Permanent magnet synchronous motor sliding mode speed control method

Abstract

The invention discloses a sliding mode speed control method for a permanent magnet synchronous motor, and belongs to the technical field related to control. The method comprises the following steps: establishing a disturbance-containing permanent magnet synchronous motor mathematical model based on a stator voltage equation, an electromagnetic torque equation and a mechanical motion equation of the permanent magnet synchronous motor; designing a non-singular fast integral terminal sliding mode surface to avoid singularity and reduce buffeting phenomena; a variable function gain term and a sliding mode surface power term are introduced on the basis of a traditional exponential reaching law to improve the reaching law; designing a permanent magnet synchronous motor sliding mode speed controller based on the improved reaching law and the sliding mode surface; and designing an improved non-singular fast terminal sliding mode disturbance observer, and introducing the improved reaching law into the non-singular fast terminal sliding mode disturbance observer. According to the technical scheme, the rotating speed control response speed of the permanent magnet synchronous motor is improved, buffeting of the system is restrained, and the robustness of the system is enhanced.

Description

TECHNICAL FIELD

[0002] The present application relates to the control related technical field, and particularly to a permanent magnet synchronous motor sliding mode speed control method. BACKGROUND

[0004] Permanent magnet synchronous motor has high power density, high energy efficiency, high reliability, and is regarded as the core component of high-performance alternating current motor drive system, and has been widely used in electric vehicles, urban rail transit, aerospace, wind power and many other fields.

[0005] With the expansion of its application field, the modern industry has higher and higher requirements for the speed control of permanent magnet synchronous motor. However, permanent magnet synchronous motor is a multivariable, strong coupling nonlinear system, and is very sensitive to parameter perturbation and inevitable external disturbance. The traditional linear control method is difficult to obtain satisfactory speed control performance. In order to improve the performance of permanent magnet synchronous motor drive system, it is necessary to develop an advanced control method to improve the speed control performance of permanent magnet synchronous motor.

[0006] In order to improve the accuracy of speed tracking of permanent magnet synchronous motor, many control methods such as sliding mode control, active disturbance rejection control, fuzzy control, adaptive control, neural network control and model predictive control are applied to the control system of permanent magnet synchronous motor. Among them, neural network control has good dynamic characteristics, but there are too many parameters in neural network control, which cannot select the best parameters to achieve the optimal control effect. Model predictive control can avoid linearization process and improve the control accuracy of the system, but its control effect is easily affected by external disturbance. Adaptive control has strong fault tolerance, but its convergence speed is slow and it is difficult to guarantee the robustness of the control system. Fuzzy control is not dependent on accurate mathematical model and has strong robustness, but it depends more on the experience of predecessors, and it is difficult to realize control under complex nonlinear conditions. Sliding mode control has the advantages of fast response, insensitivity to model parameter changes and strong robustness, and has been widely used in permanent magnet synchronous motor speed regulation system. However, the traditional sliding mode control will inevitably produce chattering phenomenon due to its discontinuous control, which will lead to the decline of the performance of the control system.

[0007] In the actual operation process of permanent magnet synchronous motor, external load disturbance and parameter mismatch will occur, which will affect the speed tracking performance of permanent magnet synchronous motor, and the accurate upper bound of external load disturbance is difficult to obtain. Increasing the gain of the coefficient in the reaching law and the sliding mode surface can enhance the anti-interference ability of the control system, but it will lead to larger chattering phenomenon and reduce the tracking accuracy of the speed.

[0008] At present, there is no effective solution to the above problems. SUMMARY

[0010] This invention addresses the problem of external load disturbances and parameter mismatches affecting the speed tracking performance of permanent magnet synchronous motors (PMSMs) during actual operation. It provides a sliding mode speed control method for PMSMs that uses a disturbance observer to estimate unknown disturbances and feed them forward to the sliding mode speed controller. This effectively enhances the robustness of the PMSM speed control system without exacerbating chattering. It not only improves the system's control accuracy and dynamic performance but also exhibits good robustness and anti-interference capabilities, providing strong support for the widespread application of PMSMs in modern industry.

[0011] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0012] A sliding mode speed control method for a permanent magnet synchronous motor includes the following steps:

[0013] S1. Establish a mathematical model of a permanent magnet synchronous motor with disturbance based on the stator voltage equation, electromagnetic torque equation and mechanical motion equation of the permanent magnet synchronous motor.

