Time-delay control with switching action using a frequency-shaped integral sliding surface

Abstract

The Time Delay Control with switching Action (TDCSA) method was recently proposed as a promising technique in a robust control area, where a plant has unknown dynamics with parameter variations and substantial disturbances are present. When TDCSA is applied to a nonlinear system with frequency resonances, TDCSA reveals a chattering problem or an undesired vibration. This undesired vibration and chattering problem comes from the switching action and high gains. Fast sliding mode dynamics or fast desired error dynamics improve the control performance, but excite the un-modeled resonance modes and cause an undesired vibration or chattering. To solve this problem, we proposed an integral sliding surface design method using frequency-shaping features. This method incorporates frequency-shaping LQ design techniques into an integral sliding surface. In this paper, the stability analysis of TDCSA using a frequency-shaped integral sliding surface is analyzed. Based on the experimental results, the frequency-shaped integral sliding surface was shown to be practicable for a single-link flexible arm. Motion control of a single-link flexible arm with un-modeled flexible modes was taken into account. The desired trajectory was tracked while minimally exciting the un-modeled flexible modes.