An optimized control method for a permanent magnet brushless DC motor servo system

Abstract

The application relates to the technical field of brushless direct-current motors, in particular to an optimization control method for a permanent magnet brushless direct-current motor servo system, which comprises the following steps: S1.1: obtaining an equivalent system basic model of the permanent magnet brushless direct-current motor servo system; S1.2: improving the equivalent system basic model of the permanent magnet brushless direct-current motor servo system, and establishing a compound repetitive control law; and S1.3: optimizing control of the parameters of the equivalent system basic model of the permanent magnet brushless direct-current motor servo system. The application proposes a repetitive control system parameter optimization method based on an improved disturbance estimator compensation, establishes an optimization control model of system parameters based on the stability of the system, realizes synchronous optimization design of the parameters of a system repetitive controller, an improved disturbance estimator and a feedback controller, and makes the system simultaneously have satisfactory non-periodic disturbance suppression performance and periodic signal tracking performance.

Description

Technical Field

[0001] This invention relates to the field of brushless DC motor technology, and in particular to an optimized control method for a permanent magnet brushless DC motor servo system. Background Technology

[0002] In engineering practice, many systems need to perform periodic control tasks, such as suppressing periodic torque fluctuations in DC doubly-fed induction generators, current control in permanent magnet synchronous motor servo systems, and inverter voltage control. Repetitive control provides an effective method for solving these periodic signal tracking / suppression problems. Its theoretical basis is the internal model principle, which achieves unbiased steady-state tracking / suppression of any target signal with period Tr by embedding an internal model of the periodic signal into a stable closed-loop system. The basic repetitive control system is a neutral time-delay system. To relax the system's stability conditions, a low-pass filter needs to be embedded in the time-delay stage to construct an improved repetitive controller. However, the improved repetitive controller is only an approximate model of the periodic signal, and the steady-state tracking error of the system is no longer zero. Therefore, the improved repetitive control system faces a trade-off between stability and tracking performance. How to simultaneously optimize the cutoff frequency of the low-pass filter and the stabilizing controller parameters is the key to solving this trade-off. Currently, incorporating a disturbance estimator is a commonly used active disturbance suppression method in existing technologies. However, most current literature chooses a fixed low-pass filter cutoff frequency, which to some extent limits the improvement of disturbance suppression performance. In practice, a higher cutoff frequency generally results in better system noise immunity. However, an excessively high cutoff frequency allows high-frequency noise to pass through, negating the filtering effect. Conversely, a cutoff frequency that is too low will filter out useful low-frequency signals and cause phase lag, leading to poor system noise immunity. To address these issues, this paper proposes an optimized control method for a permanent magnet brushless DC motor servo system, aiming to overcome the shortcomings mentioned in the background section. Summary of the Invention

[0003] The purpose of this invention is to address the deficiencies mentioned in the background art by proposing an optimized control method for a permanent magnet brushless DC motor servo system.

[0004] The technical solution adopted in this invention is as follows:

[0005] An optimized control method for a permanent magnet brushless DC motor servo system is provided, comprising the following steps:

[0006] S1.1: Obtain the basic equivalent system model of the permanent magnet brushless DC motor servo system;

[0007] S1.2: Improve the basic model of the equivalent system of the permanent magnet brushless DC motor servo system and establish a compound repetitive control law;

[0008] S1.3: Optimize and control the parameters of the basic model of the equivalent system of the permanent magnet brushless DC motor servo system.

[0009] As a preferred technical solution of the present invention: In S1.1, the equivalent system basic model of the permanent magnet brushless DC motor servo system includes three parts: the controlled object, the observer, and the state feedback.

[0010] As a preferred technical solution of the present invention: an improved disturbance estimator is added to S1.2, and the filtered estimated value is fed back to the control input terminal for compensation. At the same time, an improved repetitive controller is used to establish a compound repetitive control law.

[0011] As a preferred embodiment of the present invention: the improved disturbance estimator treats the impact of external disturbances on the system as an equivalent virtual signal at a control input, i.e., d e (t), using a full-dimensional state observer to observe d e (t) is estimated, an improved disturbance estimator is constructed by introducing a low-pass filter, and the filtered estimated value d is... e (t) Feedback compensation is sent to the control input.

[0012] As a preferred embodiment of the present invention: the improved disturbance estimator added in S1.2 is a low-pass filter F(s).

[0013]

[0014] Where T represents the time constant of the low-pass filter; s represents the input of the low-pass filter;

[0015] Improvements can be made by using the transfer function H(s):

[0016] H(s) = F(s)[1-F(s)] -1

[0017] Improve disturbance suppression performance.

