非線性積分順滑模容錯控制及其應用

Abstract

本論文探討基於積分順滑模控制策略之非線性系統主動式容錯控制(active fault-tolerant control，active FTC)設計問題。透過對於積分型順滑模控制設計之改造，我們提出了一種適用於非線性仿射系統(nonlinear affine systems)之積分順滑模容錯控制律(ISMC-based FTC law)。由於現存的積分順滑模容錯控制研究成果僅適用於一類n 組非線性二階仿射系統(a class of n second-order nonlinear affine systems)，故本論文所提出之設計方法涵蓋了現存之結果。在所提之控制方法下，受控系統被證明了可保有傳統順滑模控制(sliding mode control)的優點，包含反應快速、易於實現與強韌的穩健特性；再者，我們也證明了在所提出的控制律下，對於每一種容許損壞之情況，匹配型不確定(制動器)錯誤系統(matched uncertain (actuator) faulty system)的狀態響應會與其對應之標稱健康子系統(nominal healthy subsystem)的狀態響應一致。因此，對於每一種容許損壞之情況，設計者可根據其對應之標稱健康子系統之狀態性能(state performance)事先地對於不確定錯誤系統之狀態性能進行規範與設計。為了驗證所提出之控制方法的有效性，我們將其應用到車輛煞車容錯控制的問題上，模擬結果充分驗證了所提設計的有效性與特點。

雖然上述所提之積分順滑模容錯控制律能夠使得閉迴路系統具有理想的狀態性能，但其設計必須經過較繁複的程序，即必須針對每一種容許損壞之情況下的標稱健康子系統進行控制律設計。為了有效降低設計的複雜度，在此論文的第二部分我們進一步提出了一種改良型積分順滑模容錯控制律(improved ISMC-based FTC law)。在此改良型容錯控制方法下，欲達成控制目的所需要的理想控制力(desired control effort)能夠被自動地分配到良好無損壞的制動器，藉此降低了設計複雜度，並能使得閉迴路系統(closed-loop system)不論處於良好無錯誤的運作(nominal/fault-free operations)或某些可容許錯誤之情況(allowably faulty situations)下，其狀態響應都會與一個預先選定系統(preselected system)的狀態響應十分接近。因此，設計者可事先地預測在各種運作情況下閉迴路系統所具有的同一種狀態響應；值得注意的是，此項優點在現存的非線性容錯控制方法當中較難被達成。最後，所提出之改良型方法也被應用於衛星姿態穩定化容錯控制的議題上，並成功地展示了該方法的有效性與優點。

This dissertation addresses the issue of nonlinear active fault-tolerant control (FTC) design using the integral sliding mode control (ISMC) strategy. By revamping the ISMC technique, an ISMC-based FTC law is first proposed for a class of nonlinear affine systems, which covers the existing ISMC-based FTC results because only a class of n second-order systems was considered previously. With the presented scheme, it is shown that the advantages of conventional sliding mode control design can be retained, including rapid response, ease of implementation and high robustness to model uncertainties and/or external disturbances; moreover, the state responses of each matched uncertain allowably (actuator) faulty system and its corresponding nominal healthy subsystem are shown to be identical. As a result, designers can predictively address the state response of each matched uncertain allowably faulty system in light of the performance of its corresponding nominal healthy subsystem, which can be pre-determined. To verify the effectiveness of the proposed FTC scheme, the analytic results are also applied to a vehicle brake FTC system. Simulation results clearly demonstrate the effectiveness and benefits of the presented scheme.

Though the aforementioned FTC scheme can achieve satisfactory performances for closed-loop systems, it suffers from a complicated design procedure because it needs to organize the control laws for every nominal healthy subsystems in different allowably faulty condition. To mitigate the design burden, an improved ISMC-based FTC scheme is presented in the second part of the dissertation. The improved scheme not only can simplify the design procedure, but also has the flexibility to preselect a (sub)system and design its control law so that the state responses of closed-loop systems for normal (fault-free) operation and differently allowably (actuator) faulty situations are almost the same as that of the preselected system, because the improved scheme is shown to have the ability to automatically distribute the desired control effort to healthy control channels (actuator). Consequently, designers can predict a same state response of the closed-loop systems regardless of systems’ operation conditions, which is not easy to be realized by existing results. Finally, the improved scheme is also utilized to investigate the fault-tolerant issues of the attitude stabilization control of a spacecraft, and the simulation results clearly show the effectiveness and advantages of the improved FTC scheme.