[0014] S2. Based on the mathematical model of the permanent magnet synchronous motor, a function design for the non-singular fast integral terminal sliding surface is carried out to avoid singularity and reduce chattering.

[0015] S3. Based on the designed non-singular fast integral terminal sliding surface, a variable function gain term and a sliding surface power term are introduced on the basis of the traditional exponential reaching law to improve the reaching law of the permanent magnet synchronous motor sliding speed controller, avoid singularity and reduce chattering.

[0016] S4. Based on the improved approach law and sliding surface, a sliding control law for the sliding speed controller of permanent magnet synchronous motor is constructed.

[0017] S5. Introduce the improved reaching law into the non-singular fast terminal sliding mode disturbance observer to improve the control law of the non-singular fast terminal sliding mode disturbance observer.

[0018] Furthermore, in step S1, the mathematical model of the permanent magnet synchronous motor with disturbance is as follows:

[0019]

[0020] In the formula, Where ω is the mechanical angular velocity, J is the moment of inertia of the motor, and T is the mechanical angular velocity. L Where B is the load torque, and i is the damping coefficient. q P is the stator current along the q-axis. n Let ψ be the extreme logarithm. fLet be the magnetic flux linkage of the permanent magnet, Δα1, Δα2, and Δα3 be the bounded uncertainties of the corresponding terms, and d(t) be the total disturbance including motor parameter drift, friction, and load torque. and , , All are normal numbers.

[0021] Furthermore, in step S2, the integral term of the speed error is introduced into the sliding surface, and the integral sliding control is combined with the terminal sliding control to obtain the expression for the non-singular fast integral terminal sliding surface as follows:

[0022]

[0023] In the formula, c1 and c2 are positive constants, x0 represents the initial value of x1, q and p are both positive odd numbers, and 0 < x < 0. <q<p。

[0024] Furthermore, in step S3, the expression for the improved reaching law is as follows:

[0025]

[0026]

[0027]

[0028] In the formula, k1 and k2 are positive numbers, 1>α>0, 1>η>0, 1>σ>0, and x1 is the system state variable.

[0029] Furthermore, in step S4, the sliding mode control law of the permanent magnet synchronous motor sliding mode speed controller is:

[0030] .

[0031] Furthermore, in step S5, the mechanical angular velocity ω m With the total system disturbance d(t) as the observed variable, the corresponding system state-space equation is established, and the non-singular fast terminal sliding mode disturbance observer gain l and the sliding mode control law based on the velocity observation error are introduced.

[0032] The error equation of the non-singular fast terminal sliding mode disturbance observer is derived, and the non-singular fast terminal sliding surface is designed. By analyzing the convergence characteristics of the sliding surface, it is proved that the observation error can converge to zero in a finite time. An improved reaching law is introduced into the non-singular fast terminal sliding mode disturbance observer to improve the control law of the non-singular fast terminal sliding mode disturbance observer.

[0033] Furthermore, the equations for the nonsingular fast terminal sliding mode perturbation observer are expressed as follows:

[0034]

[0035] The error dynamic equation of the non-singular fast terminal sliding mode perturbation observer is:

[0036]

[0037] In the formula, , The non-singular fast terminal sliding surface is designed as follows:

[0038]

[0039] In the formula, τ and υ are positive constants, 1 < γ < 2, φ > γ, when the system state reaches the sliding surface:

[0040]

[0041] According to the above formula, the convergence rate of the error can be obtained as:

[0042]

[0043] Assuming time t p From any initial time arrive Integrating both sides of the above equation, we get:

[0044]

[0045] Simplifying the above inequality, we get:

[0046]

[0047] The control law for the non-singular fast terminal sliding mode perturbation observer is:

[0048]

[0049] Feedforward compensation of the estimated values ​​from the non-singular fast terminal sliding mode disturbance observer into the permanent magnet synchronous motor sliding mode speed controller yields the following control law for the sliding mode speed controller:

[0050]

[0051] The observed values ​​of the system disturbance are fed back as known quantities to the control law of the sliding mode speed controller.

