ESO-based fast integral terminal sliding mode permanent magnet synchronous motor speed regulation method

Abstract

This invention relates to the field of permanent magnet synchronous motor control technology, specifically a method for speed regulation of a permanent magnet synchronous motor based on ESO (Electronic Speed ​​Reduction). The method includes: (1) establishing a mathematical model in the d-q rotating coordinate system under a vector control strategy for the permanent magnet synchronous motor; (2) designing a fast integral terminal sliding surface and a fast reaching law based on the mathematical model to obtain a controller; (3) obtaining the control law based on the controller and the mathematical model; and (4) designing an ESO to address lumped disturbances. This scheme considers lumped disturbances, external disturbances, and internal parameter perturbations during mathematical modeling, making the modeling more reasonable. A terminal attractor is introduced into the designed fast integral terminal sliding surface to accelerate the response speed and effectively avoid singularity problems. The designed fast reaching law further improves the speed. For lumped disturbances, an extended state observer from the active disturbance rejection technology is used for real-time observation and compensation to the controller, improving the anti-disturbance performance of the control system.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet synchronous motor control technology, and in particular to a method for speed regulation of a permanent magnet synchronous motor based on ESO (Electronic Speed ​​Regulation). Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in industry due to their simple structure, high efficiency, and small size. As a complex object characterized by multiple variables, strong coupling, and nonlinearity, PMSMs are highly sensitive to changes in internal parameters and external disturbances. Currently, PMSM speed control systems mainly employ PI control. However, because PI control is heavily dependent on the system model, its robustness is poor, resulting in poor anti-interference performance and speed tracking performance under significant disturbances. With the continuous development of control technology, to achieve better control system performance and suppress the effects of disturbances, increasingly more high-performance control algorithms have been proposed, such as sliding mode control, fuzzy control, model predictive control, adaptive control, and backstepping control. Among these, sliding mode control, due to its strong robustness and ease of implementation, is gradually being applied to PMSM speed control systems.

[0003] Most current sliding mode control systems employ linear sliding surfaces, adjusting the sliding surface parameters to alter the error convergence rate and asymptotically converge the system state to the equilibrium point. To achieve faster convergence and better anti-interference performance, ensuring the system state converges within a finite time, some researchers have proposed terminal sliding mode control. This introduces nonlinear components into the linear sliding surface, accelerating the convergence near the origin while maintaining finite-time convergence. However, the presence of power terms in the terminal attractor can lead to negative power terms after differentiating the sliding surface, resulting in singularities. In practical industrial applications, various disturbances exist during motor operation, such as friction, internal motor parameter disturbances, and load disturbances, degrading control quality.

[0004] Therefore, a new technical solution is urgently needed to solve the above-mentioned technical problems. Summary of the Invention

[0005] The purpose of this invention is to overcome the problems of the prior art and provide a fast integral terminal sliding mode permanent magnet synchronous motor speed control method based on ESO, so as to solve the problems of singularity in the prior art and the technical problems of deterioration of control quality due to various disturbances during motor operation.

[0006] The above objectives are achieved through the following technical solutions:

[0007] A method for speed control of a permanent magnet synchronous motor based on ESO (Electronic Speed ​​Regulation) with fast integral terminal sliding mode includes:

[0008] Step (1) Establish a mathematical model of the permanent magnet synchronous motor in the dq rotating coordinate system under the vector control strategy;

[0009] Step (2) Based on the mathematical model, design the fast integral terminal sliding surface and the fast reaching law to obtain the controller;

[0010] Step (3) Calculate the control law based on the controller and the mathematical model;

[0011] Step (4) Design an ESO for lumped disturbances.

[0012] Further, step (1) specifically involves: the voltage equation of the permanent magnet synchronous motor in the dq rotating coordinate system is:

[0013]

[0014] Among them, u d u q and i d i q These represent the current and voltage along the d and q axes, respectively. r R is the rotor electrical angular velocity, R is the stator resistance, and L is the stator resistance. d L q For the stator dq-axis inductance, ψ f For rotor flux linkage;

[0015] Using i d * For vector control with =0, the electromagnetic torque equation of the PMSM can be simplified to:

[0016]

[0017] Among them, T e denoted as electromagnetic torque, and p as the number of pole pairs of the motor;

[0018] The dynamic equation of PMSM is then:

[0019]

[0020] Among them, w m Let B be the mechanical angular velocity of the motor, B be the coefficient of friction of the motor, and J be the moment of inertia of the motor.

