Sliding mode based inertia disturbance rejection control method for permanent magnet synchronous motor

Abstract

This invention provides a sliding mode-based anti-inertia disturbance control method for permanent magnet synchronous motors, comprising: constructing a dual-loop control system based on the motor's mechanical motion equations, setting the rotational inertia as an external input to change the rotational inertia during motor operation, thereby determining the relationship between rotational inertia identification and motor speed; introducing a continuous model inertia observer into the control system model to identify the rotational inertia online; designing an integral time-varying fast terminal sliding mode controller and incorporating the rotational inertia identified online by the observer into the sliding mode controller; performing simulations to compare the anti-inertia disturbance performance of different sliding mode controllers; building an experimental platform to adjust the load inertia by disassembling the half-shaft steel sleeve, and observing the improvement of the stability and speed of motor speed by the integral time-varying fast terminal sliding mode controller under different orders of magnitude of inertia change. This invention can identify inertia more accurately, improve the stability of motor speed, and improve the speed performance of motor speed.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet synchronous motor control, specifically relating to a sliding mode-based method for controlling permanent magnet synchronous motors against inertia disturbances. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in many industrial fields due to their advantages such as small size, high efficiency, convenient control, and good speed regulation. However, in actual operation, the moment of inertia of PMSMs often changes. For example, the main disturbance that the PMSM in the base joint of a six-axis industrial robot is subjected to is the slow time-varying effect of its moment of inertia. Similarly, the PMSMs in the spindles of CNC lathes and CNC milling machines are subjected to the time-varying effects of both load torque and moment of inertia. During servo system operation, changes in inertia can cause a mismatch between the motor control parameters set before servo system operation and the controlled object, leading to a decrease in the stability and responsiveness of the servo control system's speed. To maintain a fast and stable response, the servo control system needs to acquire moment of inertia information in real time and adjust the motor control parameters accordingly to adapt to changes in moment of inertia.

[0003] Currently, many researchers have proposed various methods for combating inertia disturbances, mainly categorized into two types: those with and without observers. For those without observers, a PMSM fuzzy self-tuning adaptive integral backstepping control is used to address the inertia disturbance problem; an adaptive non-singular fast terminal sliding mode control method is directly applied to permanent magnet linear synchronous motors; and neural networks are applied to the control system of permanent magnet linear synchronous motors with inertia disturbances. For those with observers, a Landau observer designed based on the Landau discrete-time recursive algorithm tunes the speed loop PI parameters according to the observed current inertia value using a partial model matching design method; a gradient algorithm is used to identify the rotational inertia online, and the speed loop PI parameters are adjusted in real time according to the pole placement principle; a traditional disturbance observer based on a variable gain algorithm, combined with a model reference adaptive algorithm, updates the identified rotational inertia into the improved disturbance observer; and an inertia disturbance observer established using a Kalman filter identifies and compensates for the disturbed inertia.

[0004] However, without an observer, real-time inertial observation is lacking, which cannot meet the system's requirement for high tracking accuracy. Adding an observer, on the other hand, cannot handle the complex parameter changes of a multivariate system with simple PI parameter adjustments, and requires high hardware specifications, making it difficult to implement in engineering. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a sliding mode-based anti-inertia disturbance control method for permanent magnet synchronous motors, which accurately identifies changing inertia, improves the stability of motor speed during inertia changes, and enhances the speed response during inertia changes.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A sliding mode-based control method for permanent magnet synchronous motors to resist inertia disturbances includes the following steps:

[0008] Step 1: Based on the mechanical motion equation of the motor, construct a dual-loop control system, set the moment of inertia as an external input, so that the moment of inertia changes when the motor is running, thereby determining the relationship between the moment of inertia identification and the motor speed;

[0009] Step 2: Introduce a continuous model inertia observer into the control system model to identify the rotational inertia online;

[0010] Step 3: Design an integral time-varying fast terminal sliding mode controller and introduce the rotational inertia identified online by the observer into the sliding mode controller;

[0011] Step 4: Perform simulations to compare the anti-inertia disturbance performance of different sliding mode controllers;

[0012] Step 5: Set up an experimental platform, adjust the load inertia by disassembling the half-shaft steel sleeve, and observe the improvement of the stability and speed of the motor speed by the integral time-varying fast terminal sliding mode controller under different magnitudes of inertia changes.