[0018] As a preferred embodiment of the present invention, the expression for the improved disturbance estimator obtained in S1.2 is as follows:

[0019]

[0020] in, ΔX(s) and ΔX(s) respectively represent Laplace transform of Δx(s); B + = (B T B) -1 B T Let B and C represent known real matrices with appropriate dimensions. TThe transpose of matrix B; L = [L1L2…L n ] T For the observer gain, [L1L2…L n ] T For the matrix [L1L2…L… n The transpose of ].

[0021] As a preferred embodiment of the present invention: in step S1.2, an improved repetitive controller is added as follows:

[0022] Let the period of the reference input r(t) be T. r The transfer function C of the basic repetitive controller R (s) is:

[0023]

[0024] Where e is a mathematical constant; s represents the input of the low-pass filter;

[0025] At base frequency Harmony wave (ω) f =fω v f∈Z + At point ), the gain of the repetitive controller |C R (jω k | is infinity, that is:

[0026]

[0027] Where, jω f This represents the frequency domain input of the repetitive controller;

[0028] Improved repetitive controller transfer function C M (s) is:

[0029]

[0030] Where T′ represents the time delay constant of the improved repetitive controller, and q(s) represents the first-order low-pass filter;

[0031]

[0032] Where, ω c Let represent the cutoff frequency of q(s), and its value follows the frequency characteristics below:

[0033]

[0034] Where jω represents the frequency domain input of q(s); ω r The maximum angular frequency of the periodic reference input r(t) is represented by ω, and the cutoff frequency of the filter is represented by ω. c Satisfy ωc ≥5ω r The state-space model of the improved repetitive controller is as follows:

[0035]

[0036] in, x represents the state variable of the improved repetitive controller. c (t) represents the state variables of the low-pass filter; x c (tT′) represents the time-delay state variable of the improved repetitive controller; v(t) represents the output of the repetitive controller; e(t) represents the tracking error.

[0037] As a preferred technical solution of the present invention: in S1.3, the system parameters are optimized and controlled based on the particle swarm optimization algorithm.

[0038] As a preferred embodiment of the present invention, the particle swarm optimization algorithm steps are as follows:

[0039] The parameters of the improved repetitive controller, observer, and low-pass filter are synchronously optimized using a particle swarm optimization algorithm. During the iteration process, the particle velocity and position update formulas are as follows:

[0040]

[0041] in, This represents the velocity of the i-th particle in the (k+1)-th iteration; Let X represent the velocity of the i-th particle in the k-th iteration. i This represents the position of the i-th particle, i.e., the solution vector for a set of parameters. This represents the position of the i-th particle in the k-th iteration. This represents the best position found by the i-th particle in the k-th iteration; c1 represents the best position found so far in the entire particle swarm; c2 represents the learning factor of the particle itself; r1 and r2 represent random numbers in the interval (0, 1). ω represents the position of the i-th particle in the (k+1)-th iteration; ω represents the particle's inertial weight, which decreases linearly with the number of iterations k.

[0042]

[0043] Where K is the maximum number of iterations, ω max and ω min These represent the maximum and minimum inertia weights, respectively.

[0044] As a preferred embodiment of the present invention, the objective function in the particle swarm search algorithm is defined as follows:

[0045]

[0046] Where m1, m2, and m3 are the weights corresponding to each item; N is the number of repetitive control cycles. Let these represent the fitness value and the system following error for the i-th particle in the k-th iteration, respectively. and Let represent the state variable and the estimated value of the state variable corresponding to the k-th iteration of the i-th particle, respectively.

[0047] The optimized control method for a permanent magnet brushless DC motor servo system provided by this invention has the following advantages compared with the prior art:

[0048] This invention proposes a parameter optimization method for repetitive control systems based on improved disturbance estimator compensation. An optimized control model for system parameters is established based on system stability, realizing the synchronous optimization design of parameters of the repetitive controller, improved disturbance estimator, and feedback controller, so that the system has satisfactory non-periodic disturbance suppression performance and periodic signal tracking performance at the same time. Attached Figure Description

[0049] Figure 1 This is a flowchart of a preferred embodiment of the present invention;

[0050] Figure 2 This is an estimation diagram of the improved disturbance estimator system in a preferred embodiment of the present invention;

[0051] Figure 3 This is a structural diagram of an improved repeating controller system in a preferred embodiment of the present invention. Detailed Implementation

[0052] It should be noted that, unless otherwise specified, the embodiments and features described in this embodiment can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] Reference Figure 1 A preferred embodiment of the present invention provides an optimized control method for a permanent magnet brushless DC motor servo system, comprising the following steps:

[0054] S1.1: Obtain the basic equivalent system model of the permanent magnet brushless DC motor servo system;

[0055] S1.2: Improve the basic model of the equivalent system of the permanent magnet brushless DC motor servo system and establish a compound repetitive control law;

[0056] S1.3: Optimize and control the parameters of the basic model of the equivalent system of the permanent magnet brushless DC motor servo system.

