Surface-mounted permanent magnet synchronous motor double sliding mode sensorless control method

Abstract

This invention discloses a sensorless dual sliding mode control method for surface-mounted permanent magnet synchronous motors, belonging to the field of motor control. The method first constructs a novel sliding mode controller based on a two-phase rotating coordinate system, combining the integral sliding surface with a novel reaching law. Second, based on a mathematical model in a two-phase stationary coordinate system, it constructs a novel sliding mode observer by combining the non-singular terminal sliding surface with a novel switching control function. Finally, it obtains motor speed and rotor position information from the back electromotive force, achieving sensorless control of the motor. The proposed dual sliding mode control strategy omits the low-pass filter, solving the problems of phase delay and chattering in traditional sliding mode observers. It also addresses the issues of poor anti-interference capability and slow dynamic response of PI controllers. During operation, it can quickly and accurately follow the given speed and rotor position, achieving high-precision control of the surface-mounted permanent magnet synchronous motor.

Description

Technical Field

[0001] This invention belongs to the field of surface-mount permanent magnet synchronous motor control technology, specifically relating to a sensorless control method for a surface-mount permanent magnet synchronous motor with dual sliding mode. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) possess advantages such as high efficiency, high power density, and high torque-to-inertia ratio, attracting significant attention in daily life, industry, and transportation. With in-depth research, researchers have proposed various sensorless control methods, gradually replacing the traditional mechanical control methods with position sensors. Among numerous control algorithms, sliding mode control is widely used in PMSM control due to its insensitivity to parameter disturbances and strong robustness.

[0003] The journal *Mechanical Design and Manufacturing*, 2022, Issue 1, pp. 189-192, 197, proposed a sensorless control method for an improved sliding mode observer (PMSM) using a continuous saturation function as the switching function, which reduces system chattering to some extent. However, due to the presence of a low-pass filter, phase delay still exists, leading to inaccurate tracking.

[0004] The journal *Electrical Machines and Control Applications*, September 2018, pp. 9-13, proposes an improved fast terminal sliding mode control (PMSM). This method employs a fast terminal sliding surface, enabling rapid convergence of the system state within a finite time, thus improving system startup performance and disturbance rejection. However, a drawback of this method is that singularities occur when the system state variables reach the equilibrium point, causing rapid changes in the control input.

[0005] In recent years, as control systems have become increasingly complex, proportional integral (PI) controllers are susceptible to external disturbances and system parameters, failing to meet the high-performance requirements of control systems. Sliding mode controllers, due to their strong anti-interference capabilities and high control accuracy, have become an increasingly popular research topic.

[0006] The main problems to be solved in sliding mode control systems include reducing chattering and accelerating dynamic response. A common approach to address these problems is to incorporate the reaching law into the sliding mode control algorithm. While the conventional reaching law can accelerate the system's dynamic response to some extent, it does not significantly reduce chattering. Summary of the Invention

[0007] The technical problem solved by this invention is to address the issues of stability, accuracy, and speed of PMSM speed control systems. It proposes a dual sliding mode sensorless control method for surface-mounted permanent magnet synchronous motors, aiming to solve problems such as poor rotor position and motor speed following, significant chattering, poor robustness, and slow dynamic response during dynamic motor operation.

[0008] This invention is achieved through the following technical solution: a sensorless control method for a surface-mounted permanent magnet synchronous motor with dual sliding mode, comprising the following steps:

[0009] (1) In a two-phase rotating coordinate system, the sliding surface of the novel sliding mode controller is designed as an integral sliding surface. Combined with a novel approaching law, the observation error of the motor mechanical angular velocity x1 is used as the input quantity, and the q-axis current i q As an output, the control law equation of the sliding mode controller is derived, and the stability is proved using the Lyapunov stability criterion.

[0010] (2) In a two-phase stationary coordinate system, the sliding surface of the new sliding mode observer is designed as a non-singular terminal sliding surface. Combined with the fast new switching control function, the motor current observation error x is used as the input and the motor speed and rotor position angle are used as the output. The control law equation of the sliding mode observer is derived, and the stability is proved by using the Lyapunov stability criterion.

[0011] Further, step (1) includes:

[0012] Define the speed error as the system state variable x1, which should satisfy:

[0013] x1=ω ref -ω r

[0014] In the formula: ω ref Given a rotational speed;

[0015] The sliding surface of the sliding mode controller is designed as an integral sliding surface, and its expression is:

[0016]

[0017] The advantage of this sliding surface is that the introduction of an integral term reduces the steady-state error, increases the response speed, and enhances the robustness of the system.

