Non-inductive permanent magnet synchronous motor control system based on novel predefined time sliding mode algorithm

Abstract

The invention discloses a non-inductive permanent magnet synchronous motor control system based on a novel predefined time sliding mode algorithm, and the system comprises the following steps: (1), building an accurate nonlinear dynamic model of a permanent magnet synchronous motor in consideration of uncertain disturbances such as external load and parameter uncertainty in the actual operation process of the motor; (2) designing a predefined time counter electromotive force observer, and converting to obtain motor position information and rotating speed information; (3) an adaptive predefined time disturbance observer is designed, adaptive parameters are adopted, disturbance upper bound information does not need to be known, and uncertain disturbance of the motor can be rapidly estimated; (4) designing an integral predefined time sliding mode controller to realize convergence of the system in predefined time; and (5) cascading the observer with sliding mode control to form a complete control law, so that the anti-interference performance of the system is improved, and accurate speed control of the permanent magnet synchronous motor under uncertain disturbance is realized. According to the invention, the control system adopts a novel predefined time sliding mode algorithm, the state error of the system can be converged in a set time, the problem of convergence time overestimation is avoided, and the controllability is improved; and a full-continuous smooth function is adopted, so that the buffeting problem of the sliding mode can be effectively inhibited, and the control precision is improved.

Description

Technical Field

[0001] The present invention belongs to the field of sliding mode control of permanent magnet synchronous motors, and in particular relates to a sensorless permanent magnet synchronous motor control method based on a novel predefined time sliding mode algorithm and disturbance compensation. Background Art

[0002] Permanent magnet synchronous motors are widely used in the field of new energy vehicles due to their outstanding advantages such as high efficiency, high power density, high overload capacity, and excellent performance. However, the permanent magnet synchronous motor speed control system requires an electrical sensor to provide basic rotor position information, which may cause sensor failure and control system crash in complex environments. Therefore, in order to improve reliability and reduce costs, sensorless drive is becoming more and more popular.

[0003] There are two widely recognized main methods for sensorless permanent magnet synchronous motor control: high-frequency signal injection method and motor basic voltage equation method. In the case of medium and high speed operation, the motor basic voltage equation method is mainly used to obtain rotor speed and position information from the back electromotive force. In addition, during long-term operation, the performance of the motor will be greatly affected by unknown interference such as parameter perturbation, inaccurate nominal parameters and external load, which brings great challenges to the sensorless control system. Among the many control methods, the sliding mode control algorithm is widely used in the field of motor control due to its advantages such as fast response, high accuracy and strong robustness.

[0004] In recent years, many scholars at home and abroad have conducted research on sliding mode controllers in the field of permanent magnet synchronous motors, including supertorque sliding mode control, fast terminal sliding mode control, fractional order sliding mode control, etc. However, the above finite time sliding mode controllers have the problem that the system convergence time depends on the initial state. Although fixed time sliding mode controllers have been developed, the estimation of their convergence time is usually conservative and has no obvious dependence on adjustable parameters. In order to overcome the shortcomings of existing sliding mode controllers, predefined time sliding mode controllers have begun to develop. The adjustable parameters of the new sliding mode controller directly determine the upper limit of the system's predefined convergence time, avoiding the overestimation of the convergence time, which helps the design of the controller meet our needs. Due to this feature, the predefined time sliding mode algorithm is very suitable for highly complex nonlinear systems such as permanent magnet synchronous motors. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a sensorless permanent magnet synchronous motor control system based on a novel predefined time sliding mode algorithm, comprising:

[0006] The technical solution of the present invention is: a sensorless permanent magnet synchronous motor control system based on a novel predefined time sliding mode algorithm, comprising the following steps:

[0007] Step 1: Considering the uncertain disturbances such as external load and parameter uncertainty during the actual operation of the motor, an accurate nonlinear dynamic model of the permanent magnet synchronous motor is established;

[0008] Step 2: Design a predefined time back-EMF observer to estimate the back-EMF within the predefined time, and obtain the position information and speed information through conversion;

[0009] Step 3: Design an adaptive predefined time disturbance observer to estimate the uncertain disturbance term within the predefined time, and use adaptive parameters without knowing the upper bound of the disturbance;

