer based control for systems with mismatched uncertainties, IEEE Transactions on Industrial Electronics, 2011, 59(12): 4792-4802). It can be seen that compared with other existing methods, the proposed method has faster system response speed, better disturbance rejection performance, and higher tracking accuracy for position-related periodic reference speed signals.

[0152] Fig.13 The figure is a comparison of the speed tracking error between the proposed method and the DO-based state feedback control method and the GESO-based position domain repetitive control method. It can be seen that compared with other methods, the proposed method has a smaller system overshoot and a higher tracking accuracy for the position-related periodic reference speed signal.

[0153] The above implementation cases are only preferred embodiments of the present invention and are not intended to limit the present invention in any form. Although the present invention has been disclosed as above with preferred embodiments, they are not intended to limit the present invention. Therefore, any simple modification, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A disturbance compensation and tracking control method for a variable speed rotary DC motor servo system, characterized in that: The following steps are involved: Step S1: establishing a brushless DC motor state space model according to a voltage balance equation and a torque balance equation; Step S2: Analyze the intrinsic connection between the time domain and the position domain of the system, construct the position domain internal model of the periodic signal according to the position-related periodic characteristics of the reference input signal, and establish an improved position domain repetitive controller; Step S3: construct a disturbance observer according to the state space model of the brushless DC motor, estimate the system matching and non-matching disturbances in real time to obtain the disturbance estimation value, combine the position domain repetitive control law and the disturbance estimation value, and design a composite repetitive control law based on active disturbance compensation; Step S4: using the position information of the motor rotor, establishing a digital implementation method of a position domain repetitive controller synchronized with the time domain robust stabilization controller; In step S1, a brushless DC motor state space model is established based on the voltage balance equation and the torque balance equation: The coefficient matrix is: Where u(t) is the voltage applied to the two-phase conducting winding, x(t) = [x1(t), x2(t)] T is the state variable, x1(t) is the angular velocity of the motor rotor, x2(t) is the armature current, f(x,u,M c ) is the system mismatch uncertainty, the second component f2 is the system match uncertainty, and y(t) is the system output; R0, L0 and J0 represent the nominal values ​​of phase resistance, phase inductance and moment of inertia, respectively. R0ΔR, L0ΔL and J0ΔJ represent the perturbations of phase resistance, phase inductance and moment of inertia, respectively. i(t) is the armature current, ω(t) is the angular velocity of the motor rotor, and M c (t) is the external load torque of the motor, k e is the back electromotive force coefficient, p is the number of motor poles, R is the resistance of each phase winding, L s is the inductance of each phase winding, J is the total moment of inertia of the motor rotor and load; The improved position domain repetitive controller is designed as follows: Among them, α is the phase compensation factor, s is the Laplace operator, is a low-pass filter, Γ is a position domain period; The step S3 comprises the following steps: Step S31: construct a disturbance observer according to the brushless DC motor state space model formula in step S1: in, is f(x,u,M c ), is the estimated value of the system mismatch disturbance, is the estimated value of the system matching disturbance, M(t) is the internal state of the observer, and L is the observer gain to be designed; Step S32: Combining the position domain repetitive control law and the disturbance estimation value, a composite repetitive control law based on active disturbance compensation is obtained: Among them, K x is the state feedback gain, K d is the disturbance compensation gain, which is designed as: K d =-[C(A+B u K x ) -1 B u ] -1 C(A+B u K x ) -1 B d 。 2. The disturbance compensation and tracking control method of the variable speed rotary DC motor servo system according to claim 1, characterized in that: In the step S2, an improved position domain repetitive controller is constructed according to the internal model of the position-related periodic reference signal, the improved position domain repetitive controller includes a low-pass filter, the improved repetitive controller is embedded in the main system, and an improved position domain repetitive controller based on phase compensation is obtained after phase correction.

3. The disturbance compensation and tracking control method of the variable speed rotary DC motor servo system according to claim 1, characterized in that: In step S4, the angular velocities of the position domain repetitive controller input signal and the position-related periodic reference signal are sampled for a fixed time, and the angular position information is used to implement the function of the position domain repetitive controller, thereby obtaining the output of the position domain repetitive controller.

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