Adaptive Command Filter Comtrol For Nonlinear Systems With Input Backlash

In the design of nonlinear system control scheme,nonlinear link such as backlash,friction and unknown disturbances cause negative influence on the closed-loop output signal tracking effect.Specifically,the backlash produces torque delay in a certain period of time,which will lead to undesired tracking errors of controlled system,and the impact in gear direction changing causes disturbance signals.Therefore,how to utilize adaptive control algorithm to compensate and suppress nonlinear links to improve the transient and steady-state performance of the system has been one of the focuses of control research.In this paper,the relationship between dead zone and backlash nonlinearity is analyzed by employing three common backlash models,which introduces their characteristics and application scenarios.Moreover,one studies how to realize the accurate and fast tracking of reference signal in backlash servo system.The neural network is used to fit the system uncertainty and the nmodeled dynamic in real time.With the help of the performance of the extended state observer which can observe the feedback of the "total disturbance" in real time and based on the structural characteristics of the controlled system,one designs the adaptive command filter controller.The stability and effectiveness are proved by theoretical analysis and simulation experiment.1.An adaptive command filter control of nonlinear system with input friction is formulated in this paper.First,based on the obtained state space model,a command filter control method is proposed,which can address the “explosion of complexity” problem existed in traditional backstepping design and ensure the asymptotic convergence of the tracking errors.Then,dynamic error compensation system is designed to cope with the problem of filter error between filter output and virtual control signal.Next,a HONN system is employed to simplify the calculation and approximate the uncertainties in the system.At last,simulation results are given to clarify the effectiveness of the above control theory.2.For nonlinear system subject to unknown control direction caused by input backlash,an adaptive command-filtered control strategy is presented in this work.The proposed control method not only overcomes “computational complexity explosion”inherent in traditional backstepping method,but also guarantees rapid convergence of tracking error.Meanwhile,a salient characteristic of command-filtering error is that the finite convergence time is assigned in a prior,which is proved by Lyapunov stability method.Especially,unknown control gain caused by input backlash of controlled system is handled by Nussbaum-type function.3.In this study,a finite-time adaptive prescribed performance control scheme is investigated for multi-input multi-output systems with input friction and backlash.Derived from the structure of fixed-time high-order exact differentiator,fixed-time command filter and fixed-time disturbance observer are constructed to ensure fast response of the controlled systems with setting time being determined regardless of initial states.During the period of gears contact,backlash nonlinearity is regarded as input friction effect and system disturbance.The system uncertainties caused by unknown smooth functions are handled by neural network approximators,then input friction and system disturbances are accurately compensated by fixed-time disturbance observers.Meanwhile,the proposed fixed-time command-filters are utilized to avoid repeated differentiation of virtual control signals during controller design.In particular,prescribed convergence of tracking errors for multi-input multi-output nonlinear system is ensured by finite-time performance function.