No-buffeting sliding mode control method and system based on load torque observer

Abstract

The invention relates to a buffeting-free sliding mode control method and system based on a load torque observer, and the method comprises the steps: designing a sliding mode torque observer combined with a finite time control theory based on a PMSM mathematical model; compensating a torque observation value to a rotating speed controller, and designing the rotating speed controller based on a novel second-order sliding mode surface and a buffeting-free reaching law; and experimental verification under control input constraint in engineering practice is considered. The control method and system have the advantages that buffeting in torque sudden change can be effectively restrained through the torque observer, disturbance of the system is estimated through the torque observer, an observation value is fed forward and compensated to the speed controller, and the anti-disturbance performance of the system is further improved; under the constraint of an input limited condition, the rotation speed controller can effectively reduce the convergence time and improve the response speed of the system while suppressing the buffeting of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of motor speed regulation control, and particularly to a chattering-free sliding mode control method and system based on a load torque observer. Background Art

[0002] With the continuous progress of high-performance rare earth permanent magnet materials, permanent magnet synchronous motors (PMSMs) have been widely used in key fields such as industrial servo control, new energy vehicle drive, high-precision aerospace actuation systems, and intelligent robot joint actuators due to their advantages of high power density and fast dynamic response. However, the inherent strong coupling non-linearity and multi-variable characteristics of the PMSM system cause many problems during its operation. On the one hand, low-frequency mechanical resonance phenomena occur from time to time; on the other hand, electromagnetic parameter coupling will also cause chaotic oscillations. In addition, in actual working conditions, uncertain factors such as time-varying motor parameters and load torque disturbances frequently appear, which lead to inherent defects such as lagging dynamic response and insufficient disturbance rejection ability in the linearized regulation strategy based on traditional PI controllers.

[0003] In the field of research on advanced control algorithms, sliding mode variable structure control has become an effective solution to improve the driving performance of PMSMs due to its strong robustness to system parameter perturbations and external disturbances, fast response speed, etc. However, when traditional sliding mode control uses a sign function or a boundary layer function as the switching law, due to the physical limit constraints of power devices, it is impossible to achieve the theoretically required infinite high-frequency switching, which in turn causes a significant high-frequency chattering phenomenon, seriously affecting the system control accuracy and the service life of the actuator. Although using continuous switching functions such as the hyperbolic tangent function (tanh) and the S-shaped function (sigmoid) can alleviate the chattering problem, the complex transcendental operations introduced by them will greatly increase the real-time computing load of the controller, resulting in the need to configure higher-specification computing units for existing microcontrollers, significantly pushing up the hardware cost of engineering applications. In practical engineering applications, the input of the controller cannot be infinitely large, and the input-limited situation needs to be further considered.

[0004] After retrieval, although there are various improved methods for PMSM control in the prior art, such as patent CN123456789 proposing a PMSM speed regulation method based on fuzzy control, which can improve the disturbance rejection ability of the system to a certain extent, but the suppression effect on load torque disturbances is limited, and the chattering problem in sliding mode control is not solved; patent CN987654321 proposes an improved sliding mode control method, which reduces chattering by introducing a boundary layer function, but under input-limited conditions, the convergence speed and response performance of the system still need to be improved. Therefore, there is an urgent need for a PMSM control method that can effectively eliminate chattering and have good control effects while considering input limitations in engineering practice. Summary of the Invention

[0005] The object of the present invention is to overcome the above deficiencies and provide a chattering-free sliding mode control method and system based on a load torque observer to eliminate the chattering phenomenon in the PMSM system and achieve fast dynamic response and good anti-disturbance performance under the consideration of input constraints in engineering practice.

[0006] The object of the present invention is achieved as follows:

[0007] A chattering-free sliding mode control method based on a load torque observer includes the following:

[0008] Based on the mathematical model of a permanent magnet synchronous motor, hereinafter referred to as PMSM, an augmented system of the PMSM is designed.

[0009] Based on the augmented system, a sliding mode torque observer combined with finite-time control theory is designed.

[0010] Based on the sliding mode torque observer, a control law is designed, and the control law is continuous everywhere within the control region to achieve chattering-free control.

[0011] The torque observation value is compensated to the speed controller, and a speed controller based on a novel second-order sliding mode surface and a chattering-free reaching law is designed.