[0057] In S1.1, the equivalent system basic model of the permanent magnet brushless DC motor servo system includes three parts: the controlled object, the observer, and the state feedback.

[0058] An improved disturbance estimator is added to S1.2, and the filtered estimated value is fed back to the control input for compensation. At the same time, an improved repetitive controller is used to establish a compound repetitive control law.

[0059] The improved disturbance estimator treats the impact of external disturbances on the system as an equivalent virtual signal at the control input, i.e., d. e (t), using a full-dimensional state observer to observe d e (t) is estimated, an improved disturbance estimator is constructed by introducing a low-pass filter, and the filtered estimated value d is... e (t) Feedback compensation is sent to the control input.

[0060] The improved perturbation estimator added in S1.2 selects a low-pass filter F(s).

[0061]

[0062] Where T represents the time constant of the low-pass filter; s represents the input of the low-pass filter;

[0063] Improvements can be made by using the transfer function H(s):

[0064] H(s) = F(s)[1-F(s)] -1

[0065] Improve disturbance suppression performance.

[0066] The expression for the improved disturbance estimator obtained in S1.2 is as follows:

[0067]

[0068] in, ΔX(s) and ΔX(s) respectively represent Laplace transform of Δx(s); B + = (B T B) -1 B T Let B and C represent known real matrices with appropriate dimensions. T The transpose of matrix B; L = [L1L2…Ln ] T For the observer gain, [L1L2…L n ] T For the matrix [L1L2…L… n The transpose of ].

[0069] In step S1.2, an improved repetitive controller is added as follows:

[0070] Let the period of the reference input r(t) be T. r The transfer function C of the basic repetitive controller R (s) is:

[0071]

[0072] Where e is a mathematical constant; s represents the input of the low-pass filter;

[0073] At base frequency Harmony wave (ω) f =fω v f∈Z + At point ), the gain of the repetitive controller |C R (jω k | is infinity, that is:

[0074]

[0075] Where, jω f This represents the frequency domain input of the repetitive controller;

[0076] Improved repetitive controller transfer function C M (s) is:

[0077]

[0078] Where T′ represents the time delay constant of the improved repetitive controller, and q(s) represents the first-order low-pass filter;

[0079]

[0080] Where, ω c Let represent the cutoff frequency of q(s), and its value follows the frequency characteristics below:

[0081]

[0082] Where jω represents the frequency domain input of q(s); ω r The maximum angular frequency of the periodic reference input r(t) is represented by ω, and the cutoff frequency of the filter is represented by ω. c Satisfy ω c ≥5ω rThe state-space model of the improved repetitive controller is as follows:

[0083]

[0084] in, x represents the state variable of the improved repetitive controller. c (t) represents the state variables of the low-pass filter; x c (tT′) represents the time-delay state variable of the improved repetitive controller; v(t) represents the output of the repetitive controller; e(t) represents the tracking error.

[0085] In S1.3, the system parameters are optimized and controlled based on the particle swarm optimization algorithm.

[0086] The steps of the particle swarm optimization algorithm are as follows:

[0087] The parameters of the improved repetitive controller, observer, and low-pass filter are synchronously optimized using a particle swarm optimization algorithm. During the iteration process, the particle velocity and position update formulas are as follows:

[0088]

[0089] in, This represents the velocity of the i-th particle in the (k+1)-th iteration; Let X represent the velocity of the i-th particle in the k-th iteration. i This represents the position of the i-th particle, i.e., the solution vector for a set of parameters. This represents the position of the i-th particle in the k-th iteration. This represents the best position found by the i-th particle in the k-th iteration; c1 represents the best position found so far in the entire particle swarm; c2 represents the learning factor of the particle itself; r1 and r2 represent random numbers in the interval (0, 1). ω represents the position of the i-th particle in the (k+1)-th iteration; ω represents the particle's inertial weight, which decreases linearly with the number of iterations k.

[0090]

[0091] Where K is the maximum number of iterations, ω max and ω min These represent the maximum and minimum inertia weights, respectively.

[0092] In the particle swarm search algorithm, the objective function is defined as follows:

[0093]

[0094] Where m1, m2, and m3 are the weights corresponding to each item; N is the number of repetitive control cycles. Let these represent the fitness value and the system following error for the i-th particle in the k-th iteration, respectively. and Let represent the state variable and the estimated value of the state variable corresponding to the k-th iteration of the i-th particle, respectively.

