A fast integral terminal sliding mode control method for permanent magnet synchronous motor

Abstract

The application discloses a kind of permanent magnet synchronous motor fast integral terminal sliding mode control method based on new sliding mode approach law, and the problems such as slow dynamic response, large chattering etc. existing in traditional sliding mode control method are improved. Firstly, in order to overcome the problem that integral sliding surface cannot converge in finite time and the singularity of terminal sliding surface, a fast integral terminal sliding surface is proposed;Then, a new sliding mode approach law is proposed, and the new sliding mode approach law is combined with the fast integral terminal sliding surface to design a fast integral terminal sliding mode controller, then, a sliding disturbance observer is designed to observe the motor load torque;Finally, the fast integral terminal sliding mode controller and the sliding disturbance observer are applied to the permanent magnet synchronous motor control system. Compared with the traditional sliding mode control method, the fast integral terminal sliding mode controller designed in the application has the advantages of fast dynamic response, strong robustness, etc., and can effectively improve the performance of the permanent magnet synchronous motor control system.

Description

TECHNICAL FIELD

[0001] The present application relates to the control technology field of permanent magnet synchronous motor, and particularly relates to a permanent magnet synchronous motor fast integral terminal sliding mode control method based on a novel sliding mode reaching law. BACKGROUND

[0002] With the development of modern industrial society, permanent magnet synchronous motor is widely applied to national defense and military industry, aerospace, medical instruments and other fields due to its advantages of high power factor, high torque density, simple structure, reliable operation and the like. In general, the permanent magnet synchronous motor has important research value in the development and application of motors and is the mainstream in the future motor field. At present, the PID controller is still widely applied to the permanent magnet synchronous motor speed regulation system due to its simple realization and high reliability. However, the permanent magnet synchronous motor inevitably has parameter perturbation and the like during operation, and at this time, the traditional PID control is difficult to meet the application requirements of the motor in the high-precision scene. In recent years, many scholars have proposed various modern control theory methods to improve the control performance of the motor, such as sliding mode control, model predictive control, fuzzy control, adaptive control and the like. Among these modern control theory methods, the sliding mode control is considered as one of the most effective methods for improving the control performance of the permanent magnet synchronous motor due to its simple realization and strong robustness, and has attracted attention of many domestic and foreign scholars.

[0003] In the design of the sliding mode controller, the linear sliding surface is usually used, but the linear sliding surface contains the differential quantity of the speed error, which is easy to cause high-frequency chattering of the sliding surface. Therefore, some scholars add the integral quantity of the speed error to the linear sliding surface to obtain the sliding mode controller composed of the integral sliding surface, and when the system reaches the sliding surface, the speed error exponentially approaches to zero with a predetermined time constant. However, in the integral sliding surface, the speed error cannot converge to zero in a finite time, and therefore, some scholars introduce the terminal attractor into the sliding surface to propose a terminal sliding mode control method, which can make the speed error converge to zero in a finite time. However, it can be proved by mathematical derivation that the terminal sliding mode control will have singularity problem when the speed error converges to zero.

[0004] The exponential reaching law is generally used in the sliding mode controller, and in order to accelerate the convergence speed, the coefficient of the exponential reaching law needs to be increased, but at the same time, larger output chattering will be caused. Therefore, it is difficult to balance the convergence speed and weaken the chattering by using the exponential reaching law, and finding a novel sliding mode reaching law can suppress the high-frequency chattering phenomenon of the system and improve the dynamic response of the motor. SUMMARY

[0005] The purpose of this invention is to overcome the shortcomings of existing methods and propose a fast integral terminal sliding mode control method for permanent magnet synchronous motors based on a novel sliding mode approaching law, which improves the dynamic response of the permanent magnet synchronous motor speed control system and suppresses chattering in the motor.