[0010] Step 4: Design an integral predefined time sliding mode controller to achieve system convergence within a predefined time;

[0011] Step 5: Cascade the observer and the sliding mode control to form a complete control law to achieve accurate speed control of the permanent magnet synchronous motor under uncertain disturbances;

[0012] In step 1, the accurate nonlinear dynamic model of the permanent magnet synchronous motor is:

[0013] Define a general permanent magnet synchronous motor dynamic model:

[0014]

[0015] Surface Mounted Permanent Magnet Synchronous Motor (SPMSM) meets Formula (1) is rewritten as:

[0016]

[0017] Among them, ω r is the mechanical angular velocity, is the magnetic flux, P n is the pole pair number, and is the dq axis stator inductance, is the damping friction coefficient, is the moment of inertia, i q is the q-axis current, T L is the load torque, T e is the electromagnetic torque.

[0018] In actual systems, due to inaccurate measurements, the nominal parameters are always different from the actual parameters, and the motor parameters may change during operation. These situations will cause the established model to be inaccurate, so the model is further optimized for parameter uncertainty:

[0019]

[0020] Where J is the nominal moment of inertia, ψ f is the nominal magnetic flux, B is the nominal damping friction coefficient is the inertia deviation, is the flux deviation, is the damping friction coefficient deviation.

[0021] Simplifying formula (3) we can get:

[0022]

[0023] in, is the desired current on the q axis, and g is the lumped disturbance.

[0024] In step 2, the novel predefined time back EMF observer is designed as follows:

[0025] The stator current equation and back electromotive force equation of SPMSM in the αβ coordinate system are:

[0026]

[0027] Among them, i α ,i β ,u α ,u β is the stator current and voltage in the αβ coordinate system, E α ,E β is the back electromotive force in the αβ coordinate system, θ e is the electrical angle, ω e is the electrical angular velocity.

[0028] Define a sliding surface as:

[0029]

[0030] Define the sig function and tanh function as:

[0031]

[0032] The predefined time back-EMF observer is designed as:

[0033]

[0034] in, is the stator current observed in the αβ coordinate system, is the back electromotive force observed in the αβ coordinate system. 0<δ<1, is a small positive number, a3 is related to the upper limit of the back electromotive force, so T o Determines the convergence time of the back-EMF observer.

[0035] The position and angle information of the permanent magnet synchronous motor can be obtained by using Arctan transformation:

[0036]

[0037] in, is the observed electrical angle, is the observed electrical angular velocity, is the observed mechanical angular velocity.

[0038] In step 3, the novel adaptive predefined time disturbance observer is designed as follows:

[0039] Define a sliding surface as:

[0040]

[0041] The adaptive predefined time disturbance observer can be designed as:

[0042]

[0043] in, is the observed lumped disturbance, is an auxiliary variable, 0<γ<1, is a small positive number, T d Determines the convergence time of the disturbance observer.

[0044] is the adaptive parameter control rate, which is constructed as follows:

[0045]

[0046] Among them, μ is a large positive number, k1=max{2b1 / μ 1-γ / 2 ,2b2 / μ 1+γ / 2}.

[0047] In step 4, the novel integral predefined time sliding mode controller is designed as follows:

[0048] Define a velocity tracking error state variable:

[0049] e=ω r * -ω r (13)

[0050] By taking the derivative of formula (13), we can get:

[0051]

[0052] Define an integral predefined time sliding surface as:

[0053]

[0054] The derivative of formula (15) can be obtained:

[0055]

[0056] Among them, 0<β<1, T c2 Determines the tracking error convergence time.

[0057] The integral sliding mode surface of formula (15) adopts a predefined time sliding mode approach rate:

[0058]

[0059] Where 0<α<1, is a small positive number, d3 is a positive number, T c1 Determines the convergence time of the integral sliding surface.

[0060] Combining equation (17) and equation (16), the speed loop controller expression can be obtained:

[0061]

[0062] The total convergence time of the controller is T c =T c1 +T c2 Considering the separation principle of the controller and the observer, the bandwidth of the observer is generally greater than the bandwidth of the controller. Since the disturbance observer needs to rely on the back-EMF observer data, the bandwidth of the back-EMF observer is greater than the bandwidth of the disturbance observer. So let T o >T d >T c .