[0095] In this embodiment, an equivalent system basic model of the permanent magnet brushless DC motor servo system is obtained, including three parts: the controlled object, the observer, and the state feedback. An improved disturbance estimator is added to the equivalent system basic model of the permanent magnet brushless DC motor servo system, and the filtered estimated value is fed back to the control input for compensation. Simultaneously, an improved repetitive controller is used to establish a composite repetitive control law. The improved disturbance estimator treats the influence of external disturbances on the system as an equivalent virtual signal at the control input, i.e., d. e (t), using a full-dimensional state observer to observe d e (t) is estimated, an improved disturbance estimator is constructed by introducing a low-pass filter, and the filtered estimated value d is... e (t) Feedback compensation is sent to the control input.

[0096] Reference Figure 2 The improved perturbation estimator includes a low-pass filter F(s).

[0097]

[0098] Where T represents the time constant of the low-pass filter; s represents the input of the low-pass filter;

[0099] Improvements can be made by using the transfer function H(s):

[0100] H(s) = F(s)[1-F(s)] -1

[0101] The expression for the improved disturbance estimator is as follows:

[0102]

[0103] in, ΔX(s) and ΔX(s) respectively represent Laplace transform of Δx(s); B + = (B T B) -1 B T Let B and C represent known real matrices with appropriate dimensions. T The transpose of matrix B; L = [L1L2…L n ] T For the observer gain, [L1L2…Ln ] T For the matrix [L1L2…L… n The transpose of ].

[0104] Improved disturbance suppression performance and a larger stable region are achieved by using an improved transfer function H(s).

[0105] Reference Figure 3 An improved repetitive controller is added as follows:

[0106] Let the period of the reference input r(t) be T. r The transfer function C of the basic repetitive controller R (s) is:

[0107]

[0108] Where e is a mathematical constant; s represents the input of the low-pass filter;

[0109] At base frequency Harmony wave (ω) f =fω v f∈Z + At point ), the gain of the repetitive controller |C R (jω k | is infinity, that is:

[0110]

[0111] Where, jω f This represents the frequency domain input of the repetitive controller;

[0112] Improved repetitive controller transfer function C M (s) is:

[0113]

[0114] Where T′ represents the time delay constant of the improved repetitive controller, and q(s) represents the first-order low-pass filter;

[0115]

[0116] Where, ω c Let represent the cutoff frequency of q(s), and its value follows the frequency characteristics below:

[0117]

[0118] Where jω represents the frequency domain input of q(s); ω r The maximum angular frequency of the periodic reference input r(t) is represented by ω, and the cutoff frequency of the filter is represented by ω. c Satisfy ω c ≥5ωr The state-space model of the improved repetitive controller is as follows:

[0119]

[0120] in, x represents the state variable of the improved repetitive controller. c (t) represents the state variables of the low-pass filter; x c (tT′) represents the time-delay state variable of the improved repetitive controller; v(t) represents the output of the repetitive controller; e(t) represents the tracking error.

[0121] Introducing a first-order low-pass filter q(s) reduces the gain of the repetitive controller at the fundamental frequency and harmonics of the periodic signal, thereby improving the system's tracking performance for the periodic signal.

[0122] The system parameters are optimized and controlled based on the particle swarm optimization algorithm. The parameters of the improved repetitive controller, observer, and low-pass filter are synchronously optimized using the particle swarm optimization algorithm. During the iteration process, the particle velocity and position update formulas are as follows:

[0123]

[0124] in, This represents the velocity of the i-th particle in the (k+1)-th iteration; Let X represent the velocity of the i-th particle in the k-th iteration. i This represents the position of the i-th particle, i.e., the solution vector for a set of parameters. This represents the position of the i-th particle in the k-th iteration. This represents the best position found by the i-th particle in the k-th iteration; c1 represents the best position found so far in the entire particle swarm; c2 represents the learning factor of the particle itself; r1 and r2 represent random numbers in the interval (0, 1). ω represents the position of the i-th particle in the (k+1)-th iteration; ω represents the particle's inertial weight, which decreases linearly with the number of iterations k.

[0125]

[0126] Where K is the maximum number of iterations, ω max and ω min These represent the maximum and minimum inertia weights, respectively.

[0127] The objective function is defined as follows:

[0128]

[0129] Where m1, m2, and m3 are the weights corresponding to each item; N is the number of repetitive control cycles. Let these represent the fitness value and the system following error for the i-th particle in the k-th iteration, respectively. and Let represent the state variable and the estimated value of the state variable corresponding to the k-th iteration of the i-th particle, respectively.

