The Development of Neural Network Based System Identification ...

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24 CHAPTER 2 LITERATURE REVIEW Apart from high fidelity modelling theories from standard full scaled helicopter, several minimum complexity mathematical models can also be used. Several good examples of the development of minimum complexity mathematical model are given in Shim [2000], Bisgaard [2007] and Heffley and Mnich [1988]. Although such approaches can be employed to build a simulation model, the highly non-linear aerodynamics interaction between body components and the behaviour of the high order dynamics of a rotorcraft is usually hard to model using the first principle approach (direct physical understanding of forces and moments balance of the vehicle) and such an approach can be inaccurate [Mettler, 2003, Budiyono et al., 2009, Deng et al., 2011]. A significant effort is necessary to validate the theoretical model and re-evaluate any potential shortcomings associated with the model. Most of the works adopting the first principle modelling approach in helicopter modelling use the developed model for control design without detailed validation against flight data [Kendoul, 2012, Bisgaard, 2007]. Among the few successful works that use first principle modelling to address the problem of physical parameter estimation with experimental validation are Nonami et al. [2010] and Gavrilets et al. [2001]. In Nonami et al. [2010], the non-linear helicopter dynamics is linearised to obtain two linear state equations that describe the helicopter’s lateral and longitudinal motion. The linear analytical model includes the rigid-body dynamics, main rotor dynamics and aerodynamics, stabiliser bar dynamics and aerodynamics effect from other main body components. The parameters of the model are determined using direct physical measurements and manufacturer specifications for different helicopter platforms. For parameters that are more difficult to obtain such as moment inertia in different axes, the values was measured roughly and manually retuned to match the flight data. The linear models have been validated for three different helicopter UAV platforms and results show good fit with the flight data for operating condition around hovering flight. Gavrilets et al. [2001] describes 17 states of the non-linear dynamics model of an acrobatic helicopter UAV which includes states for longitudinal and lateral main rotor flapping, the rotor speed and an integral of the rotor-speed tracking error in addition to rigid body dynamics. Flight test experiments were used to estimate several key
2.2 HELICOPTER DYNAMICS MODELLING AND SYSTEM IDENTIFICATION 25 parameters, such as the equivalent stiffness in the rotor hub and equivalent fuselage frontal drag area. The model’s accuracy was verified using comparison between model predicted responses and responses collected during flight test. Even though the prediction results obtained from the non-linear model are adequate for a variety of flight conditions, again, extensive validation needs to be carried out to fine tune many parameters in the model. Since the helicopter is a highly non-linear multi-variable system with some degree of coupling effect in its dynamics, it is preferable to design a controller that includes the effect of coupling between various inputs of the helicopter. However, it is not always a practical approach to include complete coupling effect in the controller design as this will result in increasing computational complexity and resources. Decoupling of the coupled dynamics into a much simpler dynamics representation with separated actuators not only decreases the computation burden but also serves as an effective way to incrementally design the controller for a complete dynamic system. In order to simplify the modelling problem, the dynamic model of a helicopter was described and partitioned into smaller identification problems such as coupled roll-pitch dynamics, heave dynamics, yaw dynamics or coupling of heave and yaw dynamics or with some coupling combination among these coupling cases [Mettler, 2003, Tischler and Remple, 2006]. Different degrees of coupling exist between dynamic channels when considering the helicopter as a MIMO system. As an example, in the longitudinal channel, the relationship of longitudinal cyclic pitch and longitudinal angular velocity is the main feature of the longitudinal channel. Other coupling effects that include lateral cyclic pitch, collective pitch and tail rotor’s collective pitch have some effect on the longitudinal angular velocity in a certain frequency range. Castillo-Effen et al. [2007] propose calculation methods to quantify the degree of interaction between dynamic channels by using the relative gain array number and the diagonal dominance function that quantify decoupling. By using the proposed calculation methods, the helicopter dynamics were found to behave strongly as two sets of a Two Inputs-Two Outputs (TITO) system. Strong coupling exists between lateral and longitudinal channels (φ, θ, δ lat and δ long pairing), as well as mild coupling between collective and pedal channels (r, w, δ ped
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The Development of Neural Network B
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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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4.2 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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5.6 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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