A control method for direct torque speed control of permanent magnet synchronous motor

Abstract

This invention discloses a method for direct torque control of a permanent magnet synchronous motor (PMSM). First, a mathematical model of the PMSM in synchronous rotating coordinates is established, and a PMSM SVM-DTC control system is constructed. Encoders and sensors are used to obtain the motor's speed and electrical signals. Secondly, to address the shortcomings of the PI speed controller, which is prone to overshoot, and the traditional active disturbance rejection controller, which has too many adjustable parameters, an improved active disturbance rejection control method is proposed. Based on the rapidity of the super-twisting sliding mode algorithm, this method incorporates the super-twisting sliding mode (STSM) algorithm into active disturbance rejection control (ADRC), designing a new super-twisting sliding mode active disturbance rejection control (STSM-ADRC) speed controller. Finally, the smooth and continuous hyperbolic tangent function h(s) is used instead of the sign function sgn(s) to reduce chattering in the new speed control method. This method effectively improves the system's responsiveness, reduces the number of adjustable parameters, and enhances the robustness of the PMSM direct torque control speed regulation system.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor control, and in particular relates to a novel speed control method for direct torque control of a permanent magnet synchronous motor. Background Art

[0002] Permanent magnet synchronous motors (PMSMs), a type of AC motor, have attracted significant attention in the field of motor control due to their advantages, including high density, high efficiency, and low losses. With the development of nonlinear control strategies for PMSMs, a variety of control methods have been adopted based on speed regulation systems, such as model reference adaptive control, sliding mode control, and model predictive control. These nonlinear controllers can significantly improve the speed regulation performance of PMSMs, but they suffer from drawbacks such as high computational complexity and reliance on precise mathematical models.

[0003] Active disturbance rejection control is a nonlinear robust control method proposed by Professor Han Jingqing that does not rely on an accurate mathematical model. It has strong adjustment capabilities and anti-disturbance performance, but has the disadvantage of complex parameter adjustment. In order to reduce adjustable parameters, Hui Zhang, Yuyuan Wang et al. proposed a linear active disturbance rejection controller in their 2020 paper "Research on LADRC strategy of PMSMfor road-sensing simulation based on differential evolution algorithm". Although the adjustment parameters are reduced, this method only replaces the fast optimal control synthesis function with a constant, which reduces the speed of the system. In order to simplify parameter tuning, Jian Luo, Wang Lichao et al. adopted an algorithm combining fractional-order PID and active disturbance rejection control in their 2021 paper "Low-speed control of PMSM based on ADRC+FOPID" and designed a fuzzy controller, but the fuzzy rules are difficult to establish.

[0004] Sliding mode control is a nonlinear control strategy that is independent of system parameters and disturbances. Therefore, it is robust and fast, but also associated with some chattering. In their paper "Sliding Mode Control of Permanent Magnet Synchronous Motors Using a Variable Exponential Reaching Law," Mao Liangliang, Zhou Kai, and others employed a novel sliding mode reaching law to reduce system chattering, but at the expense of increased computational complexity. High-order sliding mode extends traditional sliding mode theory by applying discontinuous control variables to high-order derivatives, effectively reducing system chattering. However, the derivative information of the sliding mode variables is difficult to obtain. Superhelical sliding mode is a second-order sliding mode variable structure control scheme developed from the background of high-order sliding mode theory. It retains the chattering suppression advantages of high-order sliding mode while eliminating the need to obtain derivative information of the sliding mode variables. However, superhelical sliding mode control relies more on precise mathematical models than active disturbance rejection control.

[0005] Therefore, in order to reduce the adjustable parameters and improve the response speed of the system, a new speed control method of direct torque control of permanent magnet synchronous motor is proposed. Summary of the Invention

[0006] The PI speed controller used in the direct torque control system of permanent magnet synchronous motor is prone to overshoot and has poor robustness. The traditional active disturbance rejection speed controller has too many parameters. The present invention proposes a new active disturbance rejection speed controller that can achieve zero speed overshoot and fewer adjustable parameters.

