機器人或機械手臂系統是一個高度非線性的多變數系統，在實際的工作環境下，外在的不確定性勢必對系統性能造成一定程度的影響，例如工作任務下的負載改變、或者是致動馬達的輸入干擾等。
本研究將針對機械手臂系統，在外擾或物理參數不確定性的影響之下，綜合「計算扭矩法」與「H∞最佳控制-變異漸近法」，設計一個非線性的強健控制器。計算扭矩法其優點在於將機械手臂系統回授線性化；而H∞控制理論的特點在於具備對干擾及不確定性的強健性，同時也能使控制能量及控制誤差最佳化。因此本文的研究設計，不但可以簡化複雜的機械手臂數學模型，也能達到最佳控制。
文末將以一個雙關節軸機械手臂為範例，在各種不同外在環境條件下，驗證所設計控制器的控制成果。

Robots or manipulator systems usually contain high nonlinearities and are classified as multi-variable systems. In many realistic environments, system performance is very sensitive to external disturbances or uncertainties: such as disturbance in actuators and the change of payload due to tasks...etc.
In this article, a robust design procedure composed of the “computed torque method” and “H∞-optimal control methodology” is proposed to achieve the desired performance by rejecting system disturbances and uncertainties.
The well-known “computed torque method” simplifies the complicated mathematical models of robot manipulators by the feedback linearization strategy. And the H∞-optimal control method can not only maintain the system robustness while encountering disturbances or uncertainties, but also lead to get an optimization result by weighting the controlled outputs and resulting a trade-off point between control energy and tracking errors.
In this research, a two-link rotary robot manipulator example is illustrated in computer simulations to attest the feasibility of the proposed control methodology under various external disturbances and parameter uncertainties.

【1】Bejczy, A.K., “Robot Arm Dynamics and Control”, Technical Memo, Jet Propulsion Laboratory, [1974].
【2】Chen, C.T., “Linear System Theory and Design”, Oxford University Press, [1999].
【3】Doyle, J.C., Glover, K., Khargoner, P.P., and Francis, B.A., “State-Space Solution to Standard H2 and H弃 Control Problem”, IEEE Trans. Automatic Control, Vol. 34, No. 8, pp. 831-847, [1989].
【4】Fu, K.S., Gonzalez, R.C. and Lee, C.S.G., “Robotics: Control, Sensing, Visions, and Intelligence”, McGraw-Hill International Edition, [1987].
【5】Hwang, C.N., “Design of Robust Controllers for Manipulators”, Journal of National Cheng-Kung University, Vol. 26, [1991].
【6】Hwang, C.N., “Formulation of H2 and H-Infinity Optimal Control Problems - A Variational Approach”, Journal of Chinese Institute of Engineers, Vol. 16, No. 6, [1993].
【7】Hwang, C.N., “Synthesis Procedure for Nonlinear Systems”, Proceedings of the NSC (National Science Council), R.O.C., Vol. 17, No.4, pp.279-294, [1993].
【8】Hwang, C.N., “A Variational Approach to H2 and H-Infinity Control Problems for Linear Nonautonomous System”, Proceedings of the NSC (National Science Council), R.O.C., Vol. 19, No.5, pp.408-422, [1995].
【9】Lee, G.W. and Cheng, F.T., “Robust Control of Manipulators Using the Computed Torque Plus H-Infinity Compensation Method”, IEE Proceedings-Control Theory Applications, Vol. 143, No. 1, [1996].
【10】Orin, D.E. and Shrader, W.W., “Efficient Computation of The Jacobian for Robot Manipulators”, The International Journal of Robotics Research, Vol. 3, No. 4, [1984].
【11】Ortega, M.G., Vargas, M., Vivas, C,, Rubio, F.R., “Robustness Improvement of a Nonlinear H-Infinity Controller for Robot Manipulators via Saturation Functions”, JOURNAL OF ROBOTIC SYSTEMS, Vol. 22, No. 8, [2005].
【12】Paul, R.P., “Robot Manipulator: Mathematics, Programming and Control”, MIT Press, Cambridge, Mass, [1981].
【13】Slotine, J.-J.E., Li, W., “Applied Nonlinear Control”, Prentice Hall, [1991].
【14】Spong, M.W., Lewis, F.L., and Abdallah, C.T., “Robot control: Dynamics, Motion Planning, and Analysis”, Institute of Electrical and Electronics Engineers, [1993].
【15】黃正能、林芳民，“機械手臂之適應H∞控制設計”，國立成功大學系統暨船舶機電工程研究所碩士論文，[2008]。
【16】楊憲東、葉芳柏，“線性與非線性H∞控制理論”，全華科技圖書股份公司，[1997]。