[0013] Furthermore, in step one, to verify whether the change in moment of inertia will cause fluctuations in the motor speed, the motion equation of the permanent magnet synchronous motor is established in the dq coordinate system as shown in equation (1). After neglecting the damping coefficient, it is simplified to equation (2). The relationship between inertia and speed is obtained from equation (2) as shown in equation (3).

[0014]

[0015]

[0016]

[0017] Among them, T e T is the electromagnetic torque. L ω is the load torque; J is the moment of inertia; B is the damping coefficient; ω m ω is the rotor mechanical angular velocity.

[0018] Furthermore, step two includes: establishing an inertia observer to observe the moment of inertia.

[0019] If the load torque of the motor is set to a constant value, then we have Differentiating equation (2) yields:

[0020]

[0021] Define state variables Control gain b = 1 / J, control quantity Equation (4) can be expressed as:

[0022]

[0023] The adjustable model obtained from equation (5) is as follows:

[0024]

[0025] in, Let z and b be the estimated values;

[0026] Define the state tracking error as The state error equation is then:

[0027]

[0028] in, To track the rate of change of error e, Let z be the rate of change of the state variable;

[0029] Define variable v = D(s)·e, Where D(s) is the linear compensator; s is the differential operator;

[0030] Estimated value of control gain This can be expressed using a proportional-integral adaptive law:

[0031]

[0032] Where v is the defined variable mentioned above, t is the time variable, and τ is the independent variable of integration;

[0033] Substituting equation (8) into equation (7), we get:

[0034]

[0035] In the formula, φ1(v,t,τ) and φ2(v,t) are nonlinear functions of v and t;

[0036] The solutions for φ1(v,t,τ) and φ2(v,t) satisfy the Popov hyperstability theory:

[0037] Combining equation (9), the Popov integral inequality Represented as:

[0038]

[0039] In the formula, η1 is a finite positive number, t1 is the value between the upper and lower limits of the integral in formula (9), η1(0,t1) is the integral term of η(0,t), η2(0,t1) is the proportional term of η(0,t), and η3(0,t1) is the constant term of η(0,t).

[0040] The solutions for φ1(v,t,τ) and φ2(v,t) obtained from equation (10) are:

[0041]

[0042] In the formula, k i ,k p These are the integral coefficient and the proportional coefficient;

[0043] The transfer function H(s) determined by equation (7) is strictly positive real:

[0044]

[0045] Let D(s) = s, then H(s) = 1, which is strictly positive; at this point, we have Therefore, we obtain for:

[0046]

[0047] The inertia identification value is obtained from equation (13):

[0048] Furthermore, step three includes:

[0049] Define the state variables of the permanent magnet synchronous motor system as follows:

[0050]

[0051] Where, ω ref Let ω be the reference mechanical angular velocity of the motor, which is a constant. m Let x1 be the actual mechanical angular velocity, x2 be state variable one, and x3 be state variable two. Let the rate of change of state variable one be denoted as _____.

[0052] According to equations (2) and (14), we get:

[0053]

[0054] Among them, K t The torque constant is T L For the load torque, i qFor q-axis current, P is the rate of change of the q-axis current. n Let ψ be the extreme logarithm. f For permanent magnet flux linkage;

[0055] Define the integral time-varying fast terminal sliding surface s of the system as:

[0056]

[0057] In the formula, c, α, β, ρ, p, q are constants, p, q are positive odd numbers, and c > 0, β > 0, ρ > 0, 1 < p / q < 2, sgn() is a sign function;

[0058] The law of convergence is defined as follows: Where ε,k, For the approach law coefficient and

[0059] The control law of the integral time-varying fast terminal sliding mode controller is calculated as follows:

[0060]

[0061] in, Here, c,α,β,ρ,p,q are the q-axis current observations, c,α,β,ρ,p,q are the sliding mode coefficients of the integral time-varying fast terminal sliding surface, and ε,k, This is the convergence law coefficient.

[0062] Furthermore, the different sliding mode controllers in step four include:

[0063] SMC stands for conventional sliding mode control.

[0064] ISMC stands for Integral Sliding Mode Control.