[0007] The solution adopted by the present invention to solve the technical problem is: a control method for direct torque control speed of a permanent magnet synchronous motor, comprising the following steps.

[0008] Step 1: During the operation of the permanent magnet synchronous motor, the encoder obtains the motor speed signal ω in real time r , establish the motion equation of permanent magnet synchronous motor

[0009]

[0010] Where, ω m is the mechanical angular velocity; T e , T L is the electromagnetic torque and load torque; P n is the number of pole pairs; J is the actual moment of inertia of the motor; B is the damping viscosity coefficient.

[0011] Step 2: According to the deformation of the permanent magnet synchronous motor motion equation shown in step 1, we can get

[0012]

[0013]

[0014] Where b0 = 1 / J0, J0 represents the moment of inertia in the simulation model; f represents the total disturbance.

[0015] Step 3: Set sliding mode variable s = yy * , then the super-helical sliding mode controller expression is

[0016]

[0017] Where k p , k i It is the parameter to be designed of the super-helical sliding mode controller and is greater than zero. r is the coefficient to be designed, and is generally taken as r=0.5.

[0018] Step 4: Design the super-helical sliding mode tracking differentiator based on the super-helical sliding mode controller expression and define the sliding mode surface function of the velocity error as

[0019] e0=v 11 -v * (5);

[0020] Where e0 represents the error between the given speed signal and its tracking signal, v 11 It is the reference speed signal after arranging the transition process.

[0021] Step 5: Design the super-helical sliding mode nonlinear state error feedback control rate based on the super-helical sliding mode controller expression, and take the control quantity

[0022]

[0023] The sliding surface function of the error is defined as

[0024] e2=z 11 -v 11 (7);

[0025] Where e2 is the speed tracking error signal of the permanent magnet synchronous motor.

[0026] Step 6: Expand the total disturbance in step 2 into a new state to obtain a linear expanded state observer.

[0027] Step 7: Introduce the hyperbolic tangent function to further reduce system chattering.

[0028] Furthermore, the sliding surface function defined in step 4 is derived to obtain The tracking differentiator can be regarded as a single-input single-output system. For a single-input system output system, in order to obtain v11, the uncertain nonlinear terms of the system are ignored, then At the same time, combined with the algorithm shown in step three

[0029] Get the super-helical sliding mode tracking differentiator

[0030]

[0031] Furthermore, step 5 combines the second-order sliding mode control of the super-helical sliding mode algorithm shown in step 3. At the same time, since the second-order differential of V11 is bounded, it is only reflected in the range of the control rate coefficient, so we get

[0032]

[0033] That is, the super-helical sliding mode state error feedback control rate is

[0034]

[0035] Furthermore, the total disturbance f is expanded into a new state, that is, the linear expanded state observer is obtained

[0036]

[0037] Furthermore, in step 7, the hyperbolic tangent function is

[0038]

[0039] Finally, the STSM-ADRC controller is obtained.

[0040] Beneficial effects of the present invention: The control strategy of the present invention reduces six adjustable parameters compared with traditional nonlinear active disturbance rejection control. Simulation results show that the STSM-ADRC control strategy proposed in the present invention improves the robustness of the permanent magnet synchronous motor speed control system, accelerates the response speed of the speed control system, and simplifies the control system compared with LADRC and PI controllers.

[0041] The present invention first establishes a mathematical model of a permanent magnet synchronous motor in synchronous rotating coordinates, constructs a permanent magnet synchronous motor SVM-DTC control system, and uses encoders and sensors to obtain the motor's speed and electrical signals. Secondly, to address the shortcomings of the PI speed controller's easy overshoot and the excessive number of adjustable parameters of the traditional active disturbance rejection controller, an improved active disturbance rejection speed control method is proposed. Based on the rapidity of the super-twisting sliding mode algorithm, the super-twisting sliding mode (STSM) algorithm is introduced into the active disturbance rejection control (ADRC) to design a new super-twisting sliding mode active disturbance rejection control (STSM-ADRC) speed controller. Then, the hyperbolic tangent function h(s) with smooth and continuous characteristics is used instead of the sign function sgn(s) to reduce the chattering of the new speed control method. This method effectively improves the system's responsiveness, reduces the number of adjustable parameters, and improves the robustness of the permanent magnet synchronous motor direct torque control speed regulation system. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a schematic diagram of a control method according to a specific embodiment of the present invention.