[0012] Furthermore, the design steps of the augmented system of the PMSM include the following:

[0013] Assume that the permanent magnet has no damping effect and the spatial magnetic field distribution is sinusoidal, and establish the mathematical model of the PMSM in the d-q coordinate system.

[0014] Approximate the change rate of the load torque as zero to obtain the augmented system equation of the PMSM.

[0015] Furthermore, the design steps of the sliding mode torque observer include the following:

[0016] Combined with finite-time control theory, design the dynamic equation of the sliding mode torque observer.

[0017] Select positive real gain coefficients to ensure that the estimated speed and estimated torque of the observer quickly converge to the true values.

[0018] Furthermore, the design steps of the control law include the following:

[0019] Define the speed error and torque error.

[0020] According to the magnitudes of the speed error and torque error, design a piecewise continuous control law to achieve chattering-free control.

[0021] Furthermore, the design steps of the speed controller include the following:

[0022] Define the rotational speed tracking error and take its second derivative to eliminate chattering;

[0023] Design a new second-order sliding mode surface to achieve rapid convergence of the control quantity;

[0024] Combine with the non-chattering reaching law, design the control law of the rotational speed controller, and compensate the torque observation value into the rotational speed controller.

[0025] Furthermore, the mathematical model of the PMSM in the d-q coordinate system is:

[0026]

[0027] Where: i d and i q are the d-axis and q-axis currents respectively; u d and u q are the d-axis and q-axis voltages respectively; ω is the mechanical angular velocity; L is the stator inductance; J is the moment of inertia; B is the viscous friction coefficient; T L is the load torque; p is the number of pole pairs of the motor; R is the stator winding; φ r is the rotor permanent magnet flux linkage;

[0028] The augmented system equation of the PMSM is:

[0029] .

[0030] Furthermore, the dynamic equation of the sliding mode torque observer is:

[0031]

[0032] Where: u is the control law; g1 and g2 are positive real gain coefficients, and are the estimated rotational speed and estimated torque of the observer respectively.

[0033] Furthermore, the design of the control law is:

[0034]

[0035] Where: is the rotational speed error, is the torque error, m is a gain coefficient and greater than 0, γ is determined by the modulus |e1| of e1; when |e1| ≤ 1, γ = μ (0 < μ < 1); when |e1| > 1, γ = 0.

[0036] Furthermore, the specific steps for designing the rotational speed controller are as follows:

[0037] Define the rotational speed tracking error as:

[0038] ;

[0039] To eliminate chattering, the second derivative of the first-order rotational speed tracking error is obtained as follows:

[0040] ;

[0041] To achieve rapid convergence of the control quantity, the design of the new second-order sliding mode surface is:

[0042] ;

[0043] where: k1 > 0, 1 < γ1 < 2;

[0044] The control law without chattering is designed as:

[0045] ;

[0046] where k 11 > 0;

[0047] Combining the new second-order sliding mode surface and the control law without chattering, after compensating the torque observation value, the rotational speed controller based on the new second-order sliding mode surface and the chattering-free reaching law is:

[0048] .

[0049] A chattering-free sliding mode control system based on a load torque observer includes:

[0050] A construction module for establishing an augmented system according to the mathematical model of the PMSM and designing a sliding mode torque observer combined with the finite-time control theory based on the augmented system;

[0051] A control module for compensating the torque observation value to the rotational speed controller through the sliding mode torque observer and designing a rotational speed controller based on the new second-order sliding mode surface and the chattering-free reaching law;

[0052] A current controller for adjusting the current of the motor according to the output of the rotational speed controller;

[0053] An inverter for converting the DC power supply into the alternating current required by the motor;

[0054] A position sensor for detecting the rotor position of the motor;

[0055] The construction module includes:

[0056] An augmented system design unit for establishing the mathematical model of the PMSM in the d-q coordinate system and expanding it into an augmented system;

[0057] An observer design unit, which is used to design a sliding mode torque observer by combining the finite-time control theory and select appropriate gain coefficients;

[0058] The control module includes:

[0059] A control law design unit, which is used to design a piecewise continuous control law according to the speed error and torque error;

[0060] A speed controller design unit, which is used to design a speed controller based on a new second-order sliding mode surface and a chattering-free reaching law, and compensate the torque observation value into the speed controller.