[0018] The approximation law equation is designed as follows:

[0019]

[0020]

[0021] In the formula: l>0; γ>1; h>0;

[0022] The control rate of the sliding mode controller is:

[0023]

[0024] To verify the reachability, stability, and existence of the system, the Lyapunov function needs to be defined as follows:

[0025]

[0026] Differentiating the above equation yields the stability condition:

[0027]

[0028] Substituting the sliding surface and the convergence law, we get:

[0029]

[0030] As can be seen from the above equation, the sliding mode controller satisfies the Lyapunov stability theory, which can make the speed error converge within a finite time.

[0031] Further, step (2) includes:

[0032] Define the current error as the system state variable x, which should satisfy:

[0033]

[0034] In the formula: For the current observed along the α and β axes;

[0035] The sliding surface of the sliding mode observer is designed to be a non-singular terminal sliding surface, expressed as follows:

[0036]

[0037] In the formula: a>0; b>0; m>1; p and q are positive odd numbers, and satisfy q <p<2q;

[0038] The switching function is designed as follows:

[0039] f(s) = -αq(s)sign(s) - βs 3

[0040] In the formula: β>0;

[0041] The sliding control rate of the sliding mode observer is:

[0042]

[0043] Combining the Lyapunov stability condition, we can obtain:

[0044]

[0045] because Therefore It is concluded that the design of the sliding mode observer satisfies the Lyapunov stability theory, which can make the velocity error converge in a finite time.

[0046] Beneficial effects: The dual sliding mode control strategy proposed in this invention solves the problems of phase delay and chattering in traditional sliding mode observers. It adopts a new switching control function to accelerate the convergence speed of state variables and improve the dynamic response of the system. It also solves the problems of poor anti-interference capability and slow dynamic response of PI controllers. During operation, it can quickly and accurately follow the given speed and rotor position, and can achieve high-precision control of surface-mounted permanent magnet synchronous motors. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the overall structure of the dual sliding mode control for the permanent magnet synchronous motor proposed in this invention.

[0048] Figure 2 This is a block diagram of the sliding mode controller structure of the present invention;

[0049] Figure 3 This is a block diagram of the sliding mode observer structure of the present invention;

[0050] Figure 4(a) shows the rotational speed of a traditional sliding mode observer combined with a PI circuit;

[0051] Figure 4(b) shows the rotational speed of the dual sliding mode control proposed in this invention;

[0052] Figure 5(a) shows the rotational speed error of a traditional sliding mode observer combined with a PI circuit;

[0053] Figure 5(b) shows the speed error diagram of the dual sliding mode control proposed in this invention;

[0054] Figure 6(a) shows the rotor position diagram of a traditional sliding mode observer combined with a PI circuit;

[0055] Figure 6(b) is a rotor position diagram of the dual sliding mode control proposed in this invention. Detailed Implementation

[0056] The technical solutions in the embodiments of the present invention will be described in more detail and in greater completeness below. The embodiments described are only partial examples. Users can obtain other embodiments based on the present invention without any creative effort. These "other embodiments" all fall within the scope of protection of the present invention.

[0057] To make the objectives, technical solutions, and advantages of this invention clearer, the specific embodiments of this invention will be further described below in conjunction with the accompanying drawings and examples.

[0058] Example 1

[0059] See the overall structure diagram of the control system of this invention. Figure 1 This is a dual closed-loop control system for speed and current. The speed loop works by sampling the three-phase stator current i from the motor. abc After Clark transformation, the α and β axis current components are obtained. These are then processed by a novel sliding mode observer to obtain the estimated speed and estimated electrical angle. The difference between the given speed and the estimated speed is processed by a novel sliding mode controller to obtain the q-axis current component. The current loop works by sampling the motor to obtain the three-phase stator current i. abc After Clark and Park transformations, the d-axis and q-axis current components are obtained, and i is used. d The vector control strategy with 0 = 0 calculates the difference between the actual d-axis and q-axis current components and the q-axis and d-axis current components output by the sliding mode controller. Then, the d-axis and q-axis voltage components are output by the PI controller. The α-axis and β-axis voltage components, after Park inverse transformation, are used as the input of the voltage space vector SVPWM to output the switching signal for driving the motor, ultimately making the motor run.

[0060] Among them, the novel sliding mode observer and the novel sliding mode controller are technologies disclosed in this invention, while the other parts of the control system are existing technologies.

[0061] The design method based on the novel sliding mode observer and novel sliding mode controller adopts the following steps:

[0062] Step 1, sample the three-phase stator current i abc Voltage u abc A mathematical model of a surface-mounted permanent magnet synchronous motor is established. The mathematical model in a two-phase stationary coordinate system is obtained by Clark transformation, and the mathematical model in a two-phase rotating coordinate system is obtained by Park transformation.

[0063] Step 2: In a two-phase rotating coordinate system, design the sliding surface of the novel sliding mode controller as an integral sliding surface. Combined with a novel reaching law, use the observed error of the motor's mechanical angular velocity x1 as the input quantity, and the q-axis current i q As an output, the control law equation of the sliding mode controller is derived, and the stability is proved using the Lyapunov stability criterion.