[0065] ITSMC stands for Integral Time-Variant Sliding Mode Control.

[0066] ITFTSMC is an integral time-varying fast terminal sliding mode control.

[0067] This invention provides a technical solution for reducing the impact of inertia disturbances on motor speed by combining an integral time-varying fast terminal sliding mode controller with a continuous model Landau observer, which has the following beneficial effects:

[0068] 1. Continuous model inertia observers can identify inertia with relatively high accuracy;

[0069] 2. The integral time-varying module can improve the stability of motor speed;

[0070] 3. The fast termination module can improve the speed-up performance of the motor. Attached Figure Description

[0071] Figure 1 This is a waveform diagram showing the change in rotational speed under changes in inertia.

[0072] Figure 2 Inertia identification diagram;

[0073] Figure 3 This is a system control block diagram;

[0074] Figure 4a , Figure 4b , Figure 4c The waveform diagram shows the static velocity response under inertial disturbance. Figure 4a The waveform diagram shows the static low-speed response under inertial disturbance. Figure 4b The waveform diagram shows the static medium-speed response under inertial disturbance. Figure 4c The waveform diagram shows the static high-speed response under inertial disturbance.

[0075] Figure 5a , Figure 5b , Figure 5c The waveform diagram shows the dynamic velocity response under inertial disturbance. Figure 5a The waveform diagram shows the low-speed to medium-speed response under inertial disturbance. Figure 5b The waveform diagram shows the low-speed to high-speed response under inertial disturbance. Figure 5c The waveform diagram shows the response of medium speed to high speed under inertial disturbance. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0077] The sliding mode-based anti-inertia disturbance control method for permanent magnet synchronous motors of the present invention includes the following steps:

[0078] Step 1: To explore the relationship between moment of inertia and motor speed, a dual-loop control system is constructed based on the motor's mechanical motion equations. The moment of inertia is set as an external input, causing the moment of inertia to change during motor operation, thereby determining the relationship between moment of inertia identification and motor speed.

[0079] To verify whether the change in rotational inertia will cause fluctuations in the motor speed, the motion equation of the permanent magnet synchronous motor is established in the dq coordinate system as shown in equation (1). After ignoring the damping coefficient, it can be simplified to equation (2). From equation (2), the relationship between inertia and speed can be obtained as shown in equation (3).

[0080]

[0081]

[0082]

[0083] Among them, T e T is the electromagnetic torque. L ω is the load torque; J is the moment of inertia; B is the damping coefficient; ω m ω is the rotor mechanical angular velocity.

[0084] pass Figure 1 The results, along with the deduction from equation (3), confirm the correctness of the inverse relationship between inertia and the rate of change of rotational speed. Figure 1 The top image is the rotational speed response diagram. Figure 1 The figure below is a diagram of the moment of inertia response.

[0085] Step 2: Introduce a continuous model inertia observer into the control system model to identify the rotational inertia online;

[0086] Establish an inertia observer to monitor the moment of inertia:

[0087] To avoid unnecessary parameter coupling between rotational inertia and load torque during inertia identification, this invention sets the load torque of the motor to a constant value, thus... Differentiating equation (2) yields:

[0088]

[0089] Define state variables Control gain b = 1 / J, control quantity Equation (4) can then be expressed as:

[0090]

[0091] From equation (5), the adjustable model can be obtained as follows:

[0092]

[0093] in, Let z be the estimated value of b.

[0094] Define the state tracking error as The state error equation is then:

[0095]

[0096] in, To track the rate of change of error e, Let z be the rate of change of the state variable z.

[0097] Define the variable v = D(s)·s, Where D(s) is the linear compensator and s is the differential operator.

[0098] Estimated value of control gain This can be expressed using a proportional-integral adaptive law:

[0099]

[0100] Where v is the defined variable mentioned above, t is the time variable, and τ is the integral variable.

[0101] Substituting equation (8) into equation (7), we get:

[0102]

[0103] In the formula, φ1(v,t,τ) and φ2(v,t) are nonlinear functions of v and t.

[0104] To make the system stable, solutions to φ1(v,t,τ) and φ2(v,t) need to be found to satisfy the Popov hyperstability theory.