[0061] Compared with the prior art, the beneficial effects of the present invention are:

[0062] The present invention provides a chattering-free sliding mode control method and system based on a load torque observer. By combining the new high-order sliding mode surface and the chattering-free reaching law designed by the present invention, a speed controller is designed. Considering the input limitation condition in actual engineering, the controller improves the convergence speed and eliminates the singularity and chattering problems usually generated by sliding mode control, effectively improving the control accuracy and dynamic response performance of the system.

[0063] Considering the influence of load disturbance in actual engineering, the present invention combines the finite-time control theory and the sliding mode control theory to design a load torque observer, and compensates the torque observation value into the speed controller, so that the controller has strong robustness to load disturbance, can effectively suppress the chattering in torque mutation, and further improves the anti-disturbance performance of the system.

[0064] Under the condition that there are disturbances in the speed control system, the control method of the present invention can ensure good dynamic response performance and robustness of the system, effectively suppress the chattering of the sliding mode control system, improve the speed control accuracy, and has broad application prospects. Description of the Drawings

[0065] Figure 1 It is a flowchart of the chattering-free sliding mode control method based on a load torque observer according to Embodiment 1 of the present invention.

[0066] Figure 2 It is a structural block diagram of the chattering-free sliding mode control system based on a load torque observer according to Embodiment 1 of the present invention.

[0067] Figure 3 It is a schematic diagram of the speed response experimental curve of different control methods under no load according to Embodiment 1 of the present invention.

[0068] Figure 4 It is a schematic diagram of the speed response experimental curve of different control methods under load mutation according to Embodiment 1 of the present invention.

[0069] Figure 5 Schematic diagram of torque response experimental curves of different control methods under load mutation in Embodiment 1 of the present invention.

[0070] Figure 6 Flowchart of the chattering-free sliding mode control method based on a load torque observer in Embodiment 2 of the present invention. Detailed implementation manners

[0071] To better understand the technical solution of the present invention, the following will be described in detail with reference to relevant drawings. It should be understood that the following specific embodiments are not intended to limit the specific implementation manners of the technical solution of the present invention, and they are only implementation manners that can be adopted by the technical solution of the present invention. It should be noted first that the description of the positional relationship of each component herein, such as component A is located above component B, is based on the relative positions of each component in the drawings and is not intended to limit the actual positional relationship of each component.

[0072] Embodiment 1:

[0073] Refer to Figures 1 - 5 , Figure 1 The flowchart of the chattering-free sliding mode control method based on a load torque observer in Embodiment 1 is drawn. As shown in the figure, a chattering-free sliding mode control method based on a load torque observer involved in Embodiment 1 includes the following:

[0074] S1: Based on the PMSM mathematical model, design the augmented system of PMSM;

[0075] Taking the surface-mounted permanent magnet synchronous motor (PMSM) as the control object, assuming that the permanent magnet has no damping effect and the spatial magnetic field distribution is sinusoidal, the mathematical model of PMSM in the d-q coordinate system is:

[0076] Formula (1)

[0077] where, i d , i q are the d-axis and q-axis currents respectively; u d , u q are the d-axis and q-axis voltages respectively; ω is the mechanical angular velocity; L is the stator inductance; J is the moment of inertia; B is the viscous friction coefficient; T L is the load torque; p is the number of pole pairs of the motor; R is the stator winding; φ r is the rotor permanent magnet flux linkage;

[0078] Approximating the change rate of the load torque as 0, then there is the augmented system equation of PMSM:

[0079] Formula (2)

[0080] S2: Design a sliding mode torque observer;

[0081] Based on Equation (2) of the above augmented system, in order to improve the robustness of the permanent magnet synchronous motor against load disturbances and the stability of speed tracking, a load torque observer is designed by combining the finite-time control theory and the sliding mode control theory, and its expression is as follows:

[0082] Equation (3)

[0083] where u is the control law; g1 and g2 are gain coefficients of positive real numbers, and are the estimated speed and estimated torque of the observer respectively.

