Research On Fractional-order Command Filtered Backstepping Control For Position Tracking Of Permanent Magnet Synchronous Motor

Permanent magnet synchronous motor(PMSM)is widely applied in position tracking control system due to its small size,simple structure and high power density.However,traditional integer-order methods are difficult to meet the requirements of high control performance.As a result,the performance of control system can be improved by applying fractional calculus theory to study PMSM model and design controller.In this dissertation,the fractional-order command filtered backstepping methods of PMSM position tracking control are studied.The main results are listed as follows:1.The integer-order mathematical models of PMSM in different coordinates are introduced.By using fractional calculus theory and parameters identification method based on optimization algorithm,the fractional-order mathematical model of PMSM is established.2.For commensurate fractional-order systems,a commensurate fractional-order command filtered backstepping control method is proposed.The second-order linear command filter is extended to the fractional-order domain,and the convergence condition is given,which solves the”explosion of complexity” problem in the fractional-order backstepping.Aiming at the filtering error caused by the command filter,a compensation mechanism is investigated to decrease the filtering errors under fractional calculus framework.Furthermore,the position tracking control issue of the commensurate fractional-order PMSM is studied.Considering the load torque disturbance of the motor,a fractional-order disturbance observer is constructed.With the combination of backstepping,the design of fractional-order command filtered backstepping controller based on disturbance observer is completed,and the stability of closed-loop system is analyzed.Simulations are given to illustrate the effectiveness of the proposed method.3.For the problem of position tracking control of fractional-order chaotic PMSM with unknown parameters and load torque disturbance,a commensurate fractional-order adaptive neural network command filtered backstepping sliding mode control method is proposed.In order to overcome the uncertainty of the system,the neural network is used to approximate the uncertain nonlinear term,and the fractional-order adaptive law is designed to update the weight vector of network online.By combining the command filter and backstepping method,the commensurate fractional-order adaptive neural network command filtered backstepping controller is designed.Further,by adding a switching term with an exponential function to the right end of the filter error compensation equation,the error compensation mechanism of command filter is improved,and the filtering error is compensated in finite-time.To improve the dynamic characteristics of sliding surface,a new fractional-order integral sliding mode surface is constructed by using a function with the characteristics of ”large-error small-gain and small-error large-gain”.The adaptive neural network command filtered backstepping sliding mode controller is designed by combining sliding mode control and backstepping method.The simulation results show the effectiveness of the proposed approach.4.For incommensurate fractional-order systems,an incommensurate fractional-order command filtered backstepping control method is derived.The fractional-order model is transformed into a continuous frequency distribution model,and the integral Lyapunov function is designed to proof the stability of the closed-loop control system based on the frequency distribution model.Furthermore,the position tracking control issue of the incommensurate fractional-order PMSM is studied.For the problems of unknown parameter,load torque disturbance and input saturation of fractional-order PMSM,considering the immeasurable state of system with uncertain function,a fractional-order observer is established by combining adaptive neural network and K-filter.The auxiliary system is developed to solve the input saturation problem,and the structure of fractional-order Levant command filter is improved.Finally,an observer-based adaptive neural network control via command filtered backstepping is presented.The effectiveness of the proposed method is shown by simulation results.5.For the problem of position asymptotic tracking control of incommensurate fractionalorder PMSM with parameter uncertainties,external load disturbance and input saturation,based on the sliding mode control technology,an incommensurate fractional-order adaptive neural network command filtered backstepping sliding mode control method is proposed.To overcome the incommensurate fractional-order in the derivation process of command filtered backstepping method,a new fractional-order integral sliding mode surface is designed.For the uncertain part of the system,the neural network with its weight being updated online is accepted to eliminate restrictions on the uncertain nonlinear functions,and a new error compensation mechanism is designed by using the adaptive technique,which the upper bounds of the approximation error and the filtering error are estimated,then the compensation law is constructed.Integrating fractional-order auxiliary system,improved command filter into backstepping method,the controller design of incommensurate fractional-order adaptive neural network command filtered backstepping sliding mode is completed,and the stability of the closed-loop system is analyzed.Simulation is provided to show the effectiveness of the approach.6.The PMSM test platform is established.By taking digital signal processor(DSP)as the control chip,the embedded coding library in MATLAB/Simulink is used to build the low level driver model and complete the software design.The executable code is generated by the automatic code generation tool,which is downloaded to the DSP development board,and the driver board is cooperated with each other to control the PMSM.