陳美勇Mei-Yung Chen楊智翔Zhi-Xiang Yang2019-09-032015-2-162019-09-032015http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22GN060173021H%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/97126本研究主要在於結合指數律(exponential law, EL)於可變步長適應滑模控制器(variable step size adaptive sliding mode controller, VSSASMC)並應用於機械手臂的追跡。在設計控制器時考慮到機械手臂的不確定量與外界干擾,於是本研究選擇具有良好強健性的滑動模式控制器為主控制器。而滑動模式控制中有一設計參數為切換增益(switching gain),此參數必須大於系統的干擾和不確定量的上界(upper bound),但是通常我們並無法直接知道上界值只能通過重覆測試調整。為了使系統能夠應付未知邊界的不確定量與干擾,本研究加入適應控制調整滑動模式中的上界參數,使控制器能應付多變的情況。 而適應控制本身則會使系統響應變慢,因此引入了指數律使系統更快收斂。而指數律不只可以與滑動模式控制結合達到減小跳切現象的效果;同時也能和適應控制結合成可變步長適應控制,使適應律的步長依誤差而調整。並且通過Lyapunov函數及Barbalat引理證明系統穩定性。最後經由實驗驗證此控制器的性能。In this study, we design an adaptive sliding mode controller which is applied on trajectory tracking of robot arms. Consider the uncertainties and external disturbances of a robot arm, we choose the sliding mode control (SMC) to be major one. We need to decide a switching gain bigger than the upper bound of system uncertainty. Usually we can’t figure out the upper bound of system uncertainty, we only decide a switching gain by trials and errors. Therefore, we propose an adaptive control to tune the switching gain of SMC that would be able to handle the unknown disturbances and uncertainties. Subsequently, the adaptive control makes system transient response slowly, so we introduce an exponential law (EL) to make system transient response faster. We not only combine EL with SMC to reduce chattering, but also combine EL with adaptive control to be the variable step size adaptive control which step size is adjust by error. Then we proof the stability of system by Lyapunov function and Barbalat’s Lemma. Consequently, the experiment results show excellent performance of this controller.可變步長適應控制滑動模式控制機械手臂上界指數律variable step-size adaptive controlsliding mode controlrobot armupper boundexponential law應用可變步長適應滑模結合指數律演算法於機械手臂追跡之控制器設計Design a Variable Step-Size Adaptive Sliding Mode Controller with Exponential Law for Robot Arm Tracking