[0105] Combining equation (9), the Popov integral inequality It can be represented as:

[0106]

[0107] In the formula, η is a finite positive constant, and t1 is the value between the upper and lower limits of the integral in formula (9). η1(0,t1) is the integral term of η(0,t), η2(0,t1) is the proportional term of η(0,t), and η3(0,t1) is the constant term of η(0,t).

[0108] From equation (10), the solutions for φ1(v,t,τ) and φ2(v,t) can be obtained as follows:

[0109]

[0110] In the formula, k i ,k p These are the integral coefficient and the proportional coefficient.

[0111] The transfer function H(s) determined by equation (7) should be strictly positive:

[0112]

[0113] Let D(s) = s, then H(s) = 1, which is strictly positive. At this point, we have... From this we can obtain for:

[0114]

[0115] The inertia identification value can be obtained from equation (13):

[0116] Inertia identification results are as follows Figure 2 As shown.

[0117] Step 3: Design an integral time-varying fast terminal sliding mode controller and introduce the rotational inertia identified online by the observer into the sliding mode controller;

[0118] To improve the dynamic performance of rotational speed when inertia changes, this invention improves the conventional sliding mode controller and designs an integral time-varying fast terminal sliding mode controller.

[0119] Define the state variables of the permanent magnet synchronous motor system as follows:

[0120]

[0121] Where, ω ref The reference mechanical angular velocity of the motor is usually a constant, ω. m Let x1 be the actual mechanical angular velocity, x2 be state variable one, and x3 be state variable two. Let be the rate of change of state variable one. According to equations (2) and (14):

[0122]

[0123] Among them, K t The torque constant is T L For the load torque, i q For q-axis current, P is the rate of change of the q-axis current. n Let ψ be the extreme logarithm. f For permanent magnet flux linkage. Define the integral time-varying fast terminal sliding surface s of the system as:

[0124]

[0125] In the formula, c, α, β, ρ, p, q are constants, p and q are positive odd numbers, and c > 0, β > 0, ρ > 0, 1 < p / q < 2, and sgn() is a sign function.

[0126] The law of convergence is defined as follows: Where ε,k, For the approach law coefficient and

[0127] The control law of the integral time-varying fast terminal sliding mode controller is calculated as follows:

[0128]

[0129] In the formula, Here, c,α,β,ρ,p,q are the q-axis current observations, c,α,β,ρ,p,q are the sliding mode coefficients of the integral time-varying fast terminal sliding surface, and ε,k, This is the convergence law coefficient.

[0130] like Figure 3 As shown in the figure, the identified inertia is introduced into the velocity loop to improve the dynamic performance of the rotational speed. Given the rotational speed, ω m This is the actual rotational speed. This is the inertia identification value. The q-axis current is given a value. T is the given value for the d-axis current. e For electromagnetic torque, K t The torque constant is The q-axis voltage setpoint, The given value for the d-axis voltage, u dc i is the DC bus voltage. q i is the actual value of the q-axis current. d i represents the actual value of the d-axis current. abc It is a three-phase current.

[0131] Step 4: Build a module in Simulink to perform simulations and compare the anti-inertia disturbance performance of different sliding mode controllers.

[0132] SMC stands for conventional sliding mode control, ISMC stands for integral sliding mode control, ITSMC stands for integral time-varying sliding mode control, and ITFTSMC stands for integral time-varying fast terminal sliding mode control.

[0133] like Figure 4a , Figure 4b , Figure 4c As shown, when an inertia disturbance is injected while the rotational speed remains constant, the motor speed will change accordingly. Among them, the sudden change in speed is more obvious under SMC and TSMC than under ITSMC and ITFTSMC, and the anti-interference ability is also worse. The speed fluctuation generated under ITSMC is greater than that under ITFTSMC. Therefore, under the inertia sudden change, ITFTSMC has the best static speed performance and the strongest anti-interference ability.

[0134] like Figure 5a , Figure 5b , Figure 5c As shown, when the motor speed is changing, the speed stability of SMC and TSMC deteriorates significantly when rotational inertia disturbance is injected, while ITFTSMC has higher speed tracking accuracy, faster response time, and stronger resistance to inertia disturbance.

[0135] Step 5: Set up an experimental platform, adjust the load inertia by disassembling the half-shaft steel sleeve, and observe the improvement of the stability and speed of the motor speed by the integral time-varying fast terminal sliding mode controller under different magnitudes of inertia changes.

