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Modelling and assembly of the full vehicle 373 equally it can obscure performance changes and so adaptive modelling of driver behaviour is not preferred except for circuit driving. Several techniques come under the headline of adaptive control; the simplest is to change the control parameters in a predetermined fashion according to the operating regime, an operation referred to as ‘gain scheduling’. Gain is the term used for any treatment given to an error state before it is fed to an input – thus the PID controller described above has a P-gain, an I-gain and a D-gain. It might be, for example, that under conditions of opposite lock the P-gain is increased since the driver needs to work quickly to retain control, or under conditions of increasing speed the P-gain is reduced since slower inputs are good for stability at higher speeds. A more complex method is to carry a model of the plant on board in the controller and to use it to better inform some form of gain scheduling, perhaps using information that cannot readily be discerned from on-board instrumentation – such as body slip angle. This is referred to as a Model Reference Adaptive Scheme (MRAS). A further variation on the theme is to use the controller to calculate model parameters using system or parameter identification methods (described above). The control system parameters can be modified based on this information – in effect there is an ongoing redesign of the control system using a classical deterministic method, based on the reference state and the plant characteristics according to the latest estimate. This is referred to as a ‘self-tuning-regulator’ and is useful for unpredictably varying systems. Finally, a method known as ‘dual control’ intentionally disturbs the system in order to learn its characteristics, while simultaneously controlling it towards a reference state. In many ways this is similar to a top level rally driver stabbing the brakes in order to assess friction levels while disturbing the overall speed of the vehicle as little as possible; the knowledge gained allows the driver to tune their braking behaviour according to recently learned characteristics. Such behaviour is in marked contrast to circuit drivers, who concentrate on learned braking points and sometimes have difficulty adapting to changing weather conditions. With the exception of the simplest gain scheduling methods, in general adaptive control techniques are unsuitable for the modelling of driver behaviour as part of any practicable process. Once again the variation in simulation output cannot readily be traced to any particular aspect of the system and hence the success or otherwise of an intended modification is difficult to interpret. In the light of the preceding description, the authors believe a PID controller, with some form of simple gain scheduling, is most appropriate for the modelling of driver behaviour in a multibody system context. The art of implementing a successful model is in selecting the state variables within the model to use with the controller. 6.13.2 A path following controller model The first hurdle to be crossed is the availability of suitable state variables and the use of gain terms to apply to them. Typically in a multibody system model, many more variables are available than in a real vehicle. Within the model, these variables can be the subject of differential equations in order to have available integral and differential terms. Table 6.4 shows a portion
374 Multibody Systems Approach to Vehicle Dynamics Table 6.4 A portion of an MSC.ADAMS command file showing the implementation of differential equations to retrieve and use integral and derivative terms for a state variable ! -- Derivative Term - not generally used -- part create equation differential_equation & differential_equation_name .test.yaw_rate_error_equation_1 & adams_id 3 & comments “Yaw Rate Error Equation - Implicit” & initial_condition 0.0 & function “DIF(3)-varval(yaw_rate_error)” & implicit on & static_hold off data_element create variable & variable_name yaw_rate_error_derivative & function “DIF1(3)” ! -- Integral Term -- part create equation differential_equation & differential_equation_name .test.yaw_rate_error_equation_2 & adams_id 4 & comments “Yaw Rate Error Equation - Explicit” & initial_condition 0.0 & function “varval(yaw_rate_error)” & implicit off & static_hold off data_element create variable & variable_name yaw_rate_error_integral & function “(DIF(4))” ! Steer input torque in response to path error. force create direct single_component_force & single_component_force_name yaw_rate_handwheel_torque & type_of_freedom rotational & action_only on & i_marker_name .hand_wheel_column.m_wheel_column & j_marker_name .hand_wheel_column.m_wheel_column & function “(“, & “ VARVAL(yaw_rate_error) * VARVAL(yp_gain) ”, & “ VARVAL(yaw_rate_error_integral) * VARVAL(yi_gain) ”, & “ VARVAL(yaw_rate_error_derivative)* VARVAL(yd_gain) ”, & “)”, & “* STEP(TIME,0.0,0.0,1.0,1.0)” of a command file from MSC.ADAMS implementing those terms for yaw rate. While it is a working example, no claim is made that is in any sense optimum. Such variables can usually be manipulated within the model using the programming syntax provided with the code being used. For simulation codes such as MSC.ADAMS, the format of such calculations can appear a little clumsy but this soon disappears with familiarity. The most recent versions of MSC.ADAMS include a ‘control toolbox’ to facilitate the implementation of PID controllers. For codes such as MATLAB/Simulink the implementation of control systems is arguably easier since they are written with the prime objective of control system modelling. However, the modelling of the vehicle as a plant is more difficult within these systems and so there
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Multibody Systems Approach to Vehic
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Multibody Systems Approach to Vehic
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Contents Preface Acknowledgements N
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Contents vii 4.10.1 Problem definit
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Contents ix 8.2.1 Active suspension
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Preface This book is intended to br
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Preface xiii vehicle design process
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Acknowledgements Mike Blundell In d
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Nomenclature xvii {z I } 1 Unit vec
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Nomenclature xix O n Frame for part
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Nomenclature xxi p Magnitude of re
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1 Introduction The most cost-effect
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Introduction 3 subsequent ‘classi
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Introduction 5 Fig. 1.4 Linearity:
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Introduction 7 While apparently a s
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Introduction 9 3. The body yaws (ro
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Introduction 11 Aspiration Definiti
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Introduction 13 Decomposition: Synt
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Introduction 15 The best multibody
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Introduction 17 shows good correlat
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Introduction 19 generated in numeri
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Introduction 21 1.9 Benchmarking ex
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2 Kinematics and dynamics of rigid
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Kinematics and dynamics of rigid bo
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3 Multibody systems simulation soft
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4 Modelling and analysis of suspens
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Modelling and analysis of suspensio
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Tyre characteristics and modelling
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8 Active systems 8.1 Introduction M
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Active systems 443 mechanical actua
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Active systems 445 Table 8.1 MSC.AD
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Active systems 447 Body acceleratio
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Active systems 449 impressions of t
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Active systems 451 For this reason,
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Appendix A: Vehicle model system sc
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Appendix B: Fortran tyre model subr
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Appendix C: Glossary of terms Agili
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Appendix C: Glossary of terms 489 a
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Appendix C: Glossary of terms 495 m
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Appendix C: Glossary of terms 501 s
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References 503 Blundell, M.V. The m
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References 505 Hudi, J. AMIGO - A m
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References 507 Palmer, D. Course no
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References 509 European ADAMS News
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Index Abuse loads, 148 3 g bump, 14
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Index 513 Elk Test, 1 El-Nasher, 29
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Index 515 generalised translational
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Index 517 steer axis inclination, 1
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