[0052] The present invention adopts the above technical solution and has the following advantages compared with the prior art:

[0053] 1. The technical solution of this invention establishes a mathematical model of a permanent magnet synchronous motor with disturbances, designs a non-singular fast integral terminal sliding surface, avoids the singularity problem in traditional sliding mode control, and effectively reduces the chattering phenomenon of the control system.

[0054] 2. Based on the traditional exponential reaching law, the present invention improves the reaching law by introducing a variable function gain term and a sliding surface power term to increase the reaching rate. With the improved reaching law and the non-singular fast integral terminal sliding surface as the core, the design of a sliding speed controller for permanent magnet synchronous motor speed is completed, realizing precise control of motor speed.

[0055] 3. The technical solution of this invention develops and improves the non-singular fast terminal sliding mode disturbance observer, which incorporates the improved reaching law into the observer design to improve the response speed and accuracy of disturbance observation; at the same time, it offsets the impact of system disturbance on control performance through a feedforward compensation mechanism.

[0056] 4. The technical solution of this invention uses Lyapunov's theorem to theoretically prove the stability of the control system. It can improve the speed control response speed of permanent magnet synchronous motor, suppress system chattering, and enhance robustness. It is suitable for industrial control scenarios with high precision and high response speed. Attached Figure Description

[0058] Figure 1 This is a flowchart of the sliding speed control method for a permanent magnet synchronous motor in an embodiment of the present invention;

[0059] Figure 2 This is a block diagram of the control system for the sliding mode speed control method of a permanent magnet synchronous motor in an embodiment of the present invention;

[0060] Figure 3 This is a comparison diagram of different switching functions in embodiments of the present invention;

[0061] Figure 4 This is a graph showing the speed tracking results of different control methods under the same step condition in the embodiments of the present invention;

[0062] Figure 5 This is a graph showing the speed tracking error results of different control methods under the same step condition in the embodiments of the present invention;

[0063] Figure 6 This is a graph showing the speed tracking results of different control methods under load changes in an embodiment of the present invention;

[0064] Figure 7 This is a comparison chart of the observation results of different observers on the disturbance in an embodiment of the present invention. Detailed Implementation

[0066] The present invention will be further described in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined in this application.

[0067] The reaching law and the sliding surface are the core components of sliding mode control in a permanent magnet synchronous motor (PMSM) sliding mode speed controller. Together, they form the design framework of the sliding mode controller. The sliding surface is a function of the system's state variables and is used to define the desired dynamic trajectory. The reaching law controls the dynamic process of the state variables reaching the sliding surface, directly affecting the system's convergence speed and chatter suppression effect. By rationally designing the sliding surface and the reaching law, the PMSM speed controller can achieve fast response and highly robust speed tracking.

[0068] The non-singular fast terminal sliding mode disturbance observer is a high-performance control method combining non-singular terminal sliding mode control and disturbance observation techniques. It is primarily used to address robust control problems in systems with model uncertainties, external disturbances, and parameter perturbations. The control law design of the non-singular fast terminal sliding mode disturbance observer integrates the finite-time convergence characteristics of terminal sliding mode control with the anti-interference capability of the disturbance observer. Its core lies in solving the singularity problem of traditional terminal sliding mode control and achieving real-time disturbance compensation. By designing a non-singular terminal sliding surface to achieve finite-time convergence, and simultaneously utilizing the disturbance observer to estimate and compensate for disturbances in real time, the dynamic performance and anti-interference capability of permanent magnet synchronous motor speed control are improved. Examples are provided below. Figures 1-2 As shown, a sliding mode speed control method for a permanent magnet synchronous motor includes the following steps:

[0069] S1. Establish a mathematical model of a permanent magnet synchronous motor with disturbance based on the stator voltage equation, electromagnetic torque equation and mechanical motion equation of the permanent magnet synchronous motor.

[0070] S2. Based on the mathematical model of the permanent magnet synchronous motor, a function design for the non-singular fast integral terminal sliding surface is carried out to avoid singularity and reduce chattering.

[0071] S3. Based on the designed non-singular fast integral terminal sliding surface, a variable function gain term and a sliding surface power term are introduced on the basis of the traditional exponential reaching law to improve the reaching law of the permanent magnet synchronous motor sliding speed controller, thereby increasing the reaching rate while suppressing chattering.

