The Development of Neural Network Based System Identification ...

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160 CHAPTER 6 NEURAL NETWORK BASED PREDICTIVE CONTROL SYSTEM respectively. The predicted output vector Ŷ and control trajectory ∆U for the MIMO case are defined as: Ŷ = [y 1 (k + 1|k) y 1 (k + 2|k) y 2 (k + 1|k) y 2 (k + 2|k) · · · y q (k + N p |k)] T ∆U = [∆u 1 (k) ∆u 1 (k + 1) ∆u 2 (k) ∆u 2 (k + 1) · · · ∆u m (k + N c )] T (6.2) The data vector R s that contains qN p set-points is defined by: ⎡ ⎤ 1 1 1 1 · · · 1 1 1 1 1 · · · 1 R s = . ⎢. . . . .. . ⎥ ⎣ ⎦ 1 } 1 1 1 {{ · · · 1 } qN p ⎤ r 1 (k) r 2 (k) = ¯R s r(k) (6.3) ⎢ . ⎥ ⎣ ⎦ r q (k) T ⎡ The first term of the objective function in Equation (6.1) is related to the minimisation of error between predicted output variables and predefined set-point. Subsequently, the second term in the objective function indicates the treatment of ∆U when minimising the objective function J(k). In Equation (6.1), the variable matrix R represents a diagonal matrix in the form of R = r w I mNc×mN c (r w ≥ 0). The constant r w is used as a tuning parameter for the desired closed-loop performance. The closer r w value to zero would cause the optimisation to prioritise the minimisation of error between the predicted output variables and the predefined set-points to the smallest value possible, without considering the magnitude and the smoothness of the control trajectory ∆U. In general, the implementation principle of NNAPC control shown in Figure 6.2 can be summarised as follows: 1. The internal dynamic model of the system is used to predict the future output response of the system. This model can be obtained and implemented either from off-line or on-line system identification algorithms. 2. Using instantaneous linearisation principle, a linear model is extracted from the NNARX model and converted to corresponding state space model. This state
6.3 PRINCIPLE OF INSTANTANEOUS LINEARISATION 161 space model obtained at every sampling instance is used to predict the future output response Ŷ over a specified prediction horizon N p. 3. A suitable reference trajectory R s is obtained from the specified output trajectory r(k) over a specified prediction horizon N p . 4. The cost function J(k) is constructed using the predicted response Ŷ and the reference trajectory, R s . 5. A set of future control trajectory ∆U is calculated by minimising the cost function J(k) to achieve the desired tracking response. 6. Apply the first element of the calculated future control trajectory ∆U as the actual control input to drive the system under consideration. 7. The procedure is repeated to calculate a new output prediction and future control trajectory using the sensor measurement at the next sample time. 6.3 PRINCIPLE OF INSTANTANEOUS LINEARISATION In order to implement the NNAPC scheme, the linearised NNARX model is extracted from the non-linear NN model (MLP, HMLP or Elman networks) at every time sample k. Given that a non-linear NN model of the dynamic system is: ŷ(k) = g [ϕ(k)] (6.4) where the regression vector is given as follows: ϕ(k) = [y(k − 1) · · · y(k − n y ) u(t − k) · · · u(k − n u )] T (6.5) The approximate linear model is obtained by linearising g(ϕ(k)) around the current state ϕ(τ). The linear model is given as follows: ỹ(k) = −a 1 ỹ(k − 1) − a 2 ỹ(k − 2) · · · − a ny ỹ(k − n y ) + b 0 ũ(k) + b 1 ũ(k − 1) + · · · + b nu ũ(k − n u ) (6.6)
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The Development of Neural Network B
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ABSTRACT This thesis presents the d
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vii the MLP network, the prediction
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PUBLICATIONS The following is a lis
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xiv TABLE OF CONTENTS CHAPTER 4 CHA
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LIST OF FIGURES 1.1 Examples of typ
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LIST OF FIGURES xix 3.13 Overview o
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LIST OF FIGURES xxi 5.2 The predict
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LIST OF FIGURES xxiii 5.13 The pred
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LIST OF FIGURES xxv 7.1 The locatio
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LIST OF TABLES 3.1 The specificatio
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NOMENCLATURE AFCS Automatic Flight
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LIST OF TABLES xxxi NNARX QP RBF RC
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2 CHAPTER 1 INTRODUCTION Surveillan
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4 CHAPTER 1 INTRODUCTION is then de
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6 CHAPTER 1 INTRODUCTION the dynami
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8 CHAPTER 1 INTRODUCTION models [Sa
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10 CHAPTER 1 INTRODUCTION improved
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12 CHAPTER 1 INTRODUCTION Chapter 3
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Chapter 2 LITERATURE REVIEW The pur
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2.1 INTRODUCTION 17 • Inefficient
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2.1 INTRODUCTION 19 Figure 2.2 The
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2.2 HELICOPTER DYNAMICS MODELLING A
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2.3 NEURAL NETWORK BASED SYSTEM IDE
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2.4 AUTOMATIC FLIGHT CONTROL SYSTEM
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2.5 SUMMARY 53 design based on the
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56 CHAPTER 3 AERIAL PLATFORM AND CU
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Chapter 4 NEURAL NETWORK BASED SYST
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4.2 THE ARTIFICIAL NEURAL NETWORKS
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4.3 SYSTEM IDENTIFICATION WITH NEUR
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Page 217 and 218: 7.2 FLIGHT TESTS IMPLEMENTATION 185
Page 219 and 220: 7.3 EXPERIMENTAL RESULTS 187 1 0.8
Page 221 and 222: 7.3 EXPERIMENTAL RESULTS 189 Longit
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Page 225 and 226: 7.3 EXPERIMENTAL RESULTS 193 Flight
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Page 239: 7.4 SUMMARY 207 data measured from
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210 CHAPTER 8 CONCLUSIONS AND FUTUR
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212 CHAPTER 8 CONCLUSIONS AND FUTUR
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214 REFERENCES B. W. Bequette. Non-
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216 REFERENCES Konstantinos Dalamag
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218 REFERENCES Wayne Johnson. Helic
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220 REFERENCES B. Mettler, Mark B.
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222 REFERENCES V. R. Puttige and S.
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224 REFERENCES D.H. Shim. Hierarchi
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226 REFERENCES Nikos Vitzilaios and
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