[0043] Figure 2 This is a schematic diagram of an active disturbance rejection controller according to a specific embodiment of the present invention.

[0044] Figure 3 This is a comparison curve of the no-load speed response of a specific embodiment of the present invention.

[0045] Figure 4 This is a speed response comparison curve under sudden torque increase according to a specific embodiment of the present invention. DETAILED DESCRIPTION

[0046] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention.

[0047] Example 1: A schematic diagram of a novel speed control method for direct torque control of a permanent magnet synchronous motor is shown in FIG. Figure 1 As shown, the principle diagram of the new active disturbance rejection controller according to the specific embodiment of the present invention is as follows Figure 2 As shown, the following steps are included.

[0048] Step 1: During the operation of the permanent magnet synchronous motor, the encoder obtains the motor speed signal ω in real time r , establish the motion equation of permanent magnet synchronous motor

[0049]

[0050] Where, ω m is the mechanical angular velocity; T e , T L are the electromagnetic torque and load torque; J is the actual moment of inertia of the motor; and B is the damping viscosity coefficient.

[0051] Step 2: According to the deformation of the permanent magnet synchronous motor motion equation shown in step 1, we can get

[0052]

[0053] In the formula b0=1 / J0, J0 represents the moment of inertia in the simulation model; f represents the total disturbance.

[0054] Step 3: The linear differential tracker of the traditional linear active disturbance rejection controller has only one adjustable parameter, but the response speed is slow. The nonlinear active disturbance rejection controller tracking differentiator has three adjustable parameters, while the super-helical sliding mode algorithm has a fast response speed and only two adjustable parameters. Therefore, the super-helical sliding mode algorithm is introduced. First, set the sliding mode variable s = yy* , then the super-helical sliding mode controller expression is

[0055]

[0056] In the formula, u, u * represents the state variable, k p , k i is the design parameter of the super-helical sliding mode controller and is greater than zero, y * represents the reference signal, y represents the tracking signal, and Sign(s) is the sign function.

[0057] Step 4: Design the super-helical sliding mode tracking differentiator based on the super-helical sliding mode controller expression, and define the sliding mode surface function of the velocity error as e0=v 11 -v * .

[0058] Where e0 represents the error between the given speed signal and its tracking signal, v 11 is the reference speed signal after being buffered by the tracking differentiator, v * Represents the reference signal.

[0059] Derivative the sliding surface function defined in step 4 yields The tracking differentiator can be viewed as a single-input single-output system. For a single-input output system, in order to obtain v 11 , ignoring the uncertain nonlinear terms of the system, then At the same time, combined with the algorithm shown in step three

[0060] Get the super-helical sliding mode tracking differentiator

[0061]

[0062] Where k1 and k2 represent control parameters greater than zero.

[0063] Step 6: In order to reduce the control parameters, the super-helical sliding mode nonlinear state error feedback control rate is designed according to the super-helical sliding mode controller expression, and the control quantity is taken as

[0064]

[0065] Where b0 represents the control parameter, u0 is the error feedback control quantity, and z12 represents the total disturbance f.

[0066] The sliding surface function of the error is also defined as

[0067] e2=z 11 -v 11 ,

[0068] Where, e2 is the speed tracking error signal of the permanent magnet synchronous motor, z 11 express Figure 2 The motor speed signal observed by the linear state observer is shown as follows, e 21 represents the derivative of e2.

