臺灣博碩士論文加值系統

模型預測控制亦可稱為移動區間控制，在工業界中是相當受注目的控制策略之一，它的控制概念即在每一個取樣時間，最佳化一個目標函數。然而在大多數的相關研究中，預測控制都局限於處理線性的系統，但在物理系統中有許多都是非線性系統。對於非線性系統，在近幾年中T-S模糊模式已被廣泛的使用，此方法可近似或完整的表示原非線性系統。在本論文中，我們將結合模型預測控制策略與T-S模糊模型方法來處理非線性系統。在設計控制器的過程中，發現模糊控制器的等級函數與系統之穩定性無關，故利用類神經網路調整此等級函數以獲取較快速的暫態響應。此論文另一重點乃介紹所謂虛擬預期變數綜合法來完成輸出追蹤控制。此設計方法的優點可在一個拖車系統的例子中明確地展現出來。雖然拖車系統是一個單輸入控制的系統，但是我們透過單一的控制架構即可控制不同的輸出，因此在不改變控制架構下，我們可適當地切換追蹤輸出值以達成饒富意思的控制任務。最後探討追蹤控制在狀態不可量測的問題，這裡我們知道很多物理系統的模糊集合的歸屬函數是滿足Lipschitz-like的特性。如果滿足前述條件，便可利用分離原理分別設計模糊控制器與模糊估測器，再由線性矩陣不等式求得控制增益及估測增益。在數值模擬方面，以H'enon map和拖車系統為例子來驗證理論的結果。

Model predictive control (MPC) is also known as receding horizon control (RHC) or moving horizon control (MHC). It is the most popular industrial control strategy, based on the idea of optimizing an objective function at each sampling. Although, many physical models are nonlinear, most researches on this issue are limited to linear systems. Recently, the Takagi-Sugeno (T-S) fuzzy
approach has been used to model nonlinear systems using the decomposition of a nonlinear system into a set of linear subsystems. In this thesis, we will combine the T-S fuzzy model with the MPC strategy to deal with nonlinear systems. Since the
grade functions of the fuzzy controller are independent to the system, in our control design we will update the grade functions via neural networks to achieve the better system performance. In addition, we will discuss the output tracking control based on output feedback design. To this end, the new concept, virtual-
desired-variable (VDV) synthesis will be presented. The advantage of using the VDV synthesis is fully illustrated when we consider
the example of the truck-trailer system. Although the system is only with a single input, we can control the different outputs via
a unified manner. Therefore, we can switch the desired output arbitrarily without changing the control structure. Finally, observer-based control design is proposed to cope with the
immeasurable state variables. For the most parts we focus on a common feature held by many physical systems where their
membership functions of fuzzy sets satisfy a Lipschitz-like property. Based on this setting, control gains and observer gains
can be designed separately. Two different types of systems, H'enon map and truck-trailer systems are considered to demonstrate the design procedure using satisfactory numerical simulation results.

Contents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Contribution of this Thesis . . . . . . . . . . . . . . . . . . . . . . .4
1.4 Organization of this Thesis . . . . . . . . . . . . . . . . . . . . . . .5
2 Fuzzy Model Predictive Control 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Discrete-Time T-S Fuzzy Model . . . . . . . . . . . . . . . . . . . . . 7
2.3 Model Predictive Control . . . . . . . . . . . . . . . . . . . . . . . .10
2.4 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Input Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Updating grade Functions Via Neural Networks 24
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Back-Propagation Network . . . . . . . . . . . . . . . . . . . . . . . .25
3.3 Nonlinear Truck-Trailer Dynamics . . . . . . . . . . . . . . . . . . . 27
3.3.1 Scenario (I): v is constant . . . . . . . . . . . . . . . . . . . . 30
3.3.2 Scenario (II): v is time-varying . . . . . . . . . . . . . . . . . . 31
3.4 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 32
4 Basic Fuzzy Tracking Control 39
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Output Tracking Control . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Constraint of Generalized Kinematics . . . . . . . . . . . . . . . . . 41
4.4 Application on the Truck-Trailer System . . . . . . . . . . . . . . . 42
4.4.1 Task I: Tracking the Straight Line . . . . . . . . . . . . . . . 43
4.4.2 Task II: Tracking the Constant Angle . . . . . . . . . . . . . 44
4.5 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 45
5 Tracking Control Design with Observer 51
5.1 Introduction . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .51
5.2 Observer-Based Output Tracking Control . . . . . . . . . . . . . . . . 51
5.3 Design Based on Separation Principle . . . . . . . . . . . . . . . . . 54
5.4 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . .. . 56
5.5 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.5.1 Simulation for H enon map . . . . . . . . . . . . . . . . . . . . 60
5.5.2 Simulation for truck-trailer system . . . . . . . . . . . . . . . 61
6 Conclusions and Future Works 69
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
6.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
References 71