[0006] This invention proposes a sliding mode control method for a permanent magnet synchronous motor speed control system. The method is characterized by being a fast integral terminal sliding mode control method for permanent magnet synchronous motors based on a novel sliding mode reaching law, comprising the following steps:

[0007] Step 1: Sample and calculate the rotor position signal of the permanent magnet synchronous motor using a rotor position sensor to obtain the mechanical angle θ and electrical angle θ of the rotor position. e Rotor mechanical angular velocity ω and rotor electrical angular velocity ω e ;

[0008] Step 2: Use a non-contact Hall current sensor to collect the stator three-phase current i of the permanent magnet synchronous motor in the ABC three-phase stationary coordinate system. A i B and i C The above signal is transformed by Clark to obtain the α-axis current i in the αβ two-phase stationary coordinate system. α and β-axis current i β Then i α and i β The direct-axis current i in the dq coordinate system under synchronous rotor rotation is obtained through Park transformation. d and cross-axis current i q ;

[0009] Step 3: To improve the dynamic response of the control system, a sliding mode disturbance observer is designed to measure the load torque T. L Using the rotor's mechanical angular velocity ω as the object of observation, the sliding mode disturbance observer model can be obtained as follows:

[0010]

[0011] In the formula, J is the moment of inertia, expressed in kg·m. 2 B is the coefficient of friction; ψ f The flux linkage between the permanent magnet and the stator is expressed in Wb; p n It is the extreme logarithm; This is the observed value of the rotor's mechanical angular velocity; γ is the load torque observation value; g is the feedback gain; u is the sliding mode switching signal; γ is the sliding mode gain; s2 is the sliding surface of the sliding mode disturbance observer; represents the estimation error of the rotor's mechanical angular velocity; sgn(·) is the sign function;

[0012] Step four: Based on the novel sliding mode reaching law and the fast integral terminal sliding mode surface, design a fast integral terminal sliding mode controller to give the rotor a given mechanical angular velocity ω. * The difference x1 between the rotor's mechanical angular velocity ω and the load torque observation value obtained in step three is used as the input to the sliding mode controller. The feedforward compensation method is incorporated into the fast integral terminal sliding mode controller to output the quadrature axis reference current.

[0013] The expression for the novel sliding mode reaching law is as follows:

[0014]

[0015]

[0016] In the formula, s is the sliding surface of the fast integral terminal sliding mode controller; ε, k, α, β, η, Δ1, Δ2, m and n are constants, all greater than 0; where Δ2>Δ1; sgn(·) is the sign function;

[0017] The expression for the sliding surface of the fast integral terminal is:

[0018]

[0019] In the formula, c1 and c2 are constants and are greater than 0, q and p are positive odd numbers, and q < p.

[0020] Step 5: Convert the quadrature-axis reference current output by the fast integral terminal sliding mode controller in Step 4. The quadrature-axis current i obtained in step two q The difference is calculated and input into a current controller with proportional-integral regulation characteristics to obtain the quadrature-axis reference voltage. Direct axis reference current Set to 0, and compare it with the direct-axis current i obtained in step two. d The difference is calculated and input into a current controller with proportional-integral regulation characteristics to obtain the direct-axis reference voltage.

[0021] Step six: Convert the quadrature-axis reference voltage obtained in step five using the inverse Park transform. and direct-axis reference voltage The α-axis reference voltage in the αβ two-phase stationary coordinate system is obtained by the inverse Park transform. and β-axis reference voltage

[0022] Step 7: Set the α-axis reference voltage and β-axis reference voltage The space vector pulse width modulation (SVM) algorithm is used to generate space vector pulse width modulation pulses, which are then used to obtain the control signal for the voltage source inverter.

[0023] Step 8: Input the voltage source inverter control signal generated in Step 7 to the corresponding power switching device in the voltage source inverter so that the voltage source inverter can output three-phase stator voltage and apply the three-phase stator voltage to the three-phase stator windings of the permanent magnet synchronous motor, thereby realizing the speed control of the permanent magnet synchronous motor.