[0069] Combined with the second-order sliding mode control of the super-helical sliding mode algorithm shown in step 3, and due to v 11 The second-order differential is bounded, which is only reflected in the error feedback control rate parameter K p , K i In the range of , we can therefore obtain (in step 4 The reference signal represents a constant and its derivative is zero. In this step, it can be directly replaced based on the same idea, but the difference is that v 11 (Buffered signal, not constant, but second derivative is bounded))

[0070]

[0071]

[0072] Where u s Represents the state variable, and sets a different subscript to distinguish it from the algorithm shown in step 3

[0073] That is, the super-helical sliding mode state error feedback control rate is

[0074]

[0075] In the formula, the control parameter K p , K i , and the control parameter k in step 3 p 、k i different

[0076] Step 8: The basic idea of the extended state observer is to expand the disturbance that can affect the controlled output into a new state variable. Consider a first-order nonlinear system with disturbances. Transformed into state space equations

[0077]

[0078] Where x is The state variables, u is the input of the system, y is the output of the system

[0079] Expand the total disturbance f to the new state x2, and we get

[0080]

[0081] The observer corresponding to the expanded state equation is

[0082]

[0083] Combined with the motion equation shown in step 2, the linear extended state observer (the motor system output speed signal ω) can be obtained. r , u is the input of the system (Te*))

[0084]

[0085] Where, β 11 , β 12 Indicates control parameters.

[0086] Step 9: Since the sign function sign(s) has a breakpoint at zero, it can cause system chatter to a certain extent. To reduce chatter, the zero point is smoothed. To avoid introducing adjustable parameters, the hyperbolic tangent function is introduced instead of the sign function to further reduce system chatter.

[0087] The hyperbolic tangent function is

[0088]

[0089] Finally, we can get Figure 2 The STSM-ADRC controller shown in this paper reduces six adjustable parameters compared to traditional nonlinear active disturbance rejection control, resulting in better engineering applicability. Simulation results show that the proposed STSM-ADRC control strategy improves the robustness of the permanent magnet synchronous motor speed control system, accelerates the speed control system's response, and simplifies the control system compared to LADRC and PI controllers.

[0090] Example 2: The schematic diagram of another novel speed control method for direct torque control of a permanent magnet synchronous motor is as follows: Figure 1 As shown, the principle diagram of the new active disturbance rejection controller according to the specific embodiment of the present invention is as follows Figure 2 As shown, the following steps are included:

[0091] Step 1: During the operation of the permanent magnet synchronous motor, the encoder obtains the motor speed signal ω in real time r , establish the motion equation of permanent magnet synchronous motor

[0092]

[0093] Where, ω m is the mechanical angular velocity; T e , T L is the electromagnetic torque and load torque, P n is the number of pole pairs; J is the actual moment of inertia of the motor; B is the damping viscosity coefficient.

[0094] Step 2: According to the deformation of the permanent magnet synchronous motor motion equation shown in step 1, we can get

[0095]

[0096] In the formula b0=1 / J0, J0 represents the moment of inertia in the simulation model; f represents the total disturbance.

[0097] Step 3: Set sliding mode variable s = yy * , then the super-helical sliding mode controller expression is

[0098]

[0099] Where k p , k i It is the parameter to be designed of the super-helical sliding mode controller and is greater than zero. r is the coefficient to be designed, and is generally taken as r=0.5.

[0100] Step 4: Design the super-helical sliding mode tracking differentiator based on the super-helical sliding mode controller expression, and define the sliding mode surface function of the velocity error as e0=v 11 -v * .

[0101] Where e0 represents the error between the given speed signal and its tracking signal, v 11 It is the reference speed signal after arranging the transition process.

[0102] Again

[0103] Get the super-helical sliding mode tracking differentiator

[0104]

[0105] Where, v * The second-order differential signal of is bounded to M.

[0106] Step 5: Proof of the stability of the super-helical sliding mode tracking differentiator

[0107] get

[0108]

[0109] Where k3 takes into account the disturbance caused by the second-order differential signal of the reference speed, k2-M≤k3≤k2+M.

[0110] Then the Lyapunov stability criterion is used to prove the stability, and the Lyapunov function is defined as

[0111]

[0112] So the derivative is

[0113]

[0114] According to Lyapunov's stability theorem, when When , there exist constants k1 and k2 greater than zero that make the system stable in a finite time.

