The Development of Neural Network Based System Identification ...

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22 CHAPTER 2 LITERATURE REVIEW in body reference frame; helicopter linear velocity in body reference frame, V B = [ u B v B w B] T ∈ R 3 and helicopter angular velocities in body reference frame, w B = [ p B q B r B] T ∈ R 3 . The overall dynamic system of a helicopter can be divided into kinematics (2.1) and system dynamics (2.2) as follows: ṗ S = R B→S V B ˙Θ S = Ψ (Θ) w B ⎡ ⎤ 1 0 tan θ cos φ Ψ (Θ) = ⎢0 cos φ − sin φ ⎥ ⎣ ⎦ 0 sin φ/cos θ cos φ/cos θ (2.1) ˙V B = 1 m F B − w B × V B ẇ B = J −1 ( M B − ( w B × Jw B)) (2.2) where m is the total mass of the vehicle, J is vehicle inertia matrix, R B→S is rotational matrix from body reference to spatial reference frame. The forces F B stated above are the total sum of aerodynamics forces generated from the main rotor, tail rotor, fuselage, vertical and horizontal stabilisers and gravitational force. The total moments M B are generated by aerodynamic forces from various vehicle components and moment generated by main rotor gyroscopic effects [Gavrilets et al., 2003, Bisgaard, 2007]. Basically, the aerodynamic forces and moments generated from main rotor and tail rotor are non-linear functions which depend on the operating conditions, vehicle motion characteristics and control inputs [Kendoul, 2012]. The control inputs associated with pilot commands are defined as, δ = [δ lon δ lat δ col δ ped ] T ∈ R 4 where δ col and δ ped are collective pitch of main rotor and tail rotor respectively, δ lon and δ lat are longitudinal and lateral cyclic pitch respectively which control the inclination of main rotor’s tip path plane according to their respective directions. The illustration of the state and input variables that features in the helicopter flight dynamics is given in Figure 2.4. The control input commands are normalised between −1 to 1 for lateral cyclic, longitudinal cyclic and tail rotor’s collective pitch, while the main rotor’s collective pitch command is normalised between 0 to 1 range.
2.2 HELICOPTER DYNAMICS MODELLING AND SYSTEM IDENTIFICATION 23 Body Reference Frame East North Inertial Frame Down Figure 2.4 The representation of state and input variables. Kendoul [2012] has suggested that in order to obtain more accurate helicopter dynamics model, the basic rigid body model needs to be extended with helicopter’s rotor dynamics and detailed aerodynamic model using theories from simple momentum theory or blade element theory. Detailed formulation of large scaled helicopter’s non-linear dynamics model can be found in Prouty [1986], Padfield [2007], Bramwell et al. [2001], Johnson [1980]. For a smaller scale helicopter, other dynamics from the actuator and stabiliser bar also need to be included in the rigid body model to increase the model fidelity [Mettler, 2003]. The dynamics model presented above depends on many parameters which need to be carefully identified through direct measurement of geometrical or structural data. For aerodynamic parameters estimation, elaborate experiment needs to be performed using wind tunnel facilities. It requires a considerable amount of theoretical knowledge and experiences about rotorcraft flight and potentially would not produce highly accurate results unless performed with extreme care. In some cases, the agreement between the predicted and measured dynamic behaviours is unsatisfactory because of the accumulated uncertainty and modelling simplification [Mettler, 2003, Kendoul, 2012].
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The Development of Neural Network B
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72 CHAPTER 3 AERIAL PLATFORM AND CU
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74 CHAPTER 3 AERIAL PLATFORM AND CU
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Chapter 4 NEURAL NETWORK BASED SYST
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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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5.6 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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