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

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