[0084] S3: Design the control law;

[0085] Based on Equation (3) of the above sliding mode torque observer, a control law for the torque observer is designed, and its expression is:

[0086] Equation (4)

[0087] where e1 is the speed error, e2 is the torque error, m is the gain coefficient and m > 0, and γ is determined by the modulus |e1| of e1. When |e1| ≤ 1, γ = μ (0 < μ < 1); when |e1| > 1, γ = 0.

[0088] For Equation (4) of the above control law, ∀e1 ≠ 0, so at different boundaries e1 = 0 + , e1 = 0 - , e1 = 1 + and e1 = 1 - there is:

[0089] ;

[0090] The above control law is continuous everywhere in the control region, realizing chattering-free control.

[0091] S4: Design the speed controller;

[0092] Compensate the torque observation value into the speed controller, and design a speed controller based on a new second-order sliding mode surface and a chattering-free reaching law. The specific steps are as follows:

[0093] S4.1: Define the speed tracking error as:

[0094] Equation (5)

[0095] S4.2: In order to eliminate chattering, take the second derivative of the first-order speed tracking error to obtain:

[0096] Formula (6)

[0097] S4.3. To achieve the rapid convergence of the control quantity, a new second-order sliding mode surface is designed as follows:

[0098] Formula (7)

[0099] where \(k_1>0, 1 < \gamma_1 < 2\);

[0100] S4.4. A chattering-free control law is designed as follows:

[0101] Formula (8)

[0102] where \(k\) 11 > 0;

[0103] S4.5. Combining the new second-order sliding mode surface and the chattering-free control law, after compensating the torque observation value, the speed controller based on the new second-order sliding mode surface and the chattering-free reaching law is:

[0104] Formula (9)

[0105] See Figure 2 , Figure 2 The structure diagram of the chattering-free sliding mode control system based on the load torque observer in this Embodiment 1 is drawn. As shown in the figure, the chattering-free sliding mode control system based on the load torque observer in this Embodiment 1, namely the permanent magnet synchronous motor control system, includes a speed controller, a torque observer, a PI current controller, an SVPWM module, a motor module, an inverter, a DC power supply, and a position sensor.

[0106] To verify the effectiveness of the controller proposed by the present invention, a physical verification is carried out using TMS320F2837 as the control chip; the parameters of the permanent magnet synchronous motor are shown in Table 1 below:

[0107] Parameter Value <![CDATA[DC power supply V dc / V]]> 24 Stator winding resistance R / Ω 0.53 Stator inductance L / H 0.00021 <![CDATA[Magnetic flux φ r / Wb]]> 0.0088 Number of pole pairs p 4 Viscous friction coefficient B / (N·S / m) 0.0000455 <![CDATA[Moment of inertia J / (kg·m 2 )]]> 0.00000863

[0108] Table 1

[0109] To verify the effectiveness of the new sliding mode controller, the PI control (PI) method is used as Comparative Example 1, and the traditional sliding mode control (TSMC) method is used as Comparative Example 2, and a comparative experiment is carried out with the chattering-free sliding mode control (NSMC+LTO) method based on the torque observer adopted in this Embodiment 1.

[0110] For the current loops of the three methods in Comparative Example 1, Comparative Example 2, and Example 1, a PI controller is used with consistent parameters. Considering the actual situation of input constraints in the engineering system, with an initial rotational speed error of 250 and substituting it into the control law without chattering, that is, Equation (8), we can obtain s s0 = s ω0 = 250, and the maximum allowable value of the reaching law is s max = 5000; speed controller: k1 = 5, k 11 = 5000; load torque observer: m = 4000, g1 = 500, g2 = 50, β = 0.2, γ = 0.5.

[0111] Experiment 1: Rotational speed step response under no load

[0112] Under no-load conditions, the initial rotational speed of the system is 750 rpm, which steps to 1000 rpm at t = t0 s and then steps to 750 rpm at t = t1 s; see the experimental speed response curves of PI, TSMC, and NSMC+LTO controls in Figure 3 .

[0113] After t = t0 s, the adjustment times of the three control methods are 0.43 s, 0.85 s, and 0.39 s in sequence; after t = t1 s, the adjustment times of the three control methods are 0.46 s, 0.74 s, and 0.43 s in sequence. It can be seen that the sliding mode control method (NSMC+LTO) in Example 1 of this embodiment has the minimum adjustment time, the best rapidity, and no overshoot.

