The Development of Neural Network Based System Identification ...

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50 CHAPTER 2 LITERATURE REVIEW Non-linear Activation Function y k W A W D Linear Activation Function Linear Activation Function Linear Activation Function u k y k W B W C Linear Activation Function W E W F W G y k+1 (a) A Z -1 u k F Z -1 B C y k+1 Linear Activation Function 1 Linear Activation Function 2 E Non-linear Activation Function (b) Figure 2.14 Different configuration of NN architectures that represent time varying linear model [Kuure-Kinsey et al., 2006a, Kuure-Kinsey and Bequette, 2008]: (a) Feed-forward NN architecture (b) Recurrent NN architecture are obtained at each time step by linearising the non-linear path of the non-linear state space model with a first order Taylor series expansion. The standard MPC formulation is then devised for the control problem using the linearised models obtained from the NN. The simulation results presented in both papers point out that the performance of the proposed controller is comparable to the non-linear MPC with good robustness performance against disturbances. Furthermore, the proposed NN based MPC requires less computation time to execute compared with the non-linear NN based MPC. Better controller performance is also achieved with RNN architecture with significant improvement compared with the feed-forward NNARX model [Kuure-Kinsey and Bequette, 2008]. The NN based predictive control proposed in Norgaard [2000] is quite similar to the
2.4 AUTOMATIC FLIGHT CONTROL SYSTEM 51 approach taken by the above-mentioned approaches. Norgaard [2000] proposes that the high computation effort involving MPC implementation with non-linear NNARX model can be reduced with the so-called ‘instantaneous linearisation’ technique. This technique is employed to extract the linear transfer function models at every time step from the non-linear NNARX model. No modifications are made to the NNARX model structure, in contrast to the approach taken by Kuure-Kinsey et al. [2006a]. Similar to abovementioned approaches, the extraction process of the linear models from the NNARX model enables the execution of linear MPC strategy, which is simpler in terms of finding the minimum of the controller’s optimisation criterion. The extracted linear models from the NNARX can also be applied for various linear controller techniques such as pole placement method and minimum variance design [Norgaard, 2000, Ab Wahab et al., 2009]. Furthermore, the usage of the instantaneous linearisation principle provides more valuable information about the dynamics of the system compared with the black-box nature of the NNARX model. The transfer function of MPC introduced in Norgaard [2000] is often regarded to be less effective in handling multi-variable dynamic processes [Wang, 2009a]. Transformation of the transfer function form into a non-minimal state space (NMSS) formulation should improve the proposed NN-MPC formulation in terms of simpler design framework and analysis. Furthermore, the NMSS form still retains the basic features of the transfer function model which only requires state variables chosen from the set of measured outputs, inputs and their time lag values. This modification to original transfer function form can avoid the use of an observer to access the state information. Since the dynamic of the helicopter based UAS is part of a highly complex system with strong non-linearity, designing an automatic flight control for such a dynamic system is difficult and presents significant challenges. Moreover, the dynamic system of the helicopter is also known to be coupled and time varying, which requires necessary compensation through the use of adaptive type controllers. Numerous types of direct adaptive NN controllers have been reported in the literature with the majority of the control techniques being only validated in numerical simulations. More extensive experiments need to be performed to evaluate the effectiveness of these approaches in a
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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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4.3 SYSTEM IDENTIFICATION WITH NEUR
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4.4 SUMMARY 117 Segment 1 Segment 2
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Chapter 5 NN BASED SYSTEM IDENTIFIC
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5.2 OFF-LINE BASED SYSTEM IDENTIFIC
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5.6 ON-LINE SYSTEM IDENTIFICATION 1
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5.6 ON-LINE SYSTEM IDENTIFICATION 1
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5.7 MODEL PERFORMANCE COMPARISON US
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5.8 SUMMARY 151 methods such as wei
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5.8 SUMMARY 153 would enable the im
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156 CHAPTER 6 NEURAL NETWORK BASED
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Chapter 7 FLIGHT CONTROL SYSTEM DES
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7.2 FLIGHT TESTS IMPLEMENTATION 185
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7.3 EXPERIMENTAL RESULTS 187 1 0.8
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7.3 EXPERIMENTAL RESULTS 189 Longit
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7.3 EXPERIMENTAL RESULTS 191 Pitch
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7.3 EXPERIMENTAL RESULTS 193 Flight
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7.3 EXPERIMENTAL RESULTS 195 140 Ya
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7.3 EXPERIMENTAL RESULTS 197 indica
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7.3 EXPERIMENTAL RESULTS 199 20 100
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7.3 EXPERIMENTAL RESULTS 201 Yaw Ra
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7.3 EXPERIMENTAL RESULTS 203 mainta
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7.3 EXPERIMENTAL RESULTS 205 Yaw Ra
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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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