Torque adaptive control method of brushless direct current motor

Abstract

The invention discloses a torque adaptive control method for a brushless direct current motor, and the method designs a global sliding mode factor based on the global sliding mode idea of the brushless direct current motor, thereby achieving the global integral sliding mode speed control. In order to solve the problem that a control system is unstable due to integral saturation caused by a traditional integral sliding mode under the condition that an initial error is relatively large, a global sliding mode factor is designed based on a global sliding mode idea, so that global integral sliding mode speed control is realized. Based on a sliding mode control algorithm and a classic PID control algorithm, a double-closed-loop model structure of a current loop and a speed loop is fused, and a global integral sliding mode control structure is adopted outside the speed loop; and designing and utilizing a load torque observer to estimate the load torque of the motor, and feeding back a sliding mode controller of a speed ring so as to realize real-time compensation of torque disturbance.

Description

(1) Technical Field

[0001] The present invention belongs to the technical field of brushless DC motor control, and particularly relates to a torque adaptive control method for a brushless DC motor. (2) Background Art

[0002] The brushless DC motor system is commonly controlled by the PID algorithm, and the drive circuit uses pulse width modulation (square wave excitation), resulting in problems such as slow response speed, large torque ripple and noise in the brushless DC motor. The use of a position sensing circuit will increase the complexity of the motor structure and may also couple noise interference. The present invention takes the optimal control of the brushless DC motor as the research goal, designs and completes a speed loop sliding mode controller and a load torque observer, and uses space voltage vector modulation technology to drive the motor; in order to solve the problem that traditional integral sliding mode causes integral saturation under the condition of large initial error, resulting in instability of the control system, a global sliding mode factor is designed based on the global sliding mode idea, so as to realize global integral sliding mode speed control.

[0003] Aiming at the problems of slow speed response, low steady-state control accuracy and poor load resistance ability in the brushless DC motor control system, the application of the motor with gradually changing load torque and step load torque is studied, and at the same time, the idea of observing the load change and feeding it back to the control for compensation is continuously optimized and applied to the brushless DC motor control system. A closed-loop control system model of the brushless DC motor is established, and the load torque observer is integrated into the speed outer loop control. Estimate the motor load torque and feed it back to the speed controller to realize real-time compensation of torque disturbance and improve the dynamic response performance and load resistance ability of the system. (3) Summary of the Invention

[0004] The present invention discloses a torque adaptive control method for a brushless DC motor, which solves the problem that traditional integral sliding mode causes integral saturation under the condition of large initial error, resulting in instability of the control system, and designs a global sliding mode factor based on the global sliding mode idea, so as to realize global integral sliding mode speed control.

[0005] The present invention discloses a torque adaptive control method for a brushless DC motor, and the method includes the following steps:

[0006] Step 1, improve the global sliding mode controller;

[0007] Step 2, design a closed-loop system state reconstruction equation according to the improved global sliding mode controller.

[0008] Step 3, the dynamic equation and characteristic equation of the system observation error can be deduced from the closed-loop system state reconstruction equation;

[0009] Step 4. Deduce the relationship between the feedback gain matrix and the poles from the dynamic equation and the characteristic equation of the system observation error.

[0010] The improved global sliding mode controller equation is:

[0011]

[0012] where s is the sliding mode surface; is the reaching law; are state variables, u is the controller expression; ε is the switching function; B m is the damping coefficient; J is the moment of inertia; ω ref is the given electrical angular velocity of the system; β, k 0 , k 1 , a are gain coefficients. The function sigmoid(s) is:

[0013]

[0014] For the brushless DC motor observer, since the load T L is a quantity to be expected to observe, it can be converted into a state variable. And considering that the load change is relatively slow within the control period, there is T L = 0. At the same time, taking the electrical angular velocity ω e as the state estimation variable, defining T L as the system input, and the electrical angular velocity ω e is defined as the system output.

[0015] The matrix form state equation structure of the root state observer is:

[0016]

[0017] where A, B, C are the gain parameters of the root state observer.