[0021] The dynamic equation of the motor can then be rewritten as:

[0022]

[0023] Among them, i q * Given the q-axis current, The total system disturbances include friction, external disturbances, and tracking errors of the q-axis current loop.

[0024] Further, step (2) is specifically as follows:

[0025] Select the rotational speed error as state variable x1, and the derivative of the error as state variable x2, then we have:

[0026]

[0027] where, w m * is the reference rotational speed of the motor, and w m * is the actual rotational speed;

[0028] Add the power term of the state variable with the integral term, and design the fast integral terminal sliding surface as:

[0029] s = x2 + αx1 + β∫|x1| γ sign(x1)dt (6)

[0030] where, α and β are constants greater than zero, γ = p / q, both p and q are positive odd numbers, and p < q, sign is the sign function;

[0031] Design the fast reaching law as:

[0032]

[0033] where, both k1 and k2 are constants greater than zero, and 0 < λ < 1.

[0034] Further, step (3) is specifically as follows: Take the derivative of equation (6), then we have:

[0035]

[0036] Combining equations (5), (7) and (8) gives the control law as:

[0037]

[0038] Further, step (4) is specifically as follows: Design the ESO as:

[0039]

[0040] where, is the observer gain, is the observed value of ω m , d(t);

[0041] Then replace the observed values in the control law to achieve disturbance compensation.

[0042] Furthermore, the disturbance compensation is implemented in the observed replacement control law, specifically as follows:

[0043] According to equation (10), the characteristic equation of the observer is:

[0044]

[0045] Configure the observer poles at the same location -w c w c Given the observer bandwidth, we can obtain:

[0046] s 2 +l1s+l2=(s+w c ) 2 (12)

[0047] Find:

[0048]

[0049] By adjusting w c To determine the gain of ESO, the observed z2 is then used to replace d(t) in the control law to achieve disturbance compensation. The compensated control law is designed as follows:

[0050]

[0051] This invention provides a fast integral terminal sliding mode permanent magnet synchronous motor speed control method based on ESO, which effectively solves the technical problem in existing technologies where the presence of power terms in the terminal attractor of state variables may lead to negative power terms after differentiation with respect to the sliding surface, resulting in disturbances. The method considers lumped disturbances, external disturbances, and internal parameter perturbations in the mathematical modeling, making the modeling more reasonable. The introduction of a terminal attractor into the designed fast integral terminal sliding surface accelerates the response speed and effectively avoids singularity problems; the designed fast reaching law further improves the speed. For lumped disturbances, an extended state observer from the active disturbance rejection technology is used for real-time observation and compensation to the controller, improving the disturbance rejection performance of the control system. Attached Figure Description

[0052] Figure 1 The flowchart is a fast integral terminal sliding mode permanent magnet synchronous motor speed control method based on ESO as described in this invention;

[0053] Figure 2 This is a block diagram of the controller in the ESO-based fast integral terminal sliding mode permanent magnet synchronous motor speed control method described in this invention.

[0054] Figure 3 This is a table of permanent magnet synchronous motor parameters used in the simulation of a fast integral terminal sliding mode permanent magnet synchronous motor speed control method based on ESO described in this invention.

[0055] Figure 4 The speed response curves of the controller and PI controller during the motor start-up phase in the ESO-based fast integral terminal sliding mode permanent magnet synchronous motor speed control method described in this invention.

[0056] Figure 5 The speed deviation response curves of the controller and PI controller during the motor start-up phase in the ESO-based fast integral terminal sliding mode permanent magnet synchronous motor speed control method described in this invention are shown.

[0057] Figure 6 The speed response curves of the controller and PI controller in the ESO-based fast integral terminal sliding mode permanent magnet synchronous motor speed control method described in this invention are shown when a sudden load is applied to the motor.

