本文主要目的在於提出新的離散時間順滑模式控制器設計法則，以期改善傳統順滑模式控制器的性能與克服其在數位化之實際應用上所面臨的一些難題。因此本設計法則不但要求能夠確保順滑模式之產生、系統狀態軌跡於有限取樣週期到達預設順滑層，同時具有減輕或消除抖振現象之能力。
首先引進一輔助控制器設計概念，推導出其結合傳統順滑模式控制之穩定條件，依據此條件，控制器參數可以經由z-平面之極-零點配置法則來決定。只要適當選取此參數，即可使系統具有：單邊、無振盪的及準順滑模式響應行為。其次，針對一有界干擾之系統，提出一強健且平滑的順滑模式控制器設計技巧，並使用一平滑函數來替代傳統開關補償行為。在系統擁有強健性能之前提下，只需調整一控制器參數即可達成減輕或消除抖振現象之目的。故可以有效克服傳統順滑模式控制因過保守估測擾動量於實際應用上所衍生之問題。

此外，本文針對雙階層結構之系統，提出階層式離散時間順滑模式控制器設計法則，此法則捨棄了傳統常用的「兩階段模式切換控制法」，直接將此兩階段式的設計理念合而為一，以階層式順滑模式控制器設計技巧取代之。控制系統的安定時間可以經由選取之順滑向量來決定，且可以同時滿足系統對粗調與微調追蹤性能之要求。因此，可以有效解決兩階段模式切換控制法之缺點，如系統動態不匹配、控制輸入不連續及安定時間計算困難等問題。

為進一步探究這些方法的可行性與有效性，本文將以上所提之設計法則，應用於不斷電系統與光碟機之尋軌伺服控制系統。由實驗結果顯示，本文所提之設計法則其共同優點為：具有強健性、能有效減輕或消除抖振現象及控制器設計與容易實現等。另就光碟機之尋軌控制而言，階層式法則還具有：可以克服系統之不動帶區間效應、縮短資料讀取時間、有效降低尋軌誤差與省掉長程尋軌控制時之阻尼調整程序等優點。

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.

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