[0024] Compared with existing sliding mode control methods, the advantages of this invention are as follows: This invention proposes a fast integral terminal sliding mode control method for permanent magnet synchronous motors based on a novel sliding mode reaching law. First, to overcome the problems of the integral sliding surface not converging in a finite time and the singularity of the terminal sliding surface, a fast integral terminal sliding surface is proposed to accelerate the convergence speed of state variables. Second, to further improve the dynamic response of the permanent magnet synchronous motor control system, a novel sliding mode reaching law is proposed. This novel sliding mode reaching law can improve the sliding mode reaching speed, reducing the output chattering of the sliding mode controller while shortening the response time of the permanent magnet synchronous motor. Combining the novel sliding mode reaching law with the fast integral terminal sliding surface to design a fast integral terminal sliding mode controller gives the system strong robustness and fast dynamic response. Attached Figure Description

[0025] Figure 1 This is a system block diagram of a fast integral terminal sliding mode control method for permanent magnet synchronous motors based on a novel sliding mode approach law;

[0026] Figure 2 This is a structural diagram of a sliding mode perturbation observer. Detailed Implementation

[0027] The embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0028] This embodiment presents a fast integral terminal sliding mode control method for permanent magnet synchronous motors based on a novel sliding mode reaching law, implemented on the hardware foundation of a typical surface-mounted permanent magnet synchronous motor digital control drive system. The most basic hardware includes a permanent magnet synchronous motor, a rotor position sensor, a contactless Hall current sensor, a digital signal processor, a voltage source inverter, and a DC power supply. dc The sliding mode control algorithm is implemented in a digital signal processor. The overall system block diagram of this invention is as follows: Figure 1 As shown. Figure 1In this invention, FITSMC stands for Fast Integral Terminal Sliding Mode Controller, PMSM stands for Permanent Magnet Synchronous Motor, and SVPWM stands for Space Vector Pulse Width Modulation. This invention relies on discrete algorithms and is implemented using a digital signal processor.

[0029] The relationship between the axes in the control system is defined as follows: the axis of the A-phase winding in the ABC three-phase stator coordinate system coincides with the α-axis in the αβ two-phase stationary coordinate system. The rotor position electrical angle θ is defined as the direct axis (d-axis) in the dq synchronous rotating coordinate system oriented by the permanent magnet magnetic field of the permanent magnet rotor coincides with the axis of the A-phase winding. e The starting point.

[0030] First, the rotor position signal of the permanent magnet synchronous motor is sampled and calculated using a rotor position sensor to obtain the mechanical angle θ and electrical angle θ of the rotor position. e Rotor mechanical angular velocity ω and rotor electrical angular velocity ω e ;

[0031] Then, a contactless Hall current sensor was used to measure the three-phase stator current i of the permanent magnet synchronous motor. A i B and i C Measurements are performed on the three-phase stator current i by a digital signal processor. A i B and i C Sampling. Then, the sampled three-phase stator current i... A i B and i C The α-axis current i in the αβ two-phase stationary coordinate system is obtained by Clark transformation. α and β-axis current i β The specific coordinate transformation expression is as follows:

[0032]

[0033] Then, in the α-axis current i in the αββ two-phase stationary coordinate system α and β-axis current i β The direct-axis current i in the dq synchronous rotating coordinate system oriented by the permanent magnet magnetic field of the permanent magnet rotor is obtained by the Park transformation. d and cross-axis current i q The specific coordinate transformation expression is as follows:

[0034]

[0035] The voltage equation, torque equation, and motion equation of a surface-mounted permanent magnet synchronous motor in a synchronous rotating coordinate system are as follows:

[0036]

[0037] In the formula, u d and u q These are the d-axis and q-axis voltages, in V; i d and i q These are the d-axis and q-axis currents, respectively, in amperes (A); L d and L q ψ represents the d-axis and q-axis inductances, respectively, in ohms (H); R is the stator resistance, in ohms (Ω); ψ f The flux linkage between the permanent magnet and the stator is expressed in Wb; T e and T L These are the electromagnetic torque and the load torque, respectively, in N·m; p n ω is the extreme logarithm; e ω and ω are the rotor's electrical angular velocity and mechanical angular velocity, respectively, in rad / s, and ω e =p n ω; J is the moment of inertia, in kg·m 2 B is the coefficient of friction.