[0058] Figure 7 This is a schematic diagram of the disturbance values ​​observed by ESO under load changes in a fast integral terminal sliding mode permanent magnet synchronous motor speed control method based on ESO as described in this invention. Detailed Implementation

[0059] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. The described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0060] like Figure 1 As shown, a fast integral terminal sliding mode speed control method for permanent magnet synchronous motors (PMSMs) based on ESO is proposed. Building upon the vector control strategy for PMSMs, a composite sliding mode controller is designed for the speed controller in the speed loop. First, a mathematical model of the PMSM is established. An integral terminal sliding surface and a fast reaching law are designed using a sliding mode method based on the reaching law. Lumped disturbances are considered during modeling, and an extended state observer is designed using active disturbance rejection technology to compensate for the observed disturbances in the controller. The specific steps include:

[0061] Step (1) Establish a mathematical model of the permanent magnet synchronous motor in the dq rotating coordinate system under the vector control strategy;

[0062] Step (2) Based on the mathematical model, design the fast integral terminal sliding surface and the fast reaching law to obtain the controller;

[0063] Step (3) Calculate the control law based on the controller and the mathematical model;

[0064] Step (4) Design an ESO for lumped disturbances.

[0065] It should be noted that, in order to verify the effectiveness of the controller, a simulation platform was built on the MATLAB Simulink platform as follows: Figure 2 The simulation model of the permanent magnet synchronous motor vector control speed regulation system shown is illustrated. The motor parameters in the simulation are as follows: Figure 3 As shown.

[0066] In this embodiment, step (1) specifically involves: when establishing the mathematical model, assuming that the motor magnetic circuit is not saturated, ignoring the effects of eddy currents and hysteresis losses, and that the three-phase stator windings of the motor are sinusoidally distributed in the magnetic field space, the voltage equation of the permanent magnet synchronous motor in the dq rotating coordinate system is:

[0067]

[0068] Among them, u d u q and i d i q These represent the current and voltage along the d and q axes, respectively. r R is the rotor electrical angular velocity, R is the stator resistance, and L is the stator resistance. d L q For the stator dq-axis inductance, ψ f For rotor flux linkage;

[0069] Using i d * For vector control with =0, the electromagnetic torque equation of the PMSM can be simplified to:

[0070]

[0071] Among them, T e denoted as electromagnetic torque, and p as the number of pole pairs of the motor;

[0072] The dynamic equation of PMSM is then:

[0073]

[0074] Among them, w m Let B be the mechanical angular velocity of the motor, B be the coefficient of friction of the motor, and J be the moment of inertia of the motor.

[0075] The dynamic equation of the motor can then be rewritten as:

[0076]

[0077] Among them, i q * Given the q-axis current, The total system disturbances include friction, external disturbances, and tracking errors of the q-axis current loop.

[0078] In this embodiment, step (2) is specifically as follows:

[0079] Select the rotational speed error as the state variable x1, and the derivative of the error as the state variable x2, then we have:

[0080]

[0081] where, w m * is the reference rotational speed of the motor, and w m is the actual rotational speed;

[0082] To improve the rapidity of the control system and avoid the singularity problem at the same time, add the power term of the state variable with an integral term, and design the fast integral terminal sliding surface as:

[0083] s = x2 + αx1 + β∫|x1| γ sign(x1)dt (6)

[0084] where, α and β are constants greater than zero, γ = p / q, both p and q are positive odd numbers, and p < q, and sign is the sign function;

[0085] Design the fast reaching law as:

[0086]

[0087] where, k1 and k2 are both constants greater than zero, and 0 < λ < 1.

[0088] In this embodiment, the singularity problem of the terminal sliding mode is avoided through the integral sliding surface, and the rapidity can be further improved by using the reaching law.