[0136] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A sliding mode based permanent magnet synchronous motor anti-inertia disturbance control method, characterized in that, Includes the following steps: Step 1: Based on the mechanical motion equations of the electric motor, a dual-loop control system is constructed. The moment of inertia is set as an external input, causing it to change during motor operation, thereby determining the relationship between moment of inertia identification and motor speed. To verify whether changes in moment of inertia cause fluctuations in motor speed, [further steps are taken]. The motion equations of the permanent magnet synchronous motor in the coordinate system are shown in equation (1). After neglecting the damping coefficient, they are simplified to equation (2). The relationship between inertia and rotational speed is obtained from equation (2) as shown in equation (3): （1） （2） （3） in, Electromagnetic torque; This is the load torque; B is the moment of inertia; B is the damping coefficient. This refers to the rotor's mechanical angular velocity; Step 2: Introduce a continuous model inertia observer into the control system model to identify the rotational inertia online, including: establishing an inertia observer to observe the rotational inertia: If the load torque of the motor is set to a constant value, then we have Taking the derivative of equation (2), we get: （4） Define state variables Control gain Control quantity Then equation (4) can be expressed as: （5） The adjustable model obtained from equation (5) is as follows: （6） in, , for The estimated value; Define the state tracking error as Then the state error equation is: （7） in, For tracking error rate of change, State variables The rate of change; Define variables , ,in, For a linear compensator; s is a differential operator; Estimated value of control gain This can be expressed using a proportional-integral adaptive law: （8） in, For time variables, The independent variable is used for integration; Substituting equation (8) into equation (7), we get: （9） In the formula, , for and Nonlinear functions; turn up and The solution satisfies Popov's hyperstability theory: Combining equation (9), Popov integral inequality Represented as: （10） In the formula, For finite positive numbers, The values ​​between the upper and lower limits of integration in formula (9) are... yes The integral term, yes The proportional term, yes The constant term; Obtained from equation (10) and The solution is: （11） In the formula, These are the integral coefficient and the proportional coefficient; The transfer function determined by equation (7) For strict accuracy: （12） Pick Then there is Strictly true; at this time there is Thus we obtain for: （13） The inertia identification value is obtained from equation (13): ; Step 3: Design an integral time-varying fast terminal sliding mode controller and introduce the rotational inertia identified online by the observer into the sliding mode controller; Step 4: Perform simulations to compare the anti-inertia disturbance performance of different sliding mode controllers; Step 5: Set up an experimental platform, adjust the load inertia by disassembling the half-shaft steel sleeve, and observe the improvement of the stability and speed of the motor speed by the integral time-varying fast terminal sliding mode controller under different magnitudes of inertia changes.

2. The method for anti-inertia disturbance control of a permanent magnet synchronous motor based on sliding mode according to claim 1, characterized in that, Step three includes: Define the state variables of the permanent magnet synchronous motor system as follows: （14） in, Let ω be the reference mechanical angular velocity of the motor, which is a constant. This is the actual mechanical angular velocity. Let the state variable be one. Let the state variable be two. Let the rate of change of state variable one be denoted as _____. According to equations (2) and (14), we get: （15） in, The torque constant is , For load torque, For q-axis current, The q-axis current change rate is... For extreme logarithms, For permanent magnet flux linkage; Define the integral time-varying fast terminal sliding surface s of the system as: （16） In the formula, It is a constant. It is a positive odd number, and , , , sgn() is a symbolic function; The law of convergence is defined as follows: ,in For the approach law coefficient and ; The control law of the integral time-varying fast terminal sliding mode controller is calculated as follows: （17） in, These are the q-axis current observations. Let be the sliding coefficient of the time-varying, fast terminal sliding surface. This is the convergence law coefficient.

3. The method for anti-inertia disturbance control of a permanent magnet synchronous motor based on sliding mode according to claim 2, characterized in that, The different sliding mode controllers in step four include: SMC stands for conventional sliding mode control. ISMC stands for Integral Sliding Mode Control. ITSMC stands for Integral Time-Variant Sliding Mode Control. ITFTSMC is an integral time-varying fast terminal sliding mode control.

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