[0064] Step 3: In a two-phase stationary coordinate system, design the sliding surface of the novel sliding mode observer as a non-singular terminal sliding surface. Combined with a fast novel switching control function, with the motor current observation error x as the input and the motor speed and rotor position angle as the output, derive the control law equation of the sliding mode observer, and prove its stability using the Lyapunov stability criterion.

[0065] Further, step 1 includes:

[0066] Neglecting the effects of temperature drift, magnetic saturation, hysteresis, eddy current losses, etc., the stator current and voltage in the dq coordinate system of a surface-mounted permanent magnet synchronous motor should satisfy the following:

[0067]

[0068] The equation of motion for the electric motor is:

[0069]

[0070] In the formula: u d u q The stator voltage components along the d and q axes; i d i q R is the stator current component along the d and q axes; L is the armature resistance; L is the inductance; p n ψ is the extreme logarithm; f B is the rotor flux linkage; J is the damping coefficient; T is the moment of inertia; L For load disturbance; ω r It is the mechanical angular velocity;

[0071] The current and voltage of the stator in the α-β coordinate system of a permanent magnet synchronous motor should satisfy the following:

[0072]

[0073] The back electromotive force satisfies:

[0074]

[0075] In the formula: i α i β These are the α-axis and β-axis current components, respectively; u α u β These are the voltage components along the α and β axes, respectively; e α e β These are the back electromotive forces along the α and β axes, respectively; θ is the rotor position angle; ω e It represents the electric angular velocity.

[0076] Further, step 2 includes:

[0077] Define the speed error as the system state variable x1, which should satisfy:

[0078] x1=ω ref -ω r

[0079] In the formula: ω ref Given a rotational speed;

[0080] The sliding surface of the novel sliding mode controller is designed as an integral sliding surface, and its expression is:

[0081]

[0082] The advantage of this sliding surface is that the introduction of the integral term reduces the steady-state error, increases the response speed, and enhances the robustness of the system.

[0083] The approximation law equation is designed as follows:

[0084]

[0085]

[0086] In the formula: l>0; γ>1; h>0;

[0087] The convergence law consists of the isodynamic term -lq(s)sign(s) and the exponential term -hs 3 Combined, when the system state is far from the sliding surface, i.e., |s|>1, the moving point approaches the sliding surface in a double power form, shortening the approach time; when the system state is close to the sliding surface, i.e., |s|≤1, in order to avoid strong chattering and still approach the sliding surface at a relatively fast speed, the constant velocity term plays a major role, so that the system state reaches the equilibrium point stably.

[0088] Finally, combining the sliding surface equation and the reaching law equation, the control rate of the new sliding controller is obtained as follows:

[0089]

[0090] See the block diagram of the new sliding mode controller. Figure 2 ;

[0091] To verify the reachability, stability, and existence of the system, the Lyapunov function needs to be defined as follows:

[0092]

[0093] Differentiating the above equation yields the stability condition:

[0094]

[0095] Substituting the sliding surface and the convergence law, we get:

[0096]

[0097] From the above formula, we can see that Therefore, the sliding mode controller satisfies the Lyapunov stability theory, which can make the speed error converge in a finite time.

[0098] Further, step 3 includes:

[0099] Define the current error as the system state variable x, which should satisfy:

[0100]

[0101] In the formula: are the observed currents of the α and β axes;

[0102] The sliding mode surface of the designed new sliding mode observer is a non-singular terminal sliding mode surface, and the expression is:

[0103]

[0104] In the formula: a > 0; b > 0; m > 1; p and q are positive odd numbers, and q < p < 2q;

[0105] Let s = 0, and the change rate of the system state variable can be expressed as:

[0106]

[0107] The error change rate consists of the linear term -x / b and the non-linear term -(a / b)e m The advantage of this sliding mode surface is that when the state variable is far from the equilibrium point, the non-linear term plays a major role, and the error convergence speed changes exponentially. When the state variable moves near the equilibrium point, the convergence speed is mainly determined by the linear term. Since 1 < p / q < 2, the singularity of the system is avoided.