[0063] In step 5, the observer and the sliding mode control are cascaded to form a complete control law, specifically: the lumped disturbance and state terms of the original permanent magnet synchronous motor sliding mode controller are replaced by the lumped disturbance and state estimated by the observer, and the system parameter mismatch and external disturbance are observed and compensated by the disturbance observer, thereby further improving the anti-interference ability of the control system. The new speed loop controller expression is:

[0064]

[0065] The present invention has the following beneficial effects:

[0066] The present invention designs a control system for an inductive permanent magnet synchronous motor based on a new type of predefined time sliding mode. First, a predefined time back electromotive force is designed to obtain the precise position and speed information of the motor. Secondly, an adaptive predefined time disturbance observer is designed, which can obtain the uncertain disturbance information during the operation of the motor without knowing the upper bound of the disturbance. Subsequently, an integral predefined sliding mode controller is designed to further improve the control accuracy. Finally, the controller and observer are cascaded to realize disturbance compensation of inductive control and improve the robustness and anti-interference ability of the control system. The new control system adopts a fully continuous smooth function, which can effectively suppress the sliding mode jitter problem. For the speed control of the inductive permanent magnet synchronous motor, the control method provided in this article can ensure that the permanent magnet synchronous motor can complete precise speed control even in the presence of certain uncertain disturbances during long-term operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 This is a framework diagram of the control system of the inductive permanent magnet synchronous motor of the present invention;

[0068] Figure 2 It is the nominal parameter diagram of SPMSM in MATLAB / Simulink simulation model;

[0069] Figure 3 The estimated effect diagram of the observer speed, where (a) is the CSMO speed estimation curve, (b) is the STO speed estimation curve, and (c) is the PTO speed estimation curve;

[0070] Figure 4 This is the estimated effect diagram of the observer's back electromotive force;

[0071] Figure 5 The estimated effect diagram of the disturbance observer load, where (a) is the step load estimation curve, (b) is the time-varying load estimation curve, and (c) is the high-frequency load estimation curve;

[0072] Figure 6 It is the estimated effect diagram of the uncertainty of disturbance observer parameters;

[0073] Figure 7 The speed response diagram of the controller under no-load condition, where (a) is the speed response curve of the three controllers, (b) is the speed response error curve of the three controllers, and (c) is the q-axis current curve of the three controllers;

[0074] Figure 8 The speed response diagram of the controller under load, where (a) is the speed response curve of the three controllers, (b) is the enlarged diagram of the speed response curve of the three controllers, and (c) is the q-axis current curve of the three controllers;

[0075] Fig. 9The speed response diagrams of IPTSMC and IPTSMC+APTDO under external loads, where (a) is the speed response curve under step load, (b) is the speed response curve under time-varying load, and (c) is the speed response curve under high-frequency load;

[0076] Fig.10 Speed ​​response curves of IPTSMC and IPTSMC+APTDO under parameter uncertainty. DETAILED DESCRIPTION

[0077] In order to make the purpose and technical solution of the present invention more specific, the present invention will be described in detail below in conjunction with the accompanying drawings and embodiments. The specific embodiments described here are only used to explain the present invention and cannot be understood as limiting the present invention.

[0078] Reference Figure 1 As shown in the figure, the framework diagram of the inductive permanent magnet synchronous motor system used in the present invention, the inductive permanent magnet synchronous motor control method based on the novel predefined time sliding mode algorithm proposed in this embodiment adopts the following steps:

[0079] Step 1: Establish an accurate nonlinear dynamic model of the permanent magnet synchronous motor.

[0080] Define a general permanent magnet synchronous motor dynamic model:

[0081]

[0082] Surface Mounted Permanent Magnet Synchronous Motor (SPMSM) meets Formula (20) is rewritten as:

[0083]

[0084] Among them, ω r is the mechanical angular velocity, is the magnetic flux, P n is the pole pair number, and is the dq axis stator inductance, is the damping friction coefficient, is the moment of inertia, i q is the q-axis current, T L is the load torque, T e is the electromagnetic torque.

