Abstract
A discrete-time sliding-mode control scheme for a certain class of systems is proposed to guarantee the existence of sliding-mode as well as to alleviate the chattering. Firstly, a process using auxiliary compensator is introduced and the explicit condition to ensure the one-sided behavior, deadbeat sliding-mode and quasi-sliding mode is derived, which is merely an inequality constraint on controller parameters. This condition also guarantees that the state trajectory starting from any initial condition, will reach the boundary layer of the switching surface in a finite number of steps. Moreover, the controller parameters can be determined via the correlation between the pole location in the z-plane and the time-domain response characteristics. Next, a robust discrete-time sliding-mode approach for a class of perturbed systems is proposed. To overcome the difficulty of conservative design due to over-estimated upper bounds on system perturbations; the discrete-time sliding-mode control law employs a smooth function to alleviate the chattering phenomenon. Conditions for stability are analyzed and given. Also, an estimated reaching time can be pre-calculated. Finally, we propose a discrete-time hierarchical sliding-mode approach for dual-stage systems. Here, we combine the dual-stage positioning servo design phase into only one stage. Therefore, the performance of the coarse tracking and fine tracking stages can be ensured simultaneously. The settling time of the controlled positioning system can be assigned through the choice of a pre-specified sliding hyperplanes. Hence, the proposed methodology can avoid the drawbacks of mode switching control design, such as discontinuity in control input, incompatible dynamic characteristics, and difficulty in estimating the overall settling time and is easy to be implemented for practical applications. Simulation and experimental studies of an uninterruptible power supply control systems, seek control of an optical pick-up head and the dual-stage positioning servo systems are performed to validate the feasibility and the effectiveness of these approaches.