[0072] S4. Based on the improved approach law and sliding surface, a sliding control law for the sliding speed controller of permanent magnet synchronous motor is constructed.

[0073] S5. The improved approach law is introduced into the non-singular fast terminal sliding mode disturbance observer to improve the control law of the non-singular fast terminal sliding mode disturbance observer and enhance the observer's response speed and observation accuracy.

[0074] In step S1, a mathematical model of the permanent magnet synchronous motor is established, as follows:

[0075] The stator voltage equation of the permanent magnet synchronous motor in the dq rotating coordinate system is:

[0076]

[0077] In the formula, u d u q These are the d-axis and q-axis stator voltages, respectively, i d i q The stator currents L and L are the d-axis and q-axis currents, respectively. d L q The inductances along the d and q axes are respectively, R is the stator resistance, and ω is the inductance along the d and q axes. e Let ψ be the electric angular velocity. f It is the magnetic flux of a permanent magnet.

[0078] The electromagnetic torque equation of a permanent magnet synchronous motor is:

[0079]

[0080] In the formula, T e For electromagnetic torque, P n The number of pole pairs is L. The stator inductance of a surface-mounted permanent magnet synchronous motor satisfies L. d =L q Then the torque equation simplifies to:

[0081]

[0082] The mechanical motion equations of a permanent magnet synchronous motor are:

[0083]

[0084] In the formula, Where ω is the mechanical angular velocity, J is the moment of inertia of the motor, and T is the mechanical angular velocity. L Where is the load torque and B is the damping coefficient.

[0085] If we consider the disturbances during operation, including the effects of motor parameter drift, friction, and load torque, the mathematical model of the permanent magnet synchronous motor with disturbances is as follows:

[0086]

[0087]

[0088]

[0089] In the formula, Δα1, Δα2, and Δα3 are the bounded uncertainties of the corresponding terms, and d(t) is the total disturbance including motor parameter drift, friction, and load torque. and , , All are normal numbers.

[0090] To facilitate the design of the sliding mode speed controller, the state variables of the permanent magnet synchronous motor system are defined as follows:

[0091]

[0092] In the formula, ω ref ω is the reference value for the motor speed. m Given the actual speed feedback value, differentiating equation (8) yields the state equation of the permanent magnet synchronous motor system as follows:

[0093]

[0094] In step S2, the method for establishing the non-singular fast integral terminal sliding surface is as follows:

[0095] Linear sliding surfaces typically contain the derivative of the speed error of the permanent magnet synchronous motor (PMSM), which can easily lead to high-frequency chattering in the sliding mode. To suppress chattering in the PMSM control system, the integral term of the speed error is introduced into the sliding surface, resulting in the integral sliding surface:

[0096]

[0097] In the formula, c1 is a positive constant. When s=0, differentiating the above formula yields:

[0098]

[0099] In the formula, x0 represents the initial value of x1. As can be seen from the above formula, when the system satisfies s=0, the system state variable x1 will converge exponentially, but it will only converge to 0 when t approaches infinity. That is, the system state variable x1 cannot converge to 0 in a finite time.

[0100] To address this issue, integral sliding mode control is combined with terminal sliding mode control that achieves finite-time convergence, resulting in the following non-singular fast integral terminal sliding surface:

[0101]

[0102] In the formula, c2 is a positive constant, q and p are both positive odd numbers, and 0 <q<p。

[0103] When s(t) = 0, the convergence time of the non-singular fast integral terminal sliding surface is:

[0104]

[0105] Based on the sliding surface of the integrating terminal, introduce While shortening the convergence time, it further reduces the steady-state error of the motor speed. The specific expression is as follows:

[0106]

[0107] The initial value of the integral, -x0, ensures that s(t) remains zero. The derivative of the above equation is:

[0108]

[0109] Substituting the above equation into the Lyapunov function From this, we can obtain:

[0110]

[0111] Therefore, the aforementioned non-singular fast integral terminal sliding surface is globally asymptotically stable, combining the advantages of integral sliding and terminal sliding. The introduction of the integral term ensures that the sliding surface of the sliding speed controller does not have singularity problems, improves steady-state accuracy, and the system state variables can converge to zero in a finite time.

