一般受控系統常因外在的干擾或系統不確定性，使得系統輸出響應偏離設計期望，強健控制的的探討變成近代控制主要研究項目。另一方面，強健控制問題可以轉化成一個求解線性矩陣不等式問題 順滑模態控制以其強健性有名，在其順滑運動過程中，系統軌跡對於匹配式雜訊具有強健性。
本文結合線性矩陣不等式的方法，設計具有強健性與無顫震的順滑控制應用於壓電驅動平台。在控制架構方面，本文以前饋控制架構並配合無顫震順滑控制器型式之回饋控制器，實現高精度之定位控制。利用已有的磁滯模型，數值模擬與實驗結果比對，顯示本文能滿足定位和追蹤上的目標。

Owing the factors of some modeling errors, the variations of paramater, and the external disturbance, that make the failure of achieving controlling and even let the system unstable. So, it is necessary to design a robust controller. In other words, the problem of the robust controller can be transformed into linear matrix inequality (lmi) problem, and it is able to be solved by lmi. Sliding mode control is well-known for its robustness. As a system trajectory lies on the sliding surface, the control shows obvious resistant in matched disturbance.
The dissertation will introduced to design a extended system which is no chattering by using lmi and sliding mode control. With the obtained model, the control structure composed of a feedforward controller and a extended system feedback controller is used to realize the high precision positioning control of the piezo driven stage. Comparaed the simulation and the experimental results, it shows the tracking and regulated aims in this study have been satisfied.

U.Itkis,“Control Systems Of Variable Structure”, New York;John Wieley, 1976.
Sira-ramirez Heberrt.(1993). On The Dynamical Sliding Mode Control Of Nonlinear System. INT, J. Control,Vol. 57, 1039-1061.
Lee Ju-Jang and Xu Yangsheng.(1994). A New Method Of Switching Surface Design For Multivariable Variables Structure Systems. IEEE, Transactions On Automatic Control, Vol. 39,No.2,pp.414-419..
Bonnie S.HECK,SUBBARVO V. Yallapragada and Michael K.H. Fan.(1995) .Numerical Methods To Design The Reaching Phase Of Output Feeback Variable Structure Control. Automatica,Vol.31,pp. 275-279,1995
Choi.H. H.(1997). New Method For Variable Structure Control Systems Design:A Linear Matrix Inequality Approach. Automatcia,Vol. 33,pp. 2089-2092,1997
Choi H.H.(1998). Variable Structure Outputfeedback Control Design For A Class Of Uncertain Dynamic Systems. Automatcia, Vol. 38,pp. 335-341.
Choi.H. H.(1999). On The Existence Of Linear Sliding Surfaces For A Class Of Uncertain Dynamics Systems With Mismatched Uncertainties. Automatcia, Vol. 35,pp. 1707-1715.
Christopher.E.,Ashu.A. and Sarrh K.Spurgeon.(1999).Sliding-Output Feedback Controller Design Using Linearmatrix Inequality. IEEE, Transactions On Automatic Control, Vol. 46,pp. 115-119.
Jame Law,and,Yong-Yan Cao.(1999). Simultaneous Linear-Quadratic Optimal Control Design Via Static Output Feedback. Int .J. Robust Nonlinear Control,Vol.9,pp.551-558.
Croft D. & Devasia. S.(1998). Hysteresis and Vibration Compensation for Piezoactuators. Journal of Guidance, Control and Dynamics, 710-717,1998
Choi.H. H.(2003). An LMI-Based Switch Surface Design Method For A Class Of Mismatched Uncertain Systems.,IEEE, Transactions On Automatic Control, Vol.48,pp1634-1638.
P.Gahinet, A.Nemirovskii, A. J. Laub, and M.Chilali.(1995). LMI Control Toolbox, The Matbworks, Inc.
C.L. Chen and W.Y. Lin, (1997).Siding mode control for nonlinear systems with global invariance. Journal of Systems and Control Engineering, Institute of Mechanical Engineers, Vol.211, Part I, pp.75-82.
C.L. Chen and R.L. Xu, (1999).Tracking control of robot manipulator using sliding mode controller with performance robustness. Journal of Dynamic Systems, Measurement and Control, Trans. ASME, Vol.121, March, pp.64-70. (EI, SCI)
李傑仁,“具非對稱型磁滯系統控制及其於壓電驅動平台定位控制之應用”,國立成功大學航太太空研究所碩士論文,2003