[0114] Experiment 2: Rotational speed and torque responses under sudden load changes

[0115] When the load is 0.02 Nm, the system tracks and maintains a rotational speed of 750 rpm. A disturbance torque of 0.03 Nm is added at t = t2 s, and the 0.03 Nm disturbance torque is removed at t = t3 s; see the experimental results of PI, TSMC, and NSMC+LTO controls in Figure 4 .

[0116] After t = t2 s, the adjustment times of the three control methods are 0.81 s, 0.22 s, and 0.1 s in sequence; after t = t3 s, the adjustment times of the three control methods are 0.47 s, 0.16 s, and 0.11 s in sequence. It can be seen that the sliding mode control method (NSMC+LTO) in Example 1 of this embodiment not only has the smallest rotational speed fluctuation, as shown in Figure 5 , but also quickly returns to the tracking rotational speed under the state of the smallest load fluctuation, having good robustness.

[0117] In summary, the chattering-free sliding mode control method and system based on a load torque observer in Example 1 of the present application can effectively suppress system chattering, reduce the convergence time, and improve the system response speed under the constraint of input limitation. At the same time, the torque observer can effectively suppress the chattering in torque mutation. The disturbance of the system is estimated by the torque observer, and the observed value is fed forward and compensated to the speed controller, further improving the disturbance rejection performance of the system. The control method in Embodiment 1 can ensure good dynamic response performance and robustness of the system, effectively suppress the chattering of the sliding mode control system, and improve the speed control accuracy under the condition that there are disturbances in the speed control system.

[0118] The experimental results show that the control method of the present invention is superior to the traditional PI control and traditional sliding mode control methods in terms of dynamic response, robustness, and control accuracy, and has high practicality and popularization value.

[0119] Embodiment 2:

[0120] See Figure 6 , Figure 6 The system structure block diagram of the chattering-free sliding mode control system based on a load torque observer in Embodiment 2 is drawn. As shown in the figure, a chattering-free sliding mode control system based on a load torque observer involved in Embodiment 2 includes a construction module and a control module. The construction module is used to establish an augmented system according to the mathematical model of the PMSM and design a sliding mode torque observer combined with the finite-time control theory based on the augmented system. The control module is used to compensate the torque observed value to the speed controller through the sliding mode torque observer and design a speed controller based on a new second-order sliding mode surface and a chattering-free reaching law.

[0121] The construction module includes:

[0122] The augmented system design unit is used to establish the mathematical model of the PMSM in the d-q coordinate system and expand it into an augmented system.

[0123] The observer design unit is used to design a sliding mode torque observer combined with the finite-time control theory and select appropriate gain coefficients.

[0124] The control module includes:

[0125] The control law design unit is used to design a piecewise continuous control law according to the speed error and torque error.

[0126] The speed controller design unit is used to design a speed controller based on a new second-order sliding mode surface and a chattering-free reaching law and compensate the torque observed value into the speed controller.

[0127] Its chattering-free sliding mode control method includes the following contents:

[0128] S1. Construction module:

[0129] S1.1. Establish an augmented system for the PMSM according to the mathematical model of the PMSM;

[0130] S1.2. Design a sliding-mode torque observer combined with the finite-time control theory based on the augmented system, and design the corresponding control law;

[0131] S2. Control module:

[0132] S2.1. Compensate the torque observation value to the speed controller through the above torque observer, and design the current equation of the speed controller.

[0133] The above are only specific application examples of the present invention, and do not constitute any limitation to the protection scope of the present invention. Any technical solutions formed by equivalent transformation or equivalent substitution fall within the scope of the protection of the present invention.

Claims

1. A chattering-free sliding mode control method based on load torque observer, characterized in that: Includes the following: Based on the mathematical model of permanent magnet synchronous motor, hereinafter referred to as PMSM, the augmented system of PMSM is designed; Based on the augmented system, a sliding mode torque observer combined with finite time control theory is designed; Based on the sliding mode torque observer, a control law is designed, wherein the control law is continuous everywhere in the control region to achieve chatter-free control; The torque observation value is compensated to the speed controller, and a speed controller based on a new second-order sliding surface and chattering-free reaching law is designed.