[0112] Integrating equation (15) yields the convergence time t of the tracking error. r2 for:

[0113]

[0114] Therefore, it has been theoretically proven that the convergence time of the designed sliding surface is shorter than that of the traditional integral terminal sliding surface. Furthermore, the introduction of the integral term can further reduce the steady-state error.

[0115] In step S3, the process of establishing the improved reaching law is as follows:

[0116] The design of the sliding mode speed controller mainly consists of two parts: the sliding surface and the reaching law. The sliding surface allows the system error to gradually converge. The reaching law ensures that the system state point has good dynamic characteristics during the approach motion process.

[0117] The traditional exponential reaching law (ERL) is expressed as follows:

[0118]

[0119] Integrating (18) from 0 to t yields the approach time t. s for:

[0120]

[0121] In the formula, s(0) is the initial value of the sliding surface. As can be seen from equations (18) and (19), when k1 and k2 increase, the approach rate and robustness of the system increase, but the chattering phenomenon will be aggravated, thus affecting the control accuracy of the system. When the state of the system is close to the sliding surface, the convergence rate of the linear term k2 is almost zero, resulting in insufficient overall convergence rate of the system.

[0122] To ensure good dynamic and static response quality in the speed control system of permanent magnet synchronous motor, this technical solution designs an improved reaching law:

[0123]

[0124]

[0125]

[0126] In the formula, k1 and k2 are positive numbers, 1>α>0, 1>η>0, 1>σ>0, and x1 is the system state variable.

[0127] The improved reaching law mainly consists of two parts: a variable function gain term based on the system state variables and a sliding surface power term. When the system state variables move far away from the sliding surface, that is... At this time, the approach law plays a dominant role. and .at the same time, Therefore, the approach speed is significantly improved. This is because the system state variables approach the sliding surface, i.e. hour, Play a leading role Furthermore, as the system state variables decrease until they reach zero, the chattering phenomenon of the system is effectively reduced. Meanwhile, It overcomes the drawback of the traditional exponential approach law, which is slow when approaching the sliding surface.

[0128] From the above derivation, it can be seen that... along with and The decrease in volume reduces the noise level, thus effectively reducing the chattering phenomenon. This ensures a fast approaching speed at each approaching stage. Compared to the traditional exponential approaching law, the designed improved approaching law has a faster approaching speed and can effectively reduce chattering caused by the fixed gain of the constant velocity term.

[0129] like Figure 3 As shown, the sign function sign(s) in the reaching law is also one of the causes of chattering. Saturation functions such as sat(s / σ) and hyperbolic tangent function tanh(s / σ) are used to reduce chattering. However, these switching functions achieve chattering suppression at the cost of increased convergence time. To simultaneously satisfy the switching speed requirement and reduce chattering, this technical solution proposes an improved nonlinear switching function λ based on power terms and piecewise functions. p The design replaces the traditional sign(s) with (s). The designed switching function can achieve a smooth transition at the 0 point and suppress system chattering.

[0130] In step S4, combining equations (9), (14), and (20-22), the sliding mode control law of the permanent magnet synchronous motor sliding mode speed controller can be expressed as:

[0131]

[0132] Stability analysis:

[0133] Define the Lyapunov function as:

[0134]

[0135] Differentiating with respect to V1, we get:

[0136]

[0137] When |s|≥σ:

[0138]

[0139] When |s|<σ:

[0140]

[0141] From equations (26) and (27), it can be seen that, exist and The time average is less than or equal to zero, which means that the designed non-singular fast integral terminal sliding mode controller is stable and effective.

[0142] In step S5, the process of establishing the improved non-singular fast terminal sliding mode perturbation observer is as follows:

[0143] To further enhance the robustness of the controlled system, a non-singular fast-terminal sliding mode disturbance observer was designed to estimate the system disturbance and feed it forward to the controller. Simultaneously, to improve the observation accuracy and shorten the response time of the non-singular fast-terminal sliding mode disturbance observer, an improved reaching law was introduced. Considering the changes in internal system parameters and external disturbances, the mechanical motion equations of the permanent magnet synchronous motor can be rewritten as:

[0144]

[0145] In a permanent magnet synchronous motor control system, the load torque disturbance changes slowly relative to other system state signals, and the first derivative of the mechanical motion equation is zero.

