Performance Optimization Based Tracking And Synchronization Control For Multi-motor Driving Servo Systems

With the wide application of many large inertia and power systems in industry,the multi-motor driving servo system(MDSS)has become one of the key techniques and research hotspots in the field of the servo control system.However,the presence of the transmis-sion device may introduce diverse nonlinearities,such as backlash,friction and disturbances,which may reduce the system control precision.In addition,the synchronization among mul-tiple motors is another important factor which may influence the system control performance.Therefore,it is necessary to investigate the tracking and synchronization control of MDSS based on the performance optimization.To deal with the unknown system states,friction nonlinearity,backlash nonlinearity and coupling problem between the load and the motor,this paper integrates the K-filter observer,state and extended disturbance observer,neural network,prescribed performance function and adaptive bias torque into the dynamic surface control,optimal control,H_?control and optimal robust guaranteed cost control to achieve the load tracking and multi-motor synchronization of MDSS.The main contributions of this paper are summarized below:(1)A modified neural dynamic surface control(DSC)with an adaptive bias torque is proposed for the MDSS with backlash,friction and other disturbances.By introducing a continuous hybrid differentiator to replace the first-order filter in each step,a modified DSC is developed to improve the load tracking precision of MDSS.However,when the MDSS enters the backlash band,the load cannot be controlled by the above DSC.Thus,an adaptive bias torque is firstly proposed based on the prescribed performance function to guarantee the load controllability and further achieve the load position tracking of MDSS.In addition,the unknown dynamics including the friction and other disturbances are approximated by the wavelet echo neural networks and then compensated in the controller design.(2)An adaptive robust H_?control scheme is proposed for the MDSS with immeasurable states and unknown disturbances to achieve both the load tracking and multi-motor synchro-nization.The neural network is incorporated into the K-filter observer to estimate both the unknown states and disturbances,which can avoid the nonlinear influence on the observer and simplify the controller structure by employing the outputs of K-filter instead of the estimated states to derive the control action.Based on the above neural network K-filter observer,a H_?dynamic surface control with minimal learning parameter technique is designed to re-duce the number of neural network weights and further guarantee the tracking error satisfying H_?performance.Finally,the mean deviation coupling control strategy is applied into the distributed synchronization controller to achieve the fast synchronization among the motors without affecting the load tracking performance.(3)A cascade optimal control framework is presented for the MDSS with multi-variable,high-order,strong-coupling and nonlinear characteristics.By dividing the MDSS into a load subsystem and a multi-motor subsystem,a cascade optimal control framework including outer and inner loops is proposed.In this framework,the optimal tracking controller(OTC)and the optimal synchronization controller(OSC)can be designed individually by decomposing a comprehensive performance index.In order to construct the OTC,the backstepping approach is incorporated into the optimal control to make the load track a reference command;then,the OSC is developed via the mean deviation coupling control strategy to guarantee that all the motors'states can converge to their average value.In addition,the state and extended disturbance observers are combined with OTC and OSC to deal with the immeasurable states and the system uncertainties.The proposed control framework not only achieves the optimal control of the load tracking and multi-motor synchronization but also has a strong robustness to the system uncertainties.(4)A novel composite controller is proposed to achieve the prescribed performance of completely tracking errors for a MDSS with uncertainties and nonlinearities.The proposed controller contains a feedforward controller and a feedback controller.The feedforward con-troller is constructed by incorporating the prescribed performance function(PPF)and a state predictor into the neural dynamic surface control approach to guarantee the transient and steady-state responses of completely tracking errors within prescribed boundaries.Different from the traditional adaptive laws which are commonly updated by the system tracking error,the proposed predictor uses the prediction error to update the neural network(NN)weights such that a smooth and fast approximation for the unknown nonlinearity can be obtained with-out incurring high-frequency oscillations.Since the uncertainties existing in the system may influence the prescribed tracking performance and the estimation accuracy of NN,an optimal robust guaranteed cost control is designed as the feedback controller to make the closed-loop system robustly stable and further guarantee that the system cost function is not more than a given upper bound.Finally,based on a four-motor servomechanism platform,simulations and experiments are conducted to demonstrate that the proposed schemes can achieve both the load tracking and multi-motor synchronization of MDSS.Moreover,compared with other control schemes,the proposed control schemes can largely improve the transient and steady-state performances.