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Summary
Summary
Semi-active Suspension Control provides an overview of vehicle ride control employing smart semi-active damping systems. These systems are able to tune the amount of damping in response to measured vehicle-ride and handling indicators.
Two physically different dampers (magnetorheological and controlled-friction) are analysed from the perspectives of mechatronics and control. Ride comfort, road holding, road damage and human-body modelling are studied.
Mathematical modelling is balanced by a large and detailed section on experimental implementation, where a variety of automotive applications are described offering a well-rounded view. The implementation of control algorithms with regard to real-life engineering constraints is emphasised.
The applications described include semi-active suspensions for a saloon car, seat suspensions for vehicles not equipped with a primary suspension, and control of heavy-vehicle dynamic-tyre loads to reduce road damage and improve handling.
Table of Contents
1 Introduction | p. 1 |
1.1 Introduction | p. 1 |
1.2 Historical Notes on Suspensions | p. 3 |
1.3 Active and Semi-active Suspensions in the Scientific Literature | p. 5 |
1.4 Comfort in a Vehicle | p. 7 |
1.4.1 Comfort Assessment | p. 10 |
1.5 Introduction to Controlled Dampers | p. 10 |
1.6 Introduction to Friction Dampers | p. 12 |
1.7 Introduction to MR Dampers | p. 14 |
2 Dampers and Vehicle Modelling | p. 17 |
2.1 Introduction | p. 17 |
2.2 Phenomenology of Hysteresis | p. 19 |
2.3 Damper Hysteresis Modelling | p. 22 |
2.3.1 Bouc-Wen Model | p. 24 |
2.3.1.1 Parameter A | p. 24 |
2.3.1.2 Parameter [gamma] | p. 25 |
2.3.1.3 Parameter v | p. 26 |
2.3.1.4 Parameter n | p. 26 |
2.4 Bouc-Wen Parameter Identification | p. 27 |
2.5 Vehicle Ride Models | p. 27 |
2.5.1 Quarter Car Model | p. 29 |
2.5.2 Half Car Model | p. 31 |
2.5.3 Full Car Model | p. 32 |
2.5.4 Half Truck Model | p. 36 |
2.6 Tyre Modelling | p. 39 |
2.7 Road Modelling | p. 40 |
3 Human Body Analysis | p. 43 |
3.1 Introduction | p. 43 |
3.2 Human Body Response | p. 44 |
3.3 Hysteretic Damping | p. 44 |
3.3.1 The Duffing Equation | p. 45 |
3.3.2 Suppression of Jumps | p. 46 |
3.4 Low-frequency Seated Human Model | p. 48 |
3.4.1 Multi-frequency Input | p. 49 |
3.5 Semi-active Control | p. 51 |
3.6 State Observer | p. 51 |
3.6.1 Luenberger State Observer | p. 51 |
3.6.2 Simple State Observer | p. 52 |
3.6.3 Ideal Control | p. 53 |
3.7 Results | p. 54 |
3.8 Seated Human with Head-and-Neck Complex | p. 57 |
3.8.1 Driver Seat (Including Cushions) | p. 58 |
3.8.2 Driver Body | p. 59 |
3.8.3 Head-and-Neck Complex (HNC) | p. 59 |
3.8.4 Analysis of the Head-and-Neck System | p. 60 |
3.8.5 Head Accelerations During Avoidance Manoeuvre | p. 64 |
4 Semi-active Control Algorithms | p. 65 |
4.1 Introduction | p. 65 |
4.2 PID Controllers | p. 67 |
4.3 Adaptive Control | p. 68 |
4.4 Robust Control | p. 69 |
4.5 Balance, Skyhook and Groundhook | p. 70 |
4.5.1 Balance Logic | p. 70 |
4.5.2 Skyhook Logic | p. 70 |
4.5.3 Groundhook Logic | p. 70 |
4.5.4 Displacement-based On-Off Groundhook Logic | p. 71 |
4.5.5 Hybrid Skyhook-Groundhook Logic | p. 71 |
4.6 Balance Logic Analysis | p. 72 |
4.7 Chattering Reduction Strategies | p. 75 |
4.8 SA Vibration Control of a 1DOF System with Sequential Dry Friction | p. 79 |
4.8.1 Sequential Damping Characteristics | p. 81 |