[0146]

[0147] From equation (29), we can see that the first derivative of the perturbation d(t) is zero:

[0148]

[0149] With mechanical angular velocity ω m With the total system disturbance d(t) as the variable, the state-space equation of the system can be expressed as:

[0150]

[0151] mechanical angular velocity ω m Using the total system disturbance d(t) as the observed value, the equation for the non-singular fast terminal sliding mode disturbance observer is obtained as follows:

[0152]

[0153] In the formula, l is the gain of the non-singular fast terminal sliding mode perturbation observer, and g(ω) m ( ) represents the velocity observation error The corresponding sliding mode control law.

[0154] From equations (31) and (32), the error equation for the perturbation nonsingular fast terminal sliding mode perturbation observer can be obtained as follows:

[0155]

[0156] In the formula, The non-singular fast terminal sliding surface is designed as follows:

[0157]

[0158] In the formula, τ and υ are positive constants 1 < γ < 2, φ > γ, when the system state reaches the sliding surface:

[0159]

[0160] According to the above formula, the convergence rate of the error can be obtained as:

[0161]

[0162] Assuming time t p From any initial time arrive .

[0163] Integrating both sides of the above equation, we get:

[0164]

[0165]

[0166] Simplifying the above inequality yields equation (39), which states that the system state variables can converge to 0 in a finite amount of time.

[0167]

[0168] The improved convergence law designed in this technical solution is selected as follows:

[0169]

[0170] Combining the above formula, As a disturbance term, the control law for the non-singular fast terminal sliding mode disturbance observer is:

[0171]

[0172] In the sliding mode control law g(ω) mUnder the influence of ), the non-singular fast terminal sliding mode disturbance observer can quickly track the given torque, and the system trajectory can reach and remain on the sliding surface within a finite time. From this, we can obtain:

[0173]

[0174] From equation (42), we can obtain:

[0175]

[0176] From equation (43), we can obtain:

[0177]

[0178] In the formula, c is a constant. From the above formula, it can be seen that in order to make the disturbance error e... d For a non-singular fast terminal sliding mode perturbation observer to converge to 0, the gain l must satisfy:

[0179]

[0180] The speed at which the perturbation observation error approaches zero depends directly on the value of l.

[0181] To verify that the designed nonsingular fast terminal sliding mode perturbation observer is stable and effective, a Lyapunov function is used for stability proof.

[0182] Define the Lyapunov function as:

[0183]

[0184] Differentiating with respect to V2, we get:

[0185]

[0186] When |s|≥σ:

[0187]

[0188] When |s|<σ:

[0189]

[0190] Therefore, the non-singular fast terminal sliding mode perturbation observer is stable and effective, where b1 and b2 represent positive constants. By choosing appropriate values ​​for b1 and b2, it can be guaranteed that the observation error of the non-singular fast terminal sliding mode perturbation observer can converge to 0 in a finite time.

[0191] By feeding forward the estimated values ​​from the non-singular fast terminal sliding mode disturbance observer into the permanent magnet synchronous motor sliding mode speed controller, the final control law of the sliding mode speed controller is obtained as follows:

[0192]

[0193] As can be seen from equation (50), the observed value of the system disturbance is fed back to the control law of the sliding mode speed controller as a known quantity. When the system is disturbed, the sliding mode speed controller can suppress the speed fluctuation caused by the disturbance in time, thereby obtaining good anti-disturbance capability without requiring a large gain of the sliding mode speed controller, which weakens the system chattering to a certain extent and enhances the robustness of the permanent magnet synchronous motor control system.

[0194] The control method of this invention (NFITSMC(NRL)) and traditional PI control, with the sliding surface as... The law of convergence is The proposed method is compared with sliding mode control (SMC). Simultaneously, to verify the effectiveness of the improved reaching law (NRL) designed in this invention, it is compared with the traditional exponential reaching law (ERL).

[0195] To ensure fairness in the comparison, the coefficients k1 and k2 in the different reaching laws remained consistent during the parameter tuning process. It is worth noting that the parameters of the aforementioned sliding mode speed controllers were all based on theoretical analysis and underwent multiple rounds of adjustment to ensure that each sliding mode speed controller exhibits a fast response speed and no overshoot under step conditions.

