Asynchronous Motor Robust Controller and Its Backstepping Design Zhang Chunpeng, Lin Fei, Song Wenchao, Chen Shousun (Department of Electrical Engineering and Applied Electronics, Tsinghua University, Beijing 100084, China) Influenced by parametric uncertainties and 'guidable conditions', makes the controller robust. Poor performance, the use of extended state observers to enhance robustness, and accurate feedback models without the need for accurate motor models.The new controller combines the advantages of Backstepping and extended state observers to ensure the stability of the error system. It has a strong anti-disturbance capability, and gives a detailed design process and a schematic block diagram of the controller, and it is verified by numerical simulation.
7:1 Zhang Chunpeng male, Ph.D. student of Shandong Tairen, research on motor control Chen Shou 193 | Hu, male, Wuxi Medical Tutor 1 doctoral supervisor, engaged in dynamic power system and motor control research.
1 Introduction Asynchronous motors are widely used due to their simple process and low cost. However, its mathematical model is a non-linear, multi-variable, strongly coupled, and uncertain object. It is necessary to use proper control methods to fully utilize the mechanical properties of the asynchronous motor. Due to factors such as winding temperature rise and skin effect during operation, the winding parameters may experience different degrees of perturbation. Most of the motor's moment of inertia and load torque are inaccurate or even unknown. Overcoming the uncertainty, realizing the high-performance control of asynchronous motors is a topic of practical significance.
In addition to the method, Adaptive Backstepping method has also been applied in motor control and has achieved certain results. Under the condition that the load characteristics are known, an adaptive controller with a mechanical parameter update law is designed, and the rotor resistance perturbation problem is specifically discussed. The given controller can adaptively control the moment of inertia and the load torque, but does not consider the perturbation of the winding parameters. Assuming that the moment of inertia is known, the parameter updating law of the load torque and rotor resistance is designed. In short, the given control strategy can only resist the uncertainty of some parameters. In addition, from the analysis of this article, we can see that the feedback path of the above controller contains the first or second derivative of some parameters, which brings certain limitations for practical applications.
Reasonably reduce the performance of the controller and affect the stability of the system.
In addition, in the expression of W, there are first-order and second-order derivatives of the flux linkage instruction and the speed instruction and the first derivative of the load torque. This means that the calculation W has a condition "that is, the controller's flux linkage and speed commands must have a bounded continuous second derivative, and the load torque must also have a bounded continuous first derivative. This conditional limitation The scope of application of the controller.
The robust design of the controller is designed to control the controller, although the derivation is rigorous, but there are poor resistance to perturbation of parameters and the need to meet the guideline condition "two defects. This article uses the ESO to improve the controller, without feedback on the amount of specific mathematical expressions This avoids the direct calculation and overcomes the uncertainty of many parameters.The controller proposed in this paper relieves the limitation of the controllable condition on the controller, and it can resist the perturbation of the motor parameters and has a strong robustness.
4.1 The ESO M and L1 settings for the feedback values ​​of the mechanical subsystems are M and Wro with the actual values, respectively. Among them: the state variables Z1, Z2 are estimated values ​​of Gm and Wm, respectively, Gm, 6) according to (4.4) And (4.5), the ESO of W can be constructed as: The state variables z3, z4 are the estimated values ​​Gt and Ft of Gj and WT, respectively; B3 and B4 are gains. Then the perturbation equation of Gt can be written as L>1Gt. 4.2 The ESO of the ESO electromagnetic subsystem with the amount of feedback from the electromagnetic subsystem is similar to the mechanical subsystem. Recall that the controller setting of R3 is R3, and 5) of the set value and actual value is rewritten as: where the state variables z5, z6 are the estimated values ​​Gt of Gt and Wt, and FtB5 and Bf> are gain-R according to the formula ( 4.12) and (4.13), we can construct W; the ESO is Z7 = where: The state variables Z7, Z8 are the estimates Gi and W of G and Wi, respectively; B7 and B8 are gains. Then the perturbation equation of G; can be written as 4.3 New error dynamic equation By constructing the corresponding ESO, the feedback amount of the original controller W becomes the new feedback amount W = T. Without considering the specific expression of Wi, the direct use of ESO The observed value Wl=T can be obtained, and the observed error of W is ~=T. This avoids the computational error caused by the parameter perturbation and also breaks through the limitation of the "conductable condition".
The error vector of the system changes from the original g to the new error vector GWxGrGwGlf.SWJ),). )* (4.16) is the new disturbance equation of the system considering the parameter perturbation. 4.4 The transformation of the controller is based on the new error vector G, select a new closed-loop Lyapunov function V2 = GTG/2, and its derivative, because Wl is converged to the actual value, so W; attenuation, can be seen as a system Continuous bounded nonlinear perturbations. The attenuation of this disturbance is related to Wl. The relationship between W; and W is described as where U = region R will shrink to the origin as the gains k and c increase and the attenuation U perturbs, so that G also gradually approaches the origin. When U decays to zero, it can be known from the Balbash-Krasovski Global Stability Theorem 8 that the control strategies given by equations (4.19) and (4.20) can guarantee that G1 is globally stable at the origin.
19) and (4.20) give the block diagram of the new controller. It can be seen that the gain of the controller is changed from the original uncertainties of -1kw and MT, -1 with uncertain coefficients L1R3 and L1M to the determined plant and 3 and -1M-. Rotational speed commands and flux linkage commands are OH=2Prad, respectively /s and W (f=0.4Wb2, load torque 10Nm; at t=0.5 1.5s, O) (f, W (f and Tl smoothly transition to 100Pi.ad/s, 0.2Wb2 and 5Nm. R,, increase 50%, while L, reduce the speed tracking curve of the controller by 10%, if the initial conditions and parameters are the same as above, and when t=1s, OHWef and Tl steps to 50Prad/s, 0.2 Wb2 and 5Nm, and stepped to 20Prad/s, 0.4Wb2 and 10Nm again at t=2s, then it is clear that W(f and Tl violates the condition of conduction at the transition “At this time, controller 1 cannot be completed. The feedback amount is calculated, and the controller 2 can still work normally.
In other words, the controller 2 completely resists the influence of the parameter perturbation.
The speed tracking curve of the controller 2 is given. In the figure, because the motor has a certain moment of inertia, the actual speed cannot be of a step nature. When the command value jumps, there will be a brief transition. In spite of this, it is not difficult to see from the figure that the controller 2 can still accurately track the rotational speed command when the parameter perturbation and the violation of the guidable condition occur at the same time.
(a) Explain that for controllers based on precise model design, motor parameter perturbation and conductable conditions “can introduce steady-state errors that significantly reduce the tracking accuracy of controller 1. (b) and indicate that by Backstepping+ The controller 2 obtained by ESO can solve the problem of parameter uncertainty and 'guidable condition' without the need for specific mathematical expressions of the feedback quantity, and can ensure that the steady-state tracking error converges to zero.
6 Conclusions In this paper, the backstepping design of the robust controller for asynchronous motors is studied from two aspects of design principles and digital simulation. Backstepping design method can change and simplify the tracking problem of asynchronous motor speed and flux linkage. However, while the problem is simplified, the disturbance equation becomes more complex and involves many uncertain parameters. The introduction of ESO avoids the parameter identification. With only a few model information, each feedback can be observed and the robustness of the controller is greatly enhanced. Combining the advantages of Backstepping and ESO to solve the problem of robust control of asynchronous motors is a new approach with good engineering application prospects.
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