RESO-based backstepping control of nonlinear systems preceded by hysteresis in piezoelectric actuators

Aiming to address hysteresis in nonlinear systems, a reduced-order extended state observer (RESO)-based command-filtered backstepping controller is proposed in this paper. First, both the hysteresis and disturbance of the system are estimated by the RESO as extended state variables. On this basis, the tracking error is set within a predefined range by utilizing the logarithmic barrier Lyapunov function (BLF), so that the error convergence speed is accelerated and the trajectory tracking accuracy is ensured. Then, the command filter is applied to obtain the virtual control signal and its derivative, which can not only avoid the problem of calculation explosion caused by the repeated derivation of control variables in the conventional backstepping control method, but also simplify the controller design. Finally, an error compensation mechanism is introduced to construct system variables by using the errors between the control variables and the filter output to reduce the influence of the error of the command filter on the tracking accuracy. Compared with the ESO backstepping control, simulation and experimental results illustrate the effectiveness of the proposed control method.