[0196] The parameters of the permanent magnet synchronous motor are as follows: rated voltage 24V, stator resistance 0.13Ω, rated power 400W, rated speed 3000rpm, number of pole pairs 2, and torque constant 6×10⁻⁶. -2 The moment of inertia is 2.8 × 10⁻⁶. -5 kg·m 2 The stator inductance is 1.5 × 10⁻⁶. -5 H, the viscous damping coefficient is 8×10 -4 N·M·S.

[0197] In this embodiment, the control parameters are k1=80, k2=240, c1=0.08, α=0.5, c2=30, q / p=1 / 9, σ=0.5, τ=2500, υ=0.1, b1=200, b2=400. The PI controller parameters are: kp =0.25, k i =0.1, the parameters of SMC are c1=7, k1=80, k2=240.

[0198] Under the step condition with a target speed of 1500 rpm, the experimental results of different control methods are as follows: Figure 4 , Figure 5 As shown, the response time of NFITSMC (NRL) is 65 ms, while the response times of PI, SMC, and NFITSMC (ERL) are 125 ms, 117 ms, and 91 ms, respectively. The mean absolute error of NFITSMC (NRL) is 22.74 rpm, while the mean absolute errors of PI, SMC, and NFITSMC (ERL) are 46.43 rpm, 52.51 rpm, and 33.24 rpm, respectively. These results indicate that the proposed control method has the shortest response time and the smallest mean absolute error. The steady-state root mean square error of NFITSMC (NRL) is 7.65 rpm, while the steady-state root mean square errors of PI, SMC, and NFITSMC (ERL) are 9.98 rpm, 12.92 rpm, and 9.09 rpm, respectively. This indicates that NFITSMC (NRL) has less chattering and higher steady-state control accuracy.

[0199] The steady-state root mean square error (RMSE) of the NFITSMC (ERL) is 9.09 rpm, while that of the SMC is 12.92 rpm. Both the SMC and NFITSMC (ERL) controllers use exponential reaching laws and have identical parameters. This indicates that the non-singular fast integral terminal sliding surface designed in this invention exhibits less chattering compared to a conventional linear sliding surface.

[0200] To verify the robustness of different control methods under external disturbances, a load torque of 0.5 N·m was applied to the motor at 0.4 s and unloaded at 1 s. The results are as follows. Figure 6 As shown, when the motor is subjected to external load disturbance, the speed drop of NFITSMC+NRL is 21.53 rpm, and the recovery time is 13 ms. The speed drops of NFITSMC+ERL, SMC, and PI are 36.67 rpm, 40.89 rpm, and 69.87 rpm, respectively, with recovery times of 19 ms, 51 ms, and 72 ms. Compared to the exponential reaching law, the speed drop and recovery time of NFITSMC+NRL are smaller, indicating that NRL has stronger robustness to external disturbances. NFITSMC+NRL+NFTSMDO further improves the anti-interference performance of the system, reducing the speed drop to 12.32 rpm and the recovery time to 0.76 ms, indicating that the designed observer can achieve real-time observation and compensation of disturbances.

[0201] To verify the observation performance of the improved non-singular fast terminal sliding mode perturbation observer, the non-singular fast terminal sliding mode perturbation observer based on the new reaching law (NFTSMDO-NRL) was compared with the non-singular fast terminal sliding mode perturbation observer based on the exponential reaching law (NFTSMDO-ERL) and the conventional sliding mode perturbation observer (SMDO). The results are as follows: Figure 7 As shown, SMDO reaches the target value within 150ms, NFTSMDO-ERL within 82ms, and NFTSMDO-NRL within 29ms. Furthermore, the chattering phenomenon under steady-state conditions is significantly less than that of the other two observers, indicating that the designed observer has higher observation accuracy and shorter response time.

[0202] The above description provides examples of the preferred embodiments of the present invention. Parts not detailed herein are common knowledge to those skilled in the art. The scope of protection of the present invention is determined by the claims. Any equivalent modifications based on the technical teachings of the present invention are also within the scope of protection of the present invention.