[0018] Substituting the matrix form state equation of the root state observer into the brushless DC motor motion equation to analyze the coefficients, we can get:

[0019]

[0020] From the above equations, the closed-loop system state reconstruction equation can be designed as:

[0021]

[0022] where, is the estimated value of the electrical angular velocity ω e ; is the expected observation of the load T L ; l 1 , l 2 is the feedback gain matrix.

[0023] The dynamic equation of the system observation error is obtained according to the closed-loop system state reconstruction equation as follows:

[0024]

[0025] The characteristic equation is obtained as follows:

[0026]

[0027] The relationship between the feedback gain matrix and the poles is as follows:

[0028]

[0029] Where m is the observer coefficient

[0030] The present invention discloses a torque adaptive control method for a brushless DC motor. In a control system with a load torque observer, when the motor system is connected to an unknown load, the observer can well estimate the load torque and feedback it to the speed controller, effectively weakening the influence of load changes on the motor speed and having good robustness. It is verified that the speed regulation effect of the brushless DC motor sliding mode control system based on the load torque observer at no load is shorter in rise time, faster in response speed, and better in control effect than that of the PID control system. When a load disturbance occurs, it has stronger robustness than the PID control system. (IV) BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Structure diagram of the load torque state observer;

[0032] Figure 2 Observation effect diagram of the load observer for the unknown load;

[0033] Figure 3 Comparison diagram of no-load start of three algorithms;

[0034] Figure 4 Observer tracking diagram of system load mutation;

[0035] Figure 5 Anti-disturbance comparison diagram of three algorithms; (V) SPECIFIC IMPLEMENTATION METHOD

[0036] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0037] Because the dynamic surface of traditional sliding mode control contains a differential term, high-frequency noise will be introduced when the control system differentiates the speed. Integral sliding mode variable structure control, on the other hand, avoids the noise introduced by the differential action and can improve the stability of the entire system. Design the integral sliding mode surface:

[0038]

[0039] where k 0 = 0, k 1 = 0 are the proportional coefficient and integral coefficient of the integral sliding mode surface respectively, and the integral term is used to improve the response speed and reduce the steady-state error.

[0040] When the system is on the sliding mode surface, the system enters the sliding mode That is:

[0041]

[0042] Solve to get

[0043] where C 0 is the initial value of the system state variable.

[0044] If the initial state is large itself, the controller may produce inaccurate state feedback, resulting in excessive overshoot and longer adjustment time. To overcome such problems and maintain the performance advantages of integral sliding mode, the global adjustment factor p(f) = e -βt is applied in the integral sliding mode control scheme and the sliding mode surface is designed as a global integral sliding mode surface. This method can balance the side effects introduced by integration and ensure that the system can adjust efficiently and stably to the expected performance level even in the face of large initial errors or high error outputs. Through this strategy, the dynamic response characteristics of the system are optimized, thus achieving a more accurate and reliable control effect. The formula for the global integral sliding mode surface is:

[0045]

[0046] Since the integral sliding mode surface introduces a global forcing factor, the sliding mode is forced into the sliding mode process at the initial state. This can effectively suppress integral saturation and weaken the large overshoot caused by integral saturation. When designing the software program, consider setting λ as λ = -k 0 e(t), and set the state of t. When the motor starts and the change error is large enough, set t to zero so that the global sliding mode acts at all times.

[0047] For the design of the sliding mode controller of the speed loop of a brushless DC motor, take the error of the motor electrical angular velocity as the state variable and the electromagnetic torque T e as the input variable, and there is:

[0048] x = ω ref -ω e

[0049] u = T e

[0050] where ω ref is the given electrical angular velocity of the system, and ω e is the actual electrical angular velocity measured by the motor, and T e is

[0051] The state equation of the brushless DC motor speed control system can be obtained:

[0052]

[0053] The global motion approaching stage of the sliding mode control can be obtained, which is included within the entire control range. Its formula is:

[0054]

[0055] where e(t) is the sliding mode surface error

[0056] Selecting the variable speed approaching rate β = 1, we can obtain:

[0057]

[0058] where ε is the gain of the switching function. If ε is selected too large, it will cause severe chattering in the system; if it is too small, the dynamic response time will increase.