[0038] To improve the system's dynamic response, a sliding mode disturbance observer is designed to monitor the load torque T. L The rotor mechanical angular velocity ω is observed, and the rotor mechanical angular velocity ω is compared with the load torque T. L As observer state variables, the observer model is constructed as follows:

[0039]

[0040] In the formula, The observed value of the rotor's mechanical angular velocity; γ is the load torque observation value; g is the feedback gain; u is the sliding mode switching signal; γ is the sliding mode gain; s2 is the sliding surface of the sliding mode disturbance observer; represents the estimation error of the rotor's mechanical angular velocity; sgn(·) is the sign function;

[0041] The sliding mode perturbation observer constructed based on equation (12) is as follows: Figure 2 As shown in the figure, S is the Laplace operator.

[0042] Next, a fast integral terminal sliding surface is constructed. Generally, linear sliding surfaces are used when designing sliding mode controllers, but these contain a small component of the velocity error, which can easily cause high-frequency jitter. By adding the integral of the velocity error to the linear sliding surface, an integral sliding surface is obtained.

[0043]

[0044] In the formula, c is a constant and greater than 0. When the system reaches the integral sliding surface, i.e., s = 0, the derivative of equation (13) can be obtained.

[0045] x1=x 1(0) e -ct (14)

[0046] In the formula, x 1(0) Let x1 be the initial state. Equation (14) indicates that when s = 0, the state variable x1 approaches zero with the time constant 1 / c as the exponent. Therefore, after reaching the sliding surface, the approach speed and dynamic characteristics of the state variable can be determined by selecting the integration constant c in advance.

[0047] However, in the integral sliding surface, the state variable x1 cannot converge in a finite time when s = 0. Therefore, some scholars have introduced a terminal attractor into the sliding surface, proposing a terminal sliding mode control method, whose sliding surface is as follows:

[0048]

[0049] In the formula, c is a constant and greater than 0, q and p are positive odd numbers, and q < p.

[0050] The terminal sliding surface equation (15) differentiated with respect to time t is:

[0051]

[0052] As can be seen from equation (16), since q / p-1 < 0, when x1 = 0, the terminal sliding mode control will have a singularity problem.

[0053] To overcome the problems of the inability of integral sliding surfaces to converge in finite time and the singularity of terminal sliding surfaces, this paper proposes a fast integral terminal sliding surface.

[0054]

[0055] In the formula, c1 and c2 are constants and are greater than 0; q and p are positive odd numbers, and q < p.

[0056] Differentiating equation (17) yields

[0057]

[0058] As can be seen from equation (18), when a fast integral terminal sliding surface is used in the sliding mode controller, the singularity problem can be effectively avoided.

[0059] To ensure global robustness of the system, the initial value of the integral I0 is chosen as...

[0060]

[0061] Thus, when t=0, s=0, meaning the system is moving on the sliding surface from the beginning.

[0062] When s = 0, we have

[0063]

[0064] Differentiating equation (20) yields

[0065]

[0066] By transforming equation (21), we can obtain x1 at t r The system converges to zero in a finite amount of time after reaching the sliding surface, meaning it converges within a finite amount of time.

[0067]

[0068] Next, the characteristics of the new reaching law will be explained. In traditional sliding mode controllers, exponential reaching laws are typically used. The general expression of an exponential reaching law is:

[0069]

[0070] In the formula, ε and k are constants, and both are greater than 0.

[0071] The drawback of the exponential reaching law is that while increasing the coefficients ε and k is necessary to accelerate convergence, it also introduces significant output chattering. Therefore, achieving a balance between convergence speed and chatter reduction is difficult when using the exponential reaching law in sliding mode controllers. To address this issue, this paper proposes a novel sliding mode reaching law that adapts to changes in system state, expressed as follows:

[0072]

[0073]

[0074] In the formula, s is the sliding surface of the fast integral terminal sliding mode controller; ε, k, α, β, η, Δ1, Δ2, m and n are constants, and all are greater than 0; where Δ2 > Δ1.

