The Development of Neural Network Based System Identification ...

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20 CHAPTER 2 LITERATURE REVIEW 2.2 HELICOPTER DYNAMICS MODELLING AND SYSTEM IDENTIFICATION Numerous advanced control designs such as non-linear control and adaptive control have been developed over the years to overcome the limitation of linear control. These designs typically require a mathematical model representation of the system to be controlled in the form of differential equations. There are two basic ways to obtain a mathematical model of the system. The first method is to deduce the model in a constructive manner using first principle modelling (direct use of Newtonian Laws to describe the system behaviour). The second method is to infer the model from an experimental data set collected during experiments with the system. The latter approach of deriving the dynamic model of the system is also known as system identification approach. The first approach of modelling involves a comprehensive mathematical description about the dynamic system. The system itself is divided into multiple components that contribute to the total forces and moments affecting the system. Various unknown parameters in the mathematical model need to be approximated or measured through the mean of experimentation or measurement of physical parameters of the system. Thus, this would make the modelling task more complex and time consuming [Norgaard, 2000]. On the other hand, the system identification approach offers a more practical and simple solution to obtain a mathematical model of the system with a reasonable effort. The system identification approach can also be viewed as a function fitting process to obtain a model that best describes the measurement data from the experiment. However, the main drawback of this approach is that the experiment needs to be conducted in such a way that the system under consideration needs to be excited through its entire range of operation [Norgaard, 2000]. The UAS helicopter dynamics is known to be a non-linear and time varying model of high order multiple-input multiple output (MIMO) system. It is also an under-actuated system with four actuator inputs: main rotor collective pitch, lateral cyclic pitch, longitudinal cyclic pitch and tail rotor collective pitch. The first principle modelling approach uses physical principles and Newton’s second law to describe the dynamic
2.2 HELICOPTER DYNAMICS MODELLING AND SYSTEM IDENTIFICATION 21 Flight Control System Summation of Forces, Inertial Translational Velocities u, v, w Atmospheric Motion + Main Rotor & Stabiliser Bar Tail Rotor Kinematics Gravity Components Euler Angles Fuselage Engine/ Transmission Summation of Moments, Inertial Rotational Velocities p, q, r Atmospheric Motion + Empennage Figure 2.3 Typical arrangement of component forces and moments generation in helicopter simulation model. Figure adapted from Padfield [2007] and Cai et al. [2013]. system behaviour. This procedure is also known as a lumped parameter approach where all components are described individually and then collected as a complete system [Padfield, 2007, Shim, 2000]. The helicopter dynamics is mainly considered as a composition of the body mass, the main rotor and the stabiliser bar, the tail rotor and the active yaw damping system. Figure 2.3 illustrates the typical arrangement of component forces and moments generation in a helicopter simulation model. The aerodynamic drag effects from the fuselage, horizontal and vertical stabiliser are normally neglected as they play a less important role under hovering and slow flight conditions for model scaled helicopter. The helicopter is basically considered as a rigid body on which forces, F B = [ F B x F B y F B z ] T and moments, M B = [ M B x M B y M B z ] T are exerted. Its motion is described using Newton-Euler equations of motion expressed in the Body Reference Frame [Shim, 2000]. Let superscript S and B represent spatial (inertial) and body reference frame respectively. The twelve dimensional state vectors consist of the helicopter’s centre of gravity (CG) position vectors in spatial reference frame, p S = [ p S x p S y p S ] T z ∈ R 3 ; Euler angles (roll, pitch and yaw), Θ B = [ φ B θ B ψ B] T ∈ R 3
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70 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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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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