[0059] For the control law design of the global integral sliding mode control, solve the equivalent control term from :

[0060]

[0061] For the control law design of the global integral sliding mode control (GISMC), solve the equivalent control term from and let The control law of the present invention is obtained:

[0062]

[0063] where the continuous function sigmoid(s) is:

[0064]

[0065] Replacing the traditional sign function sgn(s) with the continuous function sigmoid(s) makes the switching smoother and different a values can be selected to obtain a better switching effect, thus reducing chattering.

[0066] According to the Lyapunov stability condition, V(x) = s 2 / 2. From the reachability condition, it can be seen that if the system is stable, then:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] where ε > 0. When the following condition is satisfied , the system can be guaranteed to be stable. The torque adaptive control method for a brushless DC motor is characterized in that: for the observer of the brushless DC motor, since the load T L is a quantity to be expected to be observed, it can be converted into a state variable. And considering that the load change is relatively slow within the control period, there is T L = 0. At the same time, the electrical angular velocity ω e is used as the state estimation variable, the electromagnetic torque T L is defined as the system input, and the electrical angular velocity ω e is defined as the system output.

[0073] The matrix form state equation structure of the root state observer is:

[0074]

[0075] where A, B, and C are the gain coefficients of the root state observer.

[0076] By analyzing the coefficients of the brushless DC motor motion equation and substituting them into the matrix form state equation, we can obtain:

[0077]

[0078] The closed-loop system state reconstruction equation can be designed as:

[0079]

[0080] where, l 1 , l 2 is the feedback gain matrix.

[0081] As shown in Figure 1 , the block diagram of the closed-loop load torque state observer structure is obtained. According to the closed-loop system state reconstruction equation, the dynamic equation of the system observation error can be obtained as:

[0082]

[0083] Therefore, the characteristic equation is obtained as follows:

[0084]

[0085] The relationship between the feedback gain matrix and the poles can be obtained:

[0086]

[0087] where m is the observer coefficient

[0088] Observing the conditions of the feedback gain matrix, when it satisfies l 1 > 0 and l 2 < 0, it can ensure that the real part of the eigenvalues of the state observer closed-loop matrix is negative. This condition is crucial for the asymptotic stability of the load state observer. In engineering practice, the proximity of the poles to the imaginary axis directly affects the convergence speed of the observer. Generally speaking, the closer the poles are to the imaginary axis, the faster the convergence speed of the observer.

[0089] In order to improve the load disturbance resistance ability of the brushless DC motor control system, the present invention focuses on studying the application of the load torque estimation algorithm to the brushless DC motor control system by designing a state observer. The use of a load torque observer to achieve the feedforward control of the load torque increases the load disturbance ability of the system. When the brushless DC motor faces load changes, it can still maintain good control quality.

[0090] In order to reasonably tune the parameters of the load observer, a sine load is selected to observe and simulate the load torque under different values, and the response curve of the load torque state observer is obtained.

[0091] Figure 2 The observation effect diagram of the load observer for the unknown load is shown in the figure. It can be seen from the figure that the state observer can accurately estimate the load change, but there will be a certain response time. In the figure, m is taken as 600, and the response time is about 0.001 s. When m is larger, the following ability of the observer is enhanced, the response speed is faster, and the anti-disturbance ability of the system is stronger. When m is too large, overshoot will occur correspondingly, and when m is too small, the response speed will slow down.