[0115] Step 6: Design the super-helical sliding mode nonlinear state error feedback control rate based on the super-helical sliding mode controller expression, and take the control quantity

[0116]

[0117] The sliding surface function of the error is defined as

[0118] e2=z 11 -v 11 ,

[0119] Where e2 is the speed tracking error signal of the permanent magnet synchronous motor.

[0120] The basic principle of second-order sliding mode control using the super-helical sliding mode algorithm is obtained

[0121]

[0122] That is, the super-helical sliding mode state error feedback control rate is

[0123]

[0124] Step 7: Proof of the stability of the super-helical sliding mode nonlinear state error feedback control rate.

[0125] Similarly, the Lyapunov function is defined as

[0126]

[0127] Therefore the derivative is

[0128]

[0129] Therefore, according to Lyapunov's stability theorem, when When K p and K i Make the system stable within a limited time.

[0130] Step 8: The total disturbance is expanded into a new state to obtain the linear expanded state observer

[0131]

[0132] Step 9: Introduce the hyperbolic tangent function instead of the sign function to further reduce system chattering.

[0133] The hyperbolic tangent function is

[0134]

[0135] It should be understood that the above-described specific embodiments of the present invention are merely illustrative of or explanation of the principles of the present invention and are not intended to limit the present invention. Therefore, any modifications, equivalent substitutions, improvements, etc. made without departing from the spirit and scope of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for controlling the speed of a permanent magnet synchronous motor using direct torque control, characterized in that: The following steps are involved: Step 1: During the operation of the permanent magnet synchronous motor, the encoder obtains the motor speed signal ω in real time r , establish the motion equation of permanent magnet synchronous motor Where, ω m is the mechanical angular velocity; T e , T L is the electromagnetic torque and load torque; P n is the number of pole pairs; J is the actual moment of inertia of the motor; B is the damping viscosity coefficient; Step 2: According to the deformation of the permanent magnet synchronous motor motion equation shown in step 1, we can get Where b0 = 1 / J0, J0 represents the moment of inertia in the simulation model; f represents the total disturbance; Step 3: Set sliding mode variable s = yy * , then the super-helical sliding mode controller expression is Where k p ,k i is the parameter to be designed of the super-helical sliding mode controller and is greater than zero, r is the coefficient to be designed, and r=0.5; Step 4: Design the super-helical sliding mode tracking differentiator based on the super-helical sliding mode controller expression and define the sliding mode surface function of the velocity error as e0=v 11 -v * (5); Where e0 represents the error between the given speed signal and its tracking signal, v 11 To arrange the reference speed signal after the transition process; Step 5: Design the super-helical sliding mode nonlinear state error feedback control rate based on the super-helical sliding mode controller expression, and take the control quantity The sliding surface function of the error is defined as e2=z 11 -v 11 (7); Where, e2 is the speed tracking error signal of the permanent magnet synchronous motor; Step 6: Expand the total disturbance in step 2 into a new state to obtain a linear expanded state observer; Step 7: Introduce the hyperbolic tangent function to further reduce system chattering.

2. The control method according to claim 1, characterized in that: Derivative the sliding surface function defined in step 4 yields The tracking differentiator can be regarded as a single-input single-output system. For a single-input system output system, in order to obtain v11, the uncertain nonlinear terms of the system are ignored, then At the same time, combined with the algorithm shown in step three Get the super-helical sliding mode tracking differentiator 3. The control method according to claim 1, wherein: Step 5 combines the second-order sliding mode control of the super-helical sliding mode algorithm shown in step 3. At the same time, since the second-order differential of V11 is bounded, it is only reflected in the range of the control rate coefficient, so we get That is, the super-helical sliding mode state error feedback control rate is 4. The control method according to claim 1, characterized in that: In step 6, the total disturbance f is expanded into a new state, that is, the linear expanded state observer is obtained 5. The control method according to claim 1, characterized in that: In step 7, the hyperbolic tangent function is Finally, the STSM-ADRC controller is obtained.

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