Non-Linear Bandwidth Extended-State-Observer Based Non-Smooth Funnel Control for Motor-Drive Servo Systems

This paper proposes a non-smooth funnel control (NSFC) strategy based on the extended state observer (ESO) for motor-drive servo systems with unknown dynamics. These unknown dynamics, including the modeling error, the external disturbances, and the nonlinear friction, are considered as a lumped disturbance. For estimating the unknown states and the lumped disturbance, a non-linear bandwidth extended state observer (NLB-ESO) is developed. The non-linear bandwidth designed using the Gaussian function and the position observation error can deal with the ``peaking value problem" caused by the high observer gains. Furthermore, a funnel error surface is proposed based on the non-smooth error transformation and incorporated into the dynamic surface control design procedure, where the NSFC can prescribe the position tracking error in a funnel region with small steady-state error and overshoot, and short adjustment time. The non-smooth funnel error surface also avoids the singular problem in controller design by selecting the non-smooth parameter. Moreover, the stability of the closed-loop control system with the NLB-ESO is guaranteed by the Lyapunov theory. Comparative simulations and experiments show that the proposed NSFC can prescribe the tracking error in a funnel and ensure better tracking performance.