List of Figures
1.1 process of driving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 MPC scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 MPC strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Finite and in nite horizon . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Control gain of example 1 with no input constraints . . . . . . . . . . 18
2.4 State response and control input of example 1 without input-constraints 19
2.5 Control gain of example 1 with input constraints -0.45 u 0.45... 20
2.6 State response and control input of example 1 with input constraints -0.45 u 0.45 . . . . . . . . . . . . . 20
2.7 Control gain of example 2 without input constraints . . . . . . . . . . 21
2.8 Control gain of example 2 without input constraints . . . . . . . . . . 21
2.9 State response and control input of example 2 without input-constraints 22
2.10 Control gain of example 2 with -0.25 u 0.25????. . . . . . . . 22
2.11 Control gain of example 2 with -0.25 u 0.25. . . . . . . . . 23
2.12 State response and control input of example 2 with input-constraints -0.25 u 0.25 . . . . . . . . 23
3.1 MPC incoporating NNs . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Flow chart of neural networks . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Con guration of a truck-trailer system . . . . . . . . . . . . . . . . . 29
3.4 Control gains of scenario (I) . . . . . . . . . . . . . . . . . . . . . . . 33
3.5 Control gains of scenario (I) . . . . . . . . . . . . . . . . . . . . . . . 34
3.6 State responses and control input of Scenario (I) . . . . . . . . . . . . 34
3.7 Trajectories of Scenario (I): (A) MPC (B) MPCNN . . . . . . . . . . 35
3.8 Control gains of scenario (II) . . . . . . . . . . . . . . . . . . . . . . 35
3.9 Control gains of scenario (II) . . . . . . . . . . . . . . . . . . . . . . 36
3.10 Control gains of scenario (II) . . . . . . . . . . . . . . . . . . . . . . 36
3.11 Control gains of scenario (II) . . . . . . . . . . . . . . . . . . . . . . 37
3.12 State responses and control input of Scenario (II) . . . . . . . . . . . 37
3.13 Trajectories of Scenario (II) (A) MPC (B) MPCNN . . . . . . . . . . 38
4.1 Crash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Coordinates of bridge and desired path . . . . . . . . . . . . . . . . . 45
4.3 Control gain of task (I) . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4 Control gain of task (I) . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.5 State response of task (I) . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.6 Trajectories of task (I) . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.7 Control gain of task (II) . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.8 Control gain of task (II) . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.9 State response of task (II) . . . . . . . . . . . . . . . . . . . . . . . . 49
4.10 Trajectories of task (II) . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.1 An orbit of the H enon map . . . . . . . . . . . . . . . . . . . . . . . 60
5.2 Observer gains of H enon map . . . . . . . . . . . . . . . . . . . . . . 62
5.3 Response of x1, x1d and ^x1 for H enon map . . . . . . . . . . . . . . . 63
5.4 Response of x2, x2d and ^x2 for H enon map . . . . . . . . . . . . . . . 64
5.5 Control input for H enon map . . . . . . . . . . . . . . . . . . . . . . 64
5.6 An orbit of the controller H enon map . . . . . . . . . . . . . . . . . 65
5.7 Observer gains of truck-trailer system . . . . . . . . . . . . . . . . . 65
5.8 Observer gains of truck-trailer system . . . . . . . . . . . . . . . . . 66
5.9 Response of x1, x1d and ^x1 for truck-trailer system . . . . . . . . . . . 66
5.10 Response of x2, x2d and ^x2 for truck-trailer system . . . . . . . . . . . 67
5.11 Response of x3, x3d and ^x3 for truck-trailer system . . . . . . . . . . . 67
5.12 Control input for truck-trailer system . . . . . . . . . . . . . . . . . . 68
5.13 Trajectories for truck-trailer system . . . . . . . . . . . . . . . . . . . 68

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