[0092] Figure 3It is a comparison chart of no-load starting for three algorithms. To analyze the dynamic and static responses of the brushless DC motor control system based on the sliding mode algorithm, simulation comparisons are made among PI control, traditional integral sliding mode + load torque observer control, and the global integral sliding mode + load torque observer control proposed in the present invention. The target speed is set at 1500 r / min for no-load starting, and the parameters of all control algorithms are adjusted to the optimal values. The speed response curves of the brushless DC motor control system under the three control methods. At this time, for no-load starting, the influence of the load torque observer on the system can be ignored. When starting with PI control, there is an overshoot of approximately 35 r / min when the motor starts and reaches 1500 r / min, and the motor tends to be stable after 0.08 s. When using traditional integral sliding mode + load torque observer control, the motor response speed is faster than that of PI control, but there is an overshoot of approximately 55 r / min, which is 3.6%, and the motor tends to be stable after 0.04 s. When using global integral sliding mode + load torque observer control, the motor response speed is fast, and the overshoot is small, approximately 12 r / min, which is 0.8%, and the steady-state time is shorter. It can be seen that the speed response of the brushless DC motor control system under the sliding mode control algorithm is fast, and the steady-state time is short.

[0093] Figure 4 It is an observer tracking chart of system load mutation. To analyze the load disturbance rejection ability of the brushless DC motor control system based on the sliding mode algorithm after adding a load torque observer. When the motor reaches a stable state, a load disturbance of 5 N·m is suddenly applied and removed. The observed values of the load torque can observe the load mutation in a timely manner.

[0094] Figure 5 It is a comparison chart of disturbance rejection for three algorithms. The speed is set at 1500 r / min, and a 5 N·m load is suddenly added at t = 0.2 s and suddenly removed at t = 0.4 s. When using PI control, when the load is suddenly added, the speed drops by approximately 97 r / min, and when the load is suddenly removed, the speed increases by approximately 96 r / min. The motor speed tends to be stable after 0.09 s; when using traditional integral sliding mode + load torque observer control, when the load is suddenly added, the speed drops by approximately 42 r / min, and when the load is suddenly removed, the speed increases by approximately 45 r / min. The motor speed tends to be stable after 0.02 s; when using global integral sliding mode + load torque observer control, when the load is suddenly added, the speed drops by approximately 8 r / min, and when the load is suddenly removed, the speed increases by approximately 7 r / min. The motor speed tends to be stable after 0.01 s.

Claims

1. A method for adaptive torque control of a brushless DC motor, characterized in that: The method comprises the following steps: Step 1, improving the global sliding mode controller; Step 2: Design the closed-loop system state reconstruction equation based on the improved global sliding mode controller. Step 3: The dynamic equation and characteristic equation of the system observation error can be derived from the closed-loop system state reconstruction equation; Step 4: Derivation of the relationship between the feedback gain matrix and the poles through the dynamic equation of the system observation error and the characteristic equation.

2. A method for adaptively controlling torque of a brushless DC motor, characterized in that: According to claim 1, the global sliding mode controller is improved as follows: Among them, the function sigmoid(s) is: Where s is the sliding surface, is the approach rate, is the state variable, u is the controller expression; ε is the switching function; B m is the damping coefficient; J is the moment of inertia; ω ref is the given electrical angular velocity of the system; k0, k1, and a are gain coefficients.

3. The method for adaptive torque control of a brushless DC motor according to claim 1, characterized in that: The present invention aims at the brushless DC motor observer due to the load T L is a quantity that is expected to be observed, which can be converted into a state variable. Considering that the load changes relatively slowly during the control cycle, T L = 0. At the same time, the electrical angle ω e As the state estimation variable, define the electromagnetic torque T L is the system input, electrical angular velocity ω e Defined as system output; 3-1, the matrix form state equation structure of the root state observer is: Where A, B, and C are gain coefficients. 3-2, the matrix state equation of the root state observer is substituted into the analytical coefficients of the brushless DC motor motion equation to obtain: 3-3, from the above, the closed-loop system state reconstruction equation can be designed as: Among them, l1, l2 are feedback gain matrices.

4. The method for adaptive torque control of a brushless DC motor according to claim 1, characterized in that: The relationship between the feedback gain matrix and the poles is derived through the dynamic equation of the system observation error and the characteristic equation; 4-1, according to claim 1 and claim 3, the dynamic equation of the system observation error is rewritten as: 4-2, according to claim 1 and claim 3, the improved characteristic equation is: 4-3, the relationship between the feedback gain matrix and the poles can be deduced as follows: Where m is the observer coefficient.

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