| Permanent magnet synchronous motor（PMSM）is widely used in numerical control machine tools,new energy vehicles,aerospace,and other fields due to its simple structure,high efficiency,and low energy consumption.However,the PMSM is a complex,strongly coupled,multivariable and parameters variable nonlinear system.Besides,it is vulnerable to the external random disturbances,input and output signal fluctuations,chaotic oscillations,parameter perturbations and other uncertainties,which seriously affect the dynamic and static control performance of the system.In addition,the randomness of manufacturing errors,the uncertainty of loads,and the diversity of application scenarios cause serious challenges to the high-precision control of the PMSM system.Therefore,this article establishes the mathematical model,conducts dynamic characteristics analysis,proposes an adaptive inversion control scheme to suppress the inherent high-frequency nonlinear oscillation for the PMSM system,and improves the control accuracy,stability,and robustness of the system,all of which enrich the adaptive control theory of the PMSM system.The main research content of this article is as follows:（1）Investigating the issue of the adaptive backstepping control of the PMSM system with output constraints.A dynamic model of the PMSM system is established based on the Kirchhoff’s law and Lenz’s law.Nonlinear research tools such as the phase diagrams,time history diagrams,and Lyapunov exponent diagrams are constructed to reveal the nonlinear dynamic evolution mechanism of the PMSM system and clarifies the sensitivity of their dynamic characteristics to system initial values and parameter changes.An adaptive backstepping control scheme based on an interval type-2 fuzzy neural network（IT2SFNN）is designed to address the issues of high-frequency chaotic oscillations and output constraints in the PMSM.In the design process of the controller,the barrier Lyapunov function is constructed to ensure that the output constraints of the system are not violated;the IT2SFNN is used to estimate the nonlinear function of the system;the second-order tracking differentiator（TD）is designed to solve the problem of"complex term explosion"caused by repeated differentiation of virtual control signals.Lyapunov stability analysis proves that all signals in the closed-loop system are ultimately bounded.Many experimental simulation results prove that the proposed control scheme not only effectively suppresses chaotic oscillations,but also achieves high-precision tracking of the reference trajectory（stable at0.4 seconds,and the steady-state error is limited to the interval of[-0.15,0.08]）.The results of this study provide a theoretical basis and technical support for the subsequent control scheme design of the PMSM systems.（2）An accelerated adaptive backstepping control scheme is proposed to handle the issues of chaotic oscillations,input-output constraints,external random disturbances,and parameter perturbations in PMSM systems.During the controller design,the cosine barrier function is used to ensure that the output signal is limited within the state constraint range;a speed function is utilized to improve the convergence speed of tracking errors;to reduce the computational burden,a hyperbolic tangent differential tracker（HTTD）is designed to estimate the complex differential terms of the virtual control signal;fuse the IT2SFNN to approximate the nonlinearities in the system;a saturation function is designed to reduce control input chattering in the system.Stability analysis proves that all signals in the closed-loop system are bounded.The quantitative experimental simulation results prove the effectiveness of the proposed scheme（stable within 0.33 seconds,and the steady-state error converges to[-0.03,0.007]）.This research provides useful experience for the subsequent design of the adaptive control scheme with full-state constraints of the PMSM system.（3）Considering the effects of nonlinear factors such as time-varying state constraints,parameter perturbations,external disturbances,and chaotic oscillations on the system,based on the research content（2）and（3）,an adaptive control scheme based on command filter for PMSM system with full-state constraints is proposed.In order to suppress the nonlinear oscillation of the system,an adaptive backstepping controller is designed by fusing command filters,fuzzy wavelet neural networks（FWNN）,time-varying barrier Lyapunov function functions,filtering error compensation mechanisms,and backstepping control methods.In the process of controller design,the time-varying barrier functions is utilized to ensure that the time-varying constraint boundaries in the system are not violated;the FWNN is designed to estimate the unknown nonlinear functions in the system;the time-varying barrier functions are used to ensure that the time-varying constraint boundaries in the system are not violated.The command filter is used to deal with the"complex terms explosion"problem in traditional backstepping control for reducing the computational burden.Meanwhile,a filtering error compensation mechanism is designed to eliminate the impact of filtering errors.Lyapunov stability analysis proves the boundedness of all signals in the system.Many experimental simulation results demonstrate the expected tracking control effect(achieve stability within 0.25 seconds and the steady-state error convergence to the range of[-1×10-3,1×10-3]),and prove the robustness of the proposed scheme. |
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