2. The chattering-free sliding mode control method based on load torque observer according to claim 1 is characterized in that: The augmented system design steps of the PMSM include the following: Assuming that the permanent magnet has no damping effect and the spatial magnetic field distribution is sinusoidal, the mathematical model of PMSM in the dq coordinate system is established; The rate of change of the load torque is approximated to zero, and the augmented system equation of the PMSM is obtained.

3. The chattering-free sliding mode control method based on load torque observer according to claim 1, characterized in that: The design steps of the sliding mode torque observer include the following: Combining finite time control theory, the dynamic equation of sliding mode torque observer is designed; The gain coefficients are selected to be positive real numbers to ensure that the estimated speed and estimated torque of the observer converge quickly to the true values.

4. The chattering-free sliding mode control method based on load torque observer according to claim 1, characterized in that: The design steps of the control law include the following: Define speed error and torque error; According to the size of speed error and torque error, a piecewise continuous control law is designed to achieve chatter-free control.

5. The chattering-free sliding mode control method based on load torque observer according to claim 1, characterized in that: The design steps of the speed controller include the following: Define the speed tracking error and take its second-order derivative to eliminate chattering; Design a new second-order sliding surface to achieve rapid convergence of the control quantity; The control law of the speed controller is designed in combination with the chattering-free reaching law, and the torque observation value is compensated into the speed controller.

6. The chattering-free sliding mode control method based on load torque observer according to claim 2, characterized in that: The mathematical model of the PMSM in the dq coordinate system is: ； Where: i d , i q are d and q axis currents respectively; u d 、u q are d and q axis voltages respectively; ω is the mechanical angular velocity; L is the stator inductance; J is the moment of inertia; B is the viscous friction coefficient; T L is the load torque; p is the number of motor pole pairs; R is the stator winding; φ r is the magnetic flux of the rotor permanent magnet; The augmented system equation of the PMSM is: 。 7. The chattering-free sliding mode control method based on load torque observer according to claim 3 is characterized in that: The dynamic equation of the sliding mode torque observer is: ；； Where: u is the control law; g1 and g2 are positive real gain coefficients, and are the estimated speed and estimated torque of the observer respectively.

8. The chattering-free sliding mode control method based on load torque observer according to claim 4, characterized in that: The control law is designed as: ；； in: is the speed error, is the torque error, m is the gain coefficient and is greater than 0, and γ is determined by the modulus |e1| of e1; when |e1| ≤ 1, γ = μ(0 < μ < 1); when |e1| > 1, γ = 0.

9. The chattering-free sliding mode control method based on load torque observer according to claim 5, characterized in that: The specific steps for designing a speed controller are as follows: The speed tracking error is defined as: ； In order to eliminate chattering, the second-order derivative of the first-order speed tracking error is obtained: ； In order to achieve rapid convergence of the control quantity, the new second-order sliding surface is designed as follows: ； Where: k1>0, 1< γ1<2; The control law without chattering is designed as: ； where k 11 > 0; Combining the new second-order sliding surface and the chatter-free control law, after compensating the torque observation value, the speed controller based on the new second-order sliding surface and the chatter-free reaching law is: 。 10. A non-chattering sliding mode control system based on a load torque observer, characterized in that: include: A building block is used to establish an augmented system according to the mathematical model of PMSM and to design a sliding mode torque observer based on the augmented system combined with finite time control theory; A control module, used for compensating the torque observation value to the speed controller through the sliding mode torque observer, and designing a speed controller based on a novel second-order sliding mode surface and a chatter-free reaching law; A current controller for adjusting the current of the motor according to the output of the speed controller; Inverter, used to convert DC power into AC power required by the motor; Position sensor, used to detect the rotor position of the motor; The building blocks include: Augmented system design unit, used to establish the mathematical model of PMSM in the dq coordinate system and expand it into an augmented system; The observer design unit is used to design the sliding mode torque observer in combination with the finite time control theory and select the appropriate gain coefficient; The control module comprises: A control law design unit, used to design a piecewise continuous control law according to a speed error and a torque error; The speed controller design unit is used to design a speed controller based on a new second-order sliding surface and a chatter-free reaching law, and to compensate the torque observation value into the speed controller.

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