[0075] From equation (24), we can draw the following conclusion: when |x1| is large, i.e., when the system state is far from the sliding surface s, the coefficients... and k|x1|β The value is relatively large, at which point the system state follows the variable-speed approach term. sgn(s) and the exponentially approaching term k|x1| β Both rates approach the sliding surface s, with the faster approach speed. When |x1| is small, the variable exponential approach term k|x1|... β As s gradually approaches zero, the variable speed term approaches zero. sgn(s) plays a major role. When the sliding surface s approaches zero under the action of the sliding control law, the state variable x1 at time t r The coefficient of the variable-rate-approaching term converges to zero at every moment. The convergence to zero indicates that the novel sliding mode reaching law effectively eliminates chattering in the sliding mode controller output. Furthermore, the presence of f(x1) in the novel sliding mode reaching law can suppress chattering caused by drastic changes in motor speed. However, when the motor speed changes only slightly (i.e., the state variable x1 is small), the coefficient of the speed-changing reaching term... The system can rapidly increase its speed and approach the sliding surface s at a faster rate, thus improving the system's dynamic response. Therefore, the sliding controller designed using the novel sliding surface approach law described above can not only suppress output chattering but also reach the given speed more quickly when the motor experiences sudden load changes.

[0076] Combining the novel sliding mode approach law described in equation (24) with equations (11) and (17), the output of the sliding mode controller can be derived as follows.

[0077]

[0078] Sliding mode control requires a stability condition, meaning the system must remain stable under external disturbances or parameter changes. The Lyapunov function is chosen to prove the stability of the sliding mode controller.

[0079]

[0080] Differentiating V with respect to time, and combining equations (11), (17), and (26), we can obtain...

[0081]

[0082] From equation (28), we can see that Therefore, the sliding mode controller satisfies the Lyapunov stability condition.

[0083] Next, the quadrature-axis reference current in equation (26) is... The quadrature-axis current i obtained after Clark transformation q The difference is calculated, and the difference value is input into a current controller with proportional-integral regulation characteristics to obtain the quadrature-axis reference voltage. Direct axis reference current Set it to 0, and compare it with the direct-axis current i obtained after Clark transformation. d The difference is calculated, and the difference value is input into a current controller with proportional-integral regulation characteristics to obtain the direct-axis reference voltage.

[0084] Next, the obtained quadrature-axis reference voltage and direct-axis reference voltage The α-axis reference voltage in the αβ two-phase stationary coordinate system is obtained by the inverse Park transform. and β-axis reference voltage The specific coordinate transformation expression is as follows:

[0085]

[0086] Then set the α-axis reference voltage and β-axis reference voltage Space vector pulse width modulation (SPWM) pulses are generated using a space vector pulse width modulation (SPWM) algorithm, which in turn yields the control signal for the voltage source inverter. This control signal is then input to the corresponding power switching devices within the voltage source inverter to generate a three-phase stator voltage. This three-phase stator voltage is applied to the three-phase stator windings of the permanent magnet synchronous motor (PMSM), thereby achieving speed control of the PMSM.

[0087] This invention proposes a fast integral terminal sliding mode control method for permanent magnet synchronous motors (PMSMs) based on a novel sliding mode reaching law. Firstly, to overcome the problems of the integral sliding surface not converging in a finite time and the singularity of the terminal sliding surface, a fast integral terminal sliding surface is proposed to accelerate the convergence speed of state variables. Secondly, to further improve the dynamic response of the PMSM control system, a novel sliding mode reaching law is proposed. This novel sliding mode reaching law can increase the sliding mode approach speed, shortening the motor response time while reducing output chattering of the sliding mode controller. The fast integral terminal sliding mode controller is designed by combining the novel sliding mode reaching law with the fast integral terminal sliding surface, giving the system strong robustness and fast dynamic response.