[0085] In actual systems, due to inaccurate measurements, the nominal parameters are always different from the actual parameters, and the motor parameters may change during operation. These situations will cause the established model to be inaccurate, so the model is further optimized for parameter uncertainty:

[0086]

[0087] Where J is the nominal moment of inertia, ψ f is the nominal magnetic flux, B is the nominal damping friction coefficient is the inertia deviation, is the flux deviation, is the damping friction coefficient deviation.

[0088] Simplifying formula (22) we can get:

[0089]

[0090] in, is the desired current on the q axis, and g is the lumped disturbance.

[0091] Step 2, design a predefined time back EMF observer.

[0092] The stator current equation and back electromotive force equation of SPMSM in the αβ coordinate system are:

[0093]

[0094] Among them, i α ,i β ,u α ,u β is the stator current and voltage in the αβ coordinate system, E α ,E β is the back electromotive force in the αβ coordinate system, θ e is the electrical angle, ω e is the electrical angular velocity.

[0095] Define a sliding surface as:

[0096]

[0097] Define the sig function and tanh function as:

[0098]

[0099] The predefined time back-EMF observer is designed as:

[0100]

[0101] in, is the stator current observed in the αβ coordinate system, is the back electromotive force observed in the αβ coordinate system. 0<δ<1, is a small positive number, a3 is related to the upper limit of the back electromotive force, so T oDetermines the convergence time of the back-EMF observer.

[0102] The position and angle information of the permanent magnet synchronous motor can be obtained by using Arctan transformation:

[0103]

[0104] in, is the observed electrical angle, is the observed electrical angular velocity, is the observed mechanical angular velocity.

[0105] Step 3: Design an adaptive predefined time disturbance observer.

[0106] Define a sliding surface as:

[0107]

[0108] The adaptive predefined time disturbance observer can be designed as:

[0109]

[0110] in, is the observed lumped disturbance, is an auxiliary variable, 0<γ<1, is a small positive number, T d Determines the convergence time of the disturbance observer.

[0111] is the adaptive parameter control rate, which is constructed as follows:

[0112]

[0113] Among them, μ is a large positive number, k1=max{2b1 / μ 1-γ / 2 ,2b2 / μ 1+γ / 2}.

[0114] Step 4: Design an integral predefined time sliding mode controller.

[0115] Define a velocity tracking error state variable:

[0116] e=ω r * -ω r (32)

[0117] By taking the derivative of formula (32), we can get:

[0118]

[0119] Define an integral predefined time sliding surface as:

[0120]

[0121] The derivative of formula (34) can be obtained:

[0122]

[0123] Among them, 0<β<1, T c2 Determines the tracking error convergence time.

[0124] The predefined time sliding mode approach rate is adopted for the integral sliding mode surface of equation (34).

[0125]

[0126] Where 0<α<1, is a small positive number, d3 is a positive number, T c1 Determines the convergence time of the integral sliding surface.

[0127] Combining equation (36) and equation (35), the speed loop controller expression can be obtained:

[0128]

[0129] Step 5: Cascade the observer and the sliding mode control to form a complete control law. The new speed loop controller expression is:

[0130]

[0131] Simulation results verification:

[0132] The sensorless permanent magnet synchronous motor control system based on the predefined sliding mode algorithm proposed in this invention is effectively verified through the MATLAB / Simulink simulation platform. Three comparative experiments are carried out: (1) the newly proposed predefined time back electromotive force observer (PTO) is compared with the traditional sliding mode observer (CSMO) and the super torque sliding mode observer (STO); (2) the disturbance observation effect of the newly proposed adaptive predefined time disturbance observer (APTDO) for three external loads f1(t)-f3(t) and parameter uncertainty f4(t); (3) the speed tracking effect of the newly proposed integral predefined time sliding mode controller (IPTSMC) is compared with the non-singular fast terminal sliding mode controller (NFTSMC) and the fast integral terminal sliding mode controller (FITSMC).

[0133] The nominal parameters of the SPMSM in the simulation model are as follows: Figure 2 shown.

[0134] The f1(t)-f4(t) perturbation is designed as follows:

[0135]

[0136] f4(t): At 0.1s, the moment of inertia changes from 0.003kg·m 2 becomes 0.0028kg·m 2 ; At 0.2s, the viscous friction coefficient changes from 0.008N·m·s·s to 0.001N·m·s; at 0.3s, the qd-axis inductance changes from 0.175mH to 0.2mH; at 0.4s, the electronic resistance changes from 2.875Ω to 3Ω.

