A novel discrete-time sliding mode technique and its application to a HDD dual-stage track-seek and track-following servo system

A novel approach for the design of a discrete-time sliding mode controller is presented showing that the dynamics of a sliding-mode state feedback controller can be designed using a singular LQR-approach. The weighting of the control signal is set to zero and dead-beat behaviour for the sliding mode reaching dynamics is achieved. The reaching dynamics are modified when the states are a significant distance away from the sliding surface to avoid any high magnitude control action due to the partial dead-beat approach. The control law also takes into account constraints on the actuator amplitudes and a stability analysis is presented using a discrete-time version of the Popov criterion. The control approach is demonstrated in conjunction with a recently developed large-span track-seeking and track-following method for dual-stage actuator systems in a hard disk drive. It is shown how the discrete-time sliding mode control scheme can be incorporated into the observer based control system for the secondary actuator. Superior performance for the track-seeking and track-settling process is demonstrated using an existing practical set-up of a dual-stage hard disk drive servo-system.