[0130] Using the system's stability condition as the objective constraint, a target function is established to comprehensively evaluate the system's disturbance rejection performance, transient process performance, and periodic signal tracking performance. The particle swarm optimization algorithm is then used to search for the optimal combination of controller parameters that minimizes the objective function.

[0131] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0132] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. An optimized control method for a permanent magnet brushless DC motor servo system, characterized in that: Includes the following steps: S1.1: Obtain the basic equivalent system model of the permanent magnet brushless DC motor servo system; S1.2: Improve the basic model of the equivalent system of the permanent magnet brushless DC motor servo system and establish a compound repetitive control law; S1.3: Optimize and control the parameters of the basic model of the equivalent system of the permanent magnet brushless DC motor servo system; An improved disturbance estimator is added to S1.2, and the filtered estimated value is fed back to the control input for compensation. At the same time, an improved repetitive controller is used to establish a compound repetitive control law. The improved perturbation estimator added in S1.2 selects a low-pass filter. , ； in, This represents the time constant of the low-pass filter; This represents the input of the low-pass filter; By passing function Improvements to be made: ； Improve disturbance suppression performance; The expression for the improved disturbance estimator obtained in S1.2 is as follows: ； in, and They represent and The Laplace transform of; , , Represents a known real matrix with appropriate dimensions. For matrix transpose; For observer gain, For matrix transpose; In step S1.2, an improved repetitive controller is added as follows: Let the reference input be... The period is The transfer function of a basic repetitive controller for: ； in, It is a mathematical constant; This represents the input of the low-pass filter; At base frequency Harmony At this point, the gain of the repetitive controller It is infinite, that is: ； in, This represents the frequency domain input of the repetitive controller; Improved repetitive controller transfer function for: ； in, This represents the time delay constant of the improved repetitive controller. This represents a first-order low-pass filter. ； in, express The cutoff frequency follows the frequency characteristics described below: ； in, express Frequency domain input; Indicates periodic reference input The maximum angular frequency, the cutoff frequency of the filter. satisfy The state-space model of the improved repetitive controller is as follows: ； in, Represents the state variables of the improved repetitive controller; Represents the state variables of the low-pass filter; The time-delay state variables represent the improved repetitive controller; This represents the output of the repetitive controller; This indicates the tracking error.

2. The optimized control method for a permanent magnet brushless DC motor servo system according to claim 1, characterized in that: In S1.1, the equivalent system basic model of the permanent magnet brushless DC motor servo system includes three parts: the controlled object, the observer, and the state feedback.

3. The optimized control method for a permanent magnet brushless DC motor servo system according to claim 1, characterized in that: The improved disturbance estimator treats the impact of external disturbances on the system as an equivalent virtual signal at a control input, i.e. Using a full-dimensional state observer to An estimation is performed, and a low-pass filter is introduced to construct an improved disturbance estimator. The filtered estimated value is then fed back to the control input for compensation.

4. The optimized control method for a permanent magnet brushless DC motor servo system according to claim 1, characterized in that: In S1.3, the system parameters are optimized and controlled based on the particle swarm optimization algorithm.

5. The optimized control method for a permanent magnet brushless DC motor servo system according to claim 4, characterized in that: The steps of the particle swarm optimization algorithm are as follows: The parameters of the improved repetitive controller, observer, and low-pass filter are synchronously optimized using a particle swarm optimization algorithm. During the iteration process, the particle velocity and position update formulas are as follows: ； in, Indicates the first The first particle The speed of each iteration; Indicates the first The first particle The speed of the next iteration Indicates the first The position of each particle, i.e., the solution vector for a set of parameters. Indicates the first The first particle The position of the next iteration. Indicates the first The particle itself is the first The best position found in the next iteration; This represents the best position found so far by the entire particle swarm. The learning factor representing the particle itself; The learning factor represents the entire particle swarm. , Representing an interval Random numbers between; Indicates the first The first particle The position of the next iteration; The inertial weight of a particle, its value increases with the number of iterations. Linearly decreasing; ； in, The maximum number of iterations, and These represent the maximum and minimum inertia weights, respectively.

6. The optimized control method for a permanent magnet brushless DC motor servo system according to claim 5, characterized in that: In the particle swarm optimization algorithm, the objective function is defined as follows: ； in, , and These are the weights corresponding to each item; The number of repetitive control cycles. , They represent the first The first particle The fitness value and system following error corresponding to the next iteration and They represent the first The first particle The state variables and their estimated values ​​for each iteration.

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