[0137] Among them, f1(t)-f3(t) are used to simulate step load, time-varying load and high-frequency load respectively. The step load uses the differentiator (TD) function to prevent sudden large jumps, which is closer to actual application. The time-varying load is a linear combination of two sine waves with different amplitudes and phases. The high-frequency load is Gaussian white noise, with a power coefficient of 0.0001 and a frequency coefficient of 0.0004.

[0138] Figure 3 (ac) is a comparison of the speed observation effects of the PTO proposed by the present invention, CSMO and STO under a given step reference speed of 0-3s, Figure 3 (d) is the comparison of observation error effects. Figure 4 The comparison of the back electromotive force observation effect from 0 to 0.3s. Analysis Figure 3 , CSMO exhibits the most significant jitter due to its continuous gain and the phase delay caused by the introduction of the filter. STO has a better estimated speed but still exhibits high frequency jitter. PTO exhibits the best estimation accuracy and steady-state performance across the entire speed range from low to high. Analysis Figure 4 , the PTO exhibits minimal phase delay and jitter in back-EMF observation.

[0139] Figure 5 (ac) and Figure 6 They are the observation effect of the 0-0.3s adaptive predefined time disturbance observer on the external load f1(t)-f3(t) and the observation effect of the parameter uncertainty f4(t). It can be seen that APTDO shows good disturbance estimation performance under various load and parameter uncertainty conditions.

[0140] Figure 7 (ac) is a comparison of the speed tracking effects of the integral predefined sliding mode controller (IPTSMC) proposed in the present invention, the non-singular fast terminal sliding mode controller (NFTSMC) and the fast integral terminal sliding mode controller (FITSMC) for a given step reference speed under no-load conditions of 0-3s. Figure 8 (ac) is the comparison of the speed tracking effect of the fixed reference speed under the 0-1s applied load. Figure 7 ,Under no-load condition, when the reference speed changes suddenly, FITSMC will overshoot, NFTSMC has the slowest speed response, and the proposed IPTSMC shows the fastest speed response among the three controllers. Figure 8 ,When the load is applied, the FITSMC has the smallest velocity settlement, but there is a steady-state error, which increases with the size of the load. The NFTSMC has the largest velocity settlement, and the longest velocity correction time. The IPTSMC has better dynamic performance, while ensuring that the error converges to zero.

[0141] Fig. 9 (ac) and Fig.10 The speed tracking effects of IPTSMC and IPTSMC+APTDO are compared from 0 to 0.5 s under external loads of f1(t)-f3(t) and parameter uncertainty of f4(t). The above disturbances are applied at 0.1 s. It can be seen that the controller with disturbance feedback significantly improves the anti-disturbance performance and shows better speed tracking response. This further verifies the effectiveness of the proposed disturbance observer.

[0142] The above simulation results fully demonstrate that in the presence of uncertain disturbances during motor operation, the sensorless permanent magnet synchronous motor control system based on the new predefined time sliding mode algorithm can accurately and effectively complete speed control.

[0143] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A sensorless permanent magnet synchronous motor control system based on a novel predefined time sliding mode algorithm, characterized in that: The steps include: Step 1: Considering the uncertain disturbances such as external load and parameter uncertainty during the actual operation of the motor, an accurate nonlinear dynamic model of the permanent magnet synchronous motor is established; Step 2: Design a predefined time back-EMF observer to estimate the back-EMF within the predefined time, and obtain the position information and speed information through conversion; Step 3: Design an adaptive predefined time disturbance observer to calculate the uncertain disturbance term within the predefined time, and use adaptive parameters without knowing the upper bound of the disturbance; Step 4: Design an integral predefined time sliding mode controller to achieve system convergence within a predefined time; Step 5: Cascade the observer and the sliding mode control to form a complete control law to achieve precise speed control of the permanent magnet synchronous motor under uncertain disturbances.