[0088] The above embodiments illustrate and describe the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the above embodiments are merely illustrative. Therefore, any omissions, modifications, equivalent substitutions, or 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 speed control method for a permanent magnet synchronous motor, characterized in that, This method is a fast integral terminal sliding mode control method for permanent magnet synchronous motors based on a novel sliding mode reaching law. The control algorithm is implemented in a digital signal processor, and the specific steps are as follows: Step 1: Sample and calculate the rotor position signal of the permanent magnet synchronous motor using a rotor position sensor to obtain the mechanical angle θ and electrical angle θ of the rotor position. e Rotor mechanical angular velocity ω and rotor electrical angular velocity ω e ; Step 2: Use a non-contact Hall current sensor to collect the stator three-phase current i of the permanent magnet synchronous motor in the ABC three-phase stationary coordinate system. A i B and i C The above signal is transformed by Clark to obtain the α-axis current i in the αβ two-phase stationary coordinate system. α and β-axis current i β Then i α and i β The direct-axis current i in the dq coordinate system under synchronous rotor rotation is obtained through Park transformation. d and cross-axis current i q ; Step 3: To improve the dynamic response of the control system, a sliding mode disturbance observer is designed to measure the load torque T. L Using the rotor's mechanical angular velocity ω as the object of observation, the sliding mode disturbance observer model can be obtained as follows: In the formula, J is the moment of inertia, expressed in kg·m. 2 B is the coefficient of friction; ψ f The flux linkage between the permanent magnet and the stator is expressed in Wb; p n It is the extreme logarithm; This is the observed value of the rotor's mechanical angular velocity; γ is the load torque observation value; g is the feedback gain; u is the sliding mode switching signal; γ is the sliding mode gain; s2 is the sliding surface of the sliding mode disturbance observer; represents the estimation error of the rotor's mechanical angular velocity; sgn(·) is the sign function; Step four: Based on the novel sliding mode reaching law and the fast integral terminal sliding mode surface, design a fast integral terminal sliding mode controller to give the rotor a given mechanical angular velocity ω. * The difference x1 between the rotor's mechanical angular velocity ω and the load torque observation value obtained in step three is used as the input to the sliding mode controller. The feedforward compensation method is incorporated into the fast integral terminal sliding mode controller to output the quadrature axis reference current. The expression for the novel sliding mode reaching law is as follows: In the formula, s is the sliding surface of the fast integral terminal sliding mode controller; ε, k, α, β, η, Δ1, Δ2, m, and n are constants, all greater than 0; where Δ2 > Δ1; sgn(·) is the sign function; The expression for the sliding surface of the fast integral terminal is: In the formula, c1 and c2 are constants and are greater than 0, q and p are positive odd numbers, and q < p; Step 5: Convert the quadrature-axis reference current output by the fast integral terminal sliding mode controller in Step 4. The quadrature-axis current i obtained in step two q The difference is calculated and input into a current controller with proportional-integral regulation characteristics to obtain the quadrature-axis reference voltage. Direct axis reference current Set to 0, and compare it with the direct-axis current i obtained in step two. d The difference is calculated and input into a current controller with proportional-integral regulation characteristics to obtain the direct-axis reference voltage. Step six: Convert the quadrature-axis reference voltage obtained in step five using the inverse Park transform. and direct-axis reference voltage The α-axis reference voltage in the αβ two-phase stationary coordinate system is obtained by the inverse Park transform. and β-axis reference voltage Step 7: Set the α-axis reference voltage and β-axis reference voltage The space vector pulse width modulation (SVM) algorithm is used to generate space vector pulse width modulation pulses, which are then used to obtain the control signal for the voltage source inverter. Step 8: Input the voltage source inverter control signal generated in Step 7 to the corresponding power switching device in the voltage source inverter so that the voltage source inverter can output three-phase stator voltage and apply the three-phase stator voltage to the three-phase stator windings of the permanent magnet synchronous motor, thereby realizing the speed control of the permanent magnet synchronous motor.

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