基於T-S模糊模型之順滑模態可靠度控制與離散時間模型之準順滑模態控制的研究

Abstract

本篇論文主要在探討對於T-S模糊模型化連續時間非線性系統的順滑模態控制和順滑模態可靠度控制以及對於離散時間非線性系統的準順滑模態控制的設計和應用。順滑模態控制具有下列優點：如反應快速、對系統的不確定參數及雜訊不敏感、容易設計等等。而在另外一方面，T-S模糊模型已被學者證實為全近似器，可以無限逼近一非線性系統。實際上，T-S模糊模型的建構方式簡單容易，而且當原始非線性模型極為複雜時，T-S模糊模型可以幫助節省針對原始系統非線性項做控制器設計的運算時間。由於T-S模糊模型和順滑模態控制特殊的優點，這篇論文主要使用這兩種整合的方法來研究一種二階系統的穩健的控制器。這種整合的方法同時具有兩種方法的優點。首先，由於大部分藉T-S模糊模型的系統參數可由不在線運算而獲得，所以T-S模糊模型可以結省在線的運算時間。第二，此法可以保留順滑模態控制中的優點如：快速響應和穩健特性。除此之外，本論文提出的方法並不需要在線計算任何原始非線性動態的非線性項，而且增加模糊規則數並不會增加額外的在線計算負擔。在這種設計下，追蹤控制目的可以被達成，而且即使當某些制動器不能正常運作時，具有可靠度設計的穩定控制可以安全地進行運作。在另一方面，針對一類非線性控制系統的準順滑模態控制策略也在此論文中被討論。研究顯示這種控制策略不只可以達成穩定控制，也可以在不增加控制負擔的情形下減輕振顫的現象。本論文所提出的控制設計方法，也應用到許多實際的動態系統，包括有機器手臂控制，衛星姿態穩定的可靠度控制，拖車系統等等。這些模擬結果也說明了本論文所提出相關理論的優點和可行性。

This dissertation investigates the Takagi-Sugeno (T-S) fuzzy model- based sliding mode control (SMC), T-S fuzzy model- based SMC reliable design for continuous-time nonlinear control systems, and the quasi-sliding mode control (QSMC) for discrete-time nonlinear control systems. The SMC methods involve many advantages, such as fast response, small sensitivity to system uncertainties/disturbances, and easiness for design. On the other hand, T-S fuzzy model has been proved as a universal approximator, which can infinitely approximate and completely represent a nonlinear system theoretically. In reality, the construction for a T-S fuzzy model is simple, and this model can help save the operating time for calculating nonlinear terms, especially when the original nonlinear system is very complex. In light of the remarkable benefits of the T-S fuzzy system modeling method and the SMC technique, this dissertation proposes the design of robust controllers for a set of second-order systems using a combination of these two approaches. The combined scheme is shown to have the merits of both approaches. It not only alleviates the on-line computational burden by using the T-S fuzzy system model to approximate the original nonlinear one (since most of the system parameters of the T-S model can be computed off-line) but it also preserves the advantages of rapid response and robustness characteristic of the classic SMC schemes. In addition, the combined scheme does not need to on-line compute any nonlinear term of the original dynamics, and the increase in the number of fuzzy rules does not create extra on-line computational burdens for the scheme. Under the design, the tracking control mission can be achieved and the stabilization mission for reliable control can continue safely without prompt external support even when some of the actuators fail to operate. On the other hand, the QSMC scheme for a class of discrete-time nonlinear control systems has been proposed in this dissertation. It was shown that the scheme not only achieves the stabilization performance, but it also alleviates chatter without creating an extra control burden. The obtained analytical results are first applied to a two-link robot manipulator, and compared with the results of classic SMC design. Second, they are applied to the attitude stabilization of reliable control for a spacecraft. Finally, a trailer-truck system is illustrated to demonstrate the QSMC concept for a nonlinear control system. Simulation results demonstrate the benefits and feasibility for the proposed theories.