Claims

1. A method of sliding mode speed control for permanent magnet synchronous machines, characterized in that, The method comprises the following steps: S1, a mathematical model of a permanent magnet synchronous motor containing disturbance is established based on a stator voltage equation, an electromagnetic torque equation and a mechanical motion equation of the permanent magnet synchronous motor; S2, function design of a non-singular fast integral terminal sliding mode surface is performed based on the mathematical model of the permanent magnet synchronous motor, so as to avoid singularity and reduce chattering phenomenon; S3, based on the designed non-singular fast integral terminal sliding mode surface, a variable function gain term and a sliding mode surface power term are introduced based on a traditional exponential reaching law, so as to improve the reaching law of the sliding mode speed controller of the permanent magnet synchronous motor, avoid singularity and reduce chattering phenomenon; S4, based on the improved reaching law and the sliding mode surface, a sliding mode control law of the sliding mode speed controller of the permanent magnet synchronous motor is constructed; S5, the improved reaching law is introduced into the non-singular fast terminal sliding mode disturbance observer, so as to improve the control law of the non-singular fast terminal sliding mode disturbance observer.

2. The sliding-mode speed control method of a permanent magnet synchronous motor according to claim 1, characterized by, In step S1, the mathematical model of the permanent magnet synchronous motor containing disturbance is as follows: wherein, is the mechanical angular velocity, J is the moment of inertia of the motor, T L is the load torque, B is the damping coefficient, i q is the stator current of q-axis, P n is the number of pole pairs, ψ f is the flux of permanent magnet, Δα1, Δα2, Δα3 are the uncertain factors of corresponding terms respectively and are bounded, d(t) is the total disturbance including the motor parameter drift, friction and load torque, and , , are all normal numbers.

3. The sliding-mode speed control method of a permanent magnet synchronous motor according to claim 1, characterized by, In step S2, the integral term of the speed error is introduced into the sliding mode surface, integral sliding mode control is combined with terminal sliding mode control, and the expression of the non-singular fast integral terminal sliding mode surface is as follows: In the formula, c1 and c2 are normal numbers, x0 represents the initial value of x1, q and p are both positive odd numbers, and 0 < q < p.

4. The sliding-mode speed control method of a permanent magnet synchronous motor according to claim 1, characterized by, In step S3, the expression of the improved reaching law is as follows: In the formula, k1 and k2 are positive numbers, 1 > α > 0, 1 > η > 0, 1 > σ > 0, and x1 is a system state variable.

5. The sliding-mode speed control method of a permanent magnet synchronous motor according to claim 3 or 4, characterized in that, In step S4, the sliding mode control law of the sliding mode speed controller of the permanent magnet synchronous motor is as follows: 。 6. The sliding-mode speed control method of a permanent magnet synchronous motor according to claim 1, characterized by, In step S5, the mechanical angular velocity ω m With the total disturbance d(t) of the system as the observation variable, the corresponding system state space equation is established, and the non-singular fast terminal sliding mode disturbance observer gain l and the sliding mode control law based on the speed observation error are introduced. The error equation of the non-singular fast terminal sliding mode disturbance observer is derived, the non-singular fast terminal sliding mode surface is designed, the convergence characteristics of the sliding mode surface are analyzed, it is proved that the observation error can converge to zero in a finite time, the improved reaching law is introduced into the non-singular fast terminal sliding mode disturbance observer, and the control law of the non-singular fast terminal sliding mode disturbance observer is improved.

7. The sliding-mode speed control method of a permanent magnet synchronous motor according to claim 6, characterized by, The expression of the equation of the non-singular fast terminal sliding mode disturbance observer is as follows: The error dynamic equation of the non-singular fast terminal sliding mode disturbance observer is as follows: In the formula, , , the nonsingular fast terminal sliding mode surface is designed as In the formula, τ and υ are normal numbers, 1 < γ < 2, and φ > γ. When the system state reaches the sliding mode surface: According to the above formula, the convergence rate of the error is as follows: Assume time t p is from any initial time to ; integrating both sides of the equation gives: The above inequality is simplified as follows: The control law of the non-singular fast terminal sliding mode disturbance observer is as follows: The estimated value of the non-singular fast terminal sliding mode disturbance observer is fed back to the sliding mode speed controller of the permanent magnet synchronous motor, so as to obtain the control law of the sliding mode speed controller, and the observation value of the system disturbance is fed back to the control law of the sliding mode speed controller as a known quantity. ​

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