隨著預測控制在工程、科學及經濟等領域中的廣泛應用,近年來,預測控制理論研究也有相當的進展。然而,預測控制利用線性模型進行線上多步預測設計,由於線上預測需要龐大計算量,此計算時間取決於系統維度與預測步數的大小而異,使得線上預測控制的應用範圍局限在小型或反應慢速的系統中,因此本文將針對此一問題進行改善。近幾年來,由於半導體製程技術的發展迅速,同時帶動控制系統相當大的影響,使得微處理器在功能與實用上有著顯著的躍進,因此由數位控制器所取代傳統類比控制器之嵌入式系統也是現今熱門的研究方向,於是控制理論在於探討數位控制與連續時間系統之間連結的相關研究也引起許多學者投入,本論文中所採用之MLD(Mixed Logic Dynamical)建模方法也有敘述這層關係。 在本論文中,為求減輕計算負荷,在控制架構中我們利用多參數規劃方法的模式預測控制(Model Predictive Control based on Multi-Parametric Programming),將所有系統狀態視為參數變數,透過線性規劃技巧事先計算出對應狀態空間之成本函數(Cost Function)得到最佳控制增益,將其計算結果儲存在對照表(Look-Up Table)中,便可使上述線上計算負荷簡化成線性函數查表,也就是以離線方式進行控制策略之應用,此法可應用範圍也隨之更加廣闊。在章節中,我們對閉迴路系統的穩定性分析加以敘述。最後,將此方法應用在三個系統上並呈現模擬結果,以證實其控制效果。 關鍵字:模式預測控制、成本函數、多參數規劃、線性規劃、最佳控制、對照表。
In the past few years, many researchers have been devoted to the optimal control and stabilization of hybrid systems and piece-wise affine (PWA) systems. Particu- larly, PWA framework can specify a broad class of hybrid models. After obtaining the mathematical model of plant, a control scheme based on optimal feedback con- trol of the system is presented. We discuss the optimal control problem and model predictive control (MPC) for discrete time systems in this thesis. Especially, we consider the optimal control problem with constraints on states and inputs. MPC utilizes an internal model of controller system to predict the future evo- lution of the system dynamic behavior over a finite horizon. A cost function is minimized to obtain the optimal control input sequence, which is applied to the plant by means of a receding horizon policy. MPC can be applied off-line by com- puting the feedback solution after solving a multi-parametric programming. The state-space is treated as a parameter, can be used to derive the PWA state feedback control law. The resulting control law is a PWA state feedback control law defined over a polyhedral partition of the state-space, which can be stored in a look-up ta- ble. Thus, the on-line computing of the resultant MPC controller can be simplified to a linear function evaluation of a look-up table.
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