[0089] In this embodiment, step (3) is specifically as follows: Differentiate equation (6), then we have:

[0090]

[0091] Combining equations (5), (7) and (8), the control law can be obtained as:

[0092]

[0093] In this embodiment, step (4) is specifically as follows: Consider the lumped disturbance d(t) during modeling, and expand it into a state variable, and design the ESO as:

[0094]

[0095] where, is the observer gain, is the observed value of ω m , d(t);

[0096] Then, disturbance compensation is implemented in the observed replacement control law, specifically as follows:

[0097] According to equation (10), the characteristic equation of the observer is:

[0098]

[0099] The parameters of the ESO are tuned based on the bandwidth concept, and the observer poles are configured at the same location -w c w c Given the observer bandwidth, we can obtain:

[0100] s 2 +l1s+l2=(s+w c ) 2 (12)

[0101] Find:

[0102]

[0103] By adjusting w c To determine the gain of ESO, the observed z2 is then used to replace d(t) in the control law to achieve disturbance compensation. The compensated control law is designed as follows:

[0104]

[0105] To verify the advantages of this solution, such as Figure 4 and Figure 5 As shown, the speed response and speed deviation response of the two controllers during the motor start-up phase are shown. It can be seen that compared with the PI controller, the response of this scheme is faster and there is no overshoot.

[0106] To further verify the advantages of this solution, such as Figure 6 and Figure 7 As shown, the speed response and ESO observation values ​​of the two controllers under sudden load conditions are shown. It can be seen that the speed drop of this scheme is less under sudden load conditions, and the disturbance rejection is improved.

[0107] In summary, the controller described in this solution improves the control accuracy of the motor control system, and its speed and anti-interference performance are superior to those of the PI controller.

[0108] The above description is merely illustrative of the embodiments of the present invention and is not intended to limit the present invention. For those skilled in the art, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for speed regulation of a permanent magnet synchronous motor based on ESO with fast integral terminal sliding mode, characterized in that, include Step (1) Establish a mathematical model of the permanent magnet synchronous motor in the dq rotating coordinate system under the vector control strategy; Step (2) Based on the mathematical model, design the fast integral terminal sliding surface and the fast reaching law to obtain the controller; Step (3) Calculate the control law based on the controller and the mathematical model; Step (4) Design an ESO to address lumped disturbances; Step (2) specifically involves: Selecting speed error as the state variable The derivative of the error is the state variable. Then we have: （5）； in, This is the reference speed for the motor. This refers to the actual rotational speed. , Given the q-axis current; The total system disturbances include friction, external disturbances, and tracking errors of the q-axis current loop; By adding the power term to the integral term of the state variable, the sliding surface of the fast integration terminal is designed as follows: （6）； in, , A constant that is greater than zero. p and q are both positive odd numbers, and , It is a symbolic function; The fast convergence law is designed as follows: （7）； in, , All are constants greater than zero. ; The specific step (3) is as follows: Differentiating equation (6), we have: （8）； Combining equations (5), (7), and (8), the control law can be obtained as follows: （9）； The specific step (4) is as follows: Design the ESO as follows: （10）； in, , , , , , For observer gain, for , Observed values; Then, disturbance compensation is achieved in the observed replacement control law; The disturbance compensation is implemented in the observed replacement control law, specifically as follows: According to equation (10), the characteristic equation of the observer is: （11）； Configure the observer poles in the same location , Given the observer bandwidth, we can obtain: （12）； Find: （13）； By adjusting To determine the gain of the ESO, and then the observed In replacement control law To achieve disturbance compensation, the compensated control law is designed as follows: （14）。 2. The method for speed regulation of a permanent magnet synchronous motor based on ESO with fast integral terminal sliding mode as described in claim 1, characterized in that, The specific step (1) is as follows: the voltage equation of the permanent magnet synchronous motor in the dq rotating coordinate system is: （1）； in, , and , These represent the current and voltage along the d and q axes, respectively. R is the rotor electrical angular velocity, and R is the stator resistance. , For stator dq axis inductance, For rotor flux linkage; use * For vector control with =0, the electromagnetic torque equation of the PMSM can be simplified to: （2）； in, denoted as electromagnetic torque, and p as the number of pole pairs of the motor; The dynamic equation of PMSM is then: （3）； in, Let B be the mechanical angular velocity of the motor, B be the coefficient of friction of the motor, and J be the moment of inertia of the motor. The dynamic equation of the motor can then be rewritten as: （4）； in, Given the q-axis current, , The total system disturbances include friction, external disturbances, and tracking errors of the q-axis current loop.

Images