[0108] Design the switching function as follows:

[0109] f(s) = -αq(s)sign(s) - βs 3

[0110] In the formula: β > 0;

[0111] The sliding mode control rate of the designed new sliding mode observer is:

[0112]

[0113] See the structural block diagram of the new sliding mode observer in Figure 3 ;

[0114] Combined with the Lyapunov stability condition, it can be obtained that:

[0115]

[0116] Since Therefore The designed sliding mode observer satisfies the Lyapunov stability theory and can make the speed error converge within a finite time;

[0117] The designed sliding mode observer satisfies the theory and can make the speed error converge within a finite time;

[0118] The following simulation verification of this embodiment is performed using the Matlab / Simulink platform. The simulation parameters are as follows: the fixed step size ode3 algorithm is used, and the relative error is set to 2×10⁻⁶. -7 The reference speed was set to 1000 r / min, the simulation time was 0.1 s, and a 10 N·m load was suddenly applied at 0.05 s. The motor parameters were set as follows: stator inductance L = 8.5 mH, moment of inertia J = 0.001 kg·m. 2 Stator resistance R = 2.875Ω, permanent magnet flux linkage Ψ f =0.175, extreme pair P n =4; The parameter value in the PI controller is: k p =795, k i =95; In the sliding mode observer, the values ​​of each parameter are: α = 5 × 10 6 β = 1000, a = 0.3, b = 0.3, m = 5 / 3, p = 13, q = 9; In the sliding mode controller, the values ​​of each parameter are: c = 0.8, l = 1500, h = 1500.

[0119] As shown in Figure 4, the traditional sliding mode control algorithm exhibits speed fluctuations between 992 and 1010 r / min, while the dual sliding mode control algorithm shows a significant reduction in fluctuations, effectively controlling speed fluctuations within 0.4 r / min. When the motor has been running for 0.05 s, after applying a 10 N·m load, the dual sliding mode control algorithm recovers the speed to the given value 0.004 s faster than the traditional sliding mode control algorithm.

[0120] As shown in Figure 5, after the motor has been running stably for about 0.01 seconds, the speed tracking error of the traditional sliding mode control algorithm fluctuates between ±10 r / min, while the speed tracking error of the dual sliding mode control algorithm can be well controlled within ±0.15 r / min, resulting in a significant performance improvement.

[0121] As shown in Figure 6, the angle tracking error of the traditional sliding mode control algorithm is about 0.044 rad, while that of the dual sliding mode control algorithm is 0.021 rad, representing an improvement of 0.023 rad in angle error and a performance improvement of 52.3%.

[0122] In summary, this invention proposes a sensorless control method for a surface-mounted permanent magnet synchronous motor with dual sliding mode, which solves problems such as poor rotor position and motor speed following, significant chattering, poor robustness, and slow dynamic response during dynamic motor operation.

[0123] The above description is merely one embodiment of the present invention and is not intended to limit the invention. Those skilled in the art will recognize that the present invention can be modified and varied in various ways. Any 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 sensorless control method for a surface-mounted permanent magnet synchronous motor with dual sliding mode, characterized in that, Includes the following steps: Step 1: In a two-phase rotating coordinate system, design the sliding surface of the novel sliding mode controller as an integral sliding surface. Combined with a novel reaching law, use the observed error of the motor's mechanical angular velocity x1 as the input quantity, and the q-axis current i q As an output, the control law equation of the sliding mode controller is derived, and the stability is proved using the Lyapunov stability criterion. Step 2: In a two-phase stationary coordinate system, the sliding surface of the novel sliding mode observer is designed as a non-singular terminal sliding surface. Combined with a fast novel switching control function, the motor current observation error x is used as the input, and the motor speed and rotor position angle are used as the output. The control law equation of the sliding mode observer is derived, and the stability is proved by using the Lyapunov stability criterion. Step 1 includes: Define the speed error as the system state variable x1, which should satisfy: x1=ω ref -oh r In the formula: ω ref Given the rotational speed; ω r It is the mechanical angular velocity; The sliding surface of the sliding mode controller is designed as an integral sliding surface, and its expression is: In the formula: c = 0.8; The approximation law equation is designed as follows: In the formula: l>0; γ>1; h>0; The control rate of the sliding mode controller is: In the formula: i q p represents the stator current component along the q-axis. n ψ is the extreme logarithm; f B is the rotor flux linkage; J is the damping coefficient; T is the moment of inertia; L For load disturbance; To verify the reachability, stability, and existence of the system, the Lyapunov function needs to be defined as follows: Differentiating the above equation yields the stability condition: As can be seen from the above equation, the sliding mode controller satisfies the Lyapunov stability theory, which can make the speed error converge in a finite time. Step 2 includes: Define the current error as the system state variable x, which should satisfy: In the formula: For the current observed along the α and β axes; The sliding surface of the sliding mode observer is designed to be a non-singular terminal sliding surface, expressed as follows: In the formula: a>0; b>0; m>1; p and q are positive odd numbers, and satisfy q <p<2q; The switching function is designed as follows: f(s)=-αq(s)sign(s)-βs 3 In the formula: L is the stator inductance; β > 0; The sliding control rate of the sliding mode observer is: In the formula: R is the armature resistance; Combining the Lyapunov stability condition, we can obtain: because Therefore The designed sliding mode observer satisfies Lyapunov's stability theory, which can make the velocity error converge in a finite time.

Images