2. According to claim 1, a sensorless permanent magnet synchronous motor control system based on a novel predefined time sliding mode algorithm is characterized in that: The precise modeling of the permanent magnet synchronous motor includes: Define a general permanent magnet synchronous motor dynamic model: Surface Mounted Permanent Magnet Synchronous Motor (SPMSM) meets Formula (1) is rewritten as: Among them, ω r is the mechanical angular velocity, is the magnetic flux, P n is the pole pair number, and is the dq axis stator inductance, is the damping friction coefficient, is the moment of inertia, i q is the q-axis current, T L is the load torque, T e is the electromagnetic torque. In actual systems, due to inaccurate measurements, the nominal parameters are always different from the actual parameters, and the motor parameters may change during operation. These situations will cause the established model to be inaccurate, so the model is further optimized for parameter uncertainty: Where J is the nominal moment of inertia, ψ f is the nominal magnetic flux, B is the nominal damping friction coefficient is the inertia deviation, is the flux deviation, is the damping friction coefficient deviation. Simplifying formula (3) we can get: in, is the desired current on the q axis, and g is the lumped disturbance.

3. A permanent magnet synchronous motor control system based on a novel predefined time sliding mode algorithm according to claim 1, characterized in that: The predefined time back electromotive force observer comprises: The stator current equation and back electromotive force equation of SPMSM in the αβ coordinate system are: Among them, i α ,i β ,u α ,u β is the stator current and voltage in the αβ coordinate system, E α ,E β is the back electromotive force in the αβ coordinate system, θ e is the electrical angle, ω e is the electrical angular velocity. Define a sliding surface as: Define the sig function and tanh function as: The predefined time back-EMF observer is designed as: in, is the stator current observed in the αβ coordinate system, is the back electromotive force observed in the αβ coordinate system. 0<δ<1, ò1 is a small positive number, a3 is related to the upper limit of the back electromotive force, so T o Determines the convergence time of the back-EMF observer. The position and angle information of the permanent magnet synchronous motor can be obtained by using Arctan transformation: in, is the observed electrical angle, is the observed electrical angular velocity, is the observed mechanical angular velocity.

4. The inductive permanent magnet synchronous motor control system based on a novel predefined time sliding mode algorithm according to claim 1 is characterized in that: The adaptive predefined time disturbance observer comprises: Define a sliding surface as: The adaptive predefined time disturbance observer can be designed as: in, is the observed lumped disturbance, is an auxiliary variable, 0<γ<1, ò2 is a small positive number, T d Determines the convergence time of the disturbance observer. is the adaptive parameter control rate, which is constructed as follows: Among them, μ is a large positive number, k1=max{2b1 / μ 1-γ / 2 ,2b2 / μ 1+γ / 2 }.

5. The inductive permanent magnet synchronous motor control system based on a novel predefined time sliding mode algorithm according to claim 1 is characterized in that: The integral predefined time controller comprises: Define a velocity tracking error state variable: e=ω r * -oh r (13) By taking the derivative of formula (13), we can get: Define an integral predefined time sliding surface as: The derivative of formula (15) can be obtained: Among them, 0<β<1, T c2 Determines the tracking error convergence time. The integral sliding mode surface of formula (15) adopts a predefined time sliding mode approach rate: Among them, 0<α<1, ò3 is a small positive number, d3 is a positive number, T c1 Determines the convergence time of the integral sliding surface. Combining equation (17) and equation (16), the speed loop controller expression can be obtained: The total convergence time of the controller is T c =T c1 +T c2 Considering the separation principle of the controller and the observer, the bandwidth of the observer is generally greater than the bandwidth of the controller. Since the disturbance observer needs to rely on the back-EMF observer data, the bandwidth of the back-EMF observer is greater than the bandwidth of the disturbance observer. So let T o >T d >T c .

6. The inductive permanent magnet synchronous motor control system based on a novel predefined time sliding mode algorithm according to claim 1 is characterized in that: The observer is cascaded with the sliding mode control to form a complete control law, which is: The lumped disturbance and state terms of the original permanent magnet synchronous motor sliding mode controller are replaced by the lumped disturbance and state estimated by the observer. The system parameter mismatch and external disturbance are observed and compensated by the disturbance observer, thereby further improving the anti-interference ability of the control system. The new speed loop controller expression is:

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