4.8.2 Free Vibration: Phase Plane Trajectories | p. 82 |
4.8.3 Free Vibration: Shock Absorbing Properties | p. 83 |
4.8.4 Harmonically-Excited Vibration | p. 85 |
4.8.4.1 Time Histories | p. 85 |
4.8.4.2 Amplitude-Frequency Characteristics | p. 85 |
4.8.5 Random Vibration | p. 87 |
4.8.5.1 Simulation of White Noise Sample Functions | p. 89 |
4.8.5.2 Numerical Solution of the Equation of Motion | p. 91 |
4.8.5.3 Numerical Results | p. 92 |
4.9 Stability of SA Control with Sequential Dry Friction | p. 93 |
4.10 Quarter Car Response with Sequential Dry Friction | p. 95 |
5 Friction Dampers | p. 99 |
5.1 Introduction | p. 99 |
5.2 Friction Force Modelling | p. 99 |
5.2.1 Static Friction Models | p. 100 |
5.2.2 Dynamic Friction Models | p. 102 |
5.2.3 Seven-parameter Friction Model | p. 102 |
5.3 The Damper Electrohydraulic Drive | p. 104 |
5.4 Friction Damper Hydraulic Drive Modelling | p. 107 |
5.4.1 Power Consumption | p. 115 |
5.4.2 The Feedback Chain | p. 115 |
5.5 Pilot Implementation of Friction Damper Control | p. 116 |
5.6 Automotive Friction Damper Design | p. 122 |
5.7 Switched State Feedback Control | p. 126 |
5.8 Preliminary Simulation Results | p. 129 |
5.9 Friction Damper Electrohydraulic Drive Assessment | p. 141 |
5.10 Electrohydraulic Drive Parameters Validation | p. 151 |
5.11 Performance Enhancement of the Friction Damper System | p. 156 |
5.11.1 Damper Design Modification | p. 157 |
5.11.2 Hydraulic Drive Optimisation | p. 159 |
5.11.3 Friction Damper Controller Enhancement | p. 161 |
6 Magnetorheological Dampers | p. 165 |
6.1 Introduction | p. 165 |
6.2 Magnetorheological Fluids | p. 165 |
6.3 MR Fluid Devices | p. 167 |
6.3.1 Basic Operating Modes | p. 167 |
6.3.2 Flow Simulation | p. 168 |
6.3.2.1 Pressure-driven Flow Mode with Either Pole Fixed | p. 168 |
6.3.2.2 Direct Shear Mode with Relatively Movable Poles | p. 177 |
6.3.2.3 Squeeze-film Mode | p. 180 |
6.4 MR Damper Design | p. 180 |
6.4.1 Input Data and Choice of the Design Solution | p. 181 |
6.4.2 Selection of the Working MR Fluid | p. 181 |
6.4.2.1 MR Fluid Figures of Merit | p. 182 |
6.4.2.2 Choice of the MR Fluid | p. 183 |
6.4.3 Determination of the Optimal Gap Size and Hydraulic Design | p. 185 |
6.4.3.1 Controllable Force and Dynamic Range | p. 185 |
6.4.3.2 Parameters of the Hydraulic Circuit | p. 186 |
6.4.4 Magnetic Circuit Design | p. 187 |
6.5 MRD Modelling and Characteristics Identification | p. 189 |
6.5.1 Experimental Data | p. 190 |
6.5.2 Parametric Model Simulation | p. 192 |
6.5.3 Fuzzy-logic-based Model | p. 200 |
6.5.4 Modelling the Variable Field Strength | p. 203 |
6.5.5 GA-based Method for MR Damper Model Parameters Identification | p. 209 |
7 Case Studies | p. 219 |
7.1 Introduction | p. 219 |
7.1.1 Some Aspects of Data Acquisition and Control | p. 219 |
7.2 Car Dynamics Experimental Analysis | p. 221 |
7.2.1 The Experimental Set-up | p. 221 |
7.2.2 Post-processing and Measurement Results | p. 224 |
7.2.3 Suspension Spring and Tyre Tests | p. 229 |
7.3 Passively-Damped Car Validation | p. 230 |
7.4 Case Study 1: SA Suspension Unit with FD | p. 232 |
7.4.1 Frequency-domain Analysis | p. 233 |
7.4.2 Time-domain Analysis | p. 234 |
7.4.3 Semi-active System Validation | p. 242 |
7.5 Case Study 2: MR-based SA Seat Suspension | p. 245 |
7.5.1 Numerical Results | p. 248 |
7.5.2 Conclusions | p. 250 |
7.6 Case Study 3: Road Damage Reduction with MRD Truck Suspension | p. 251 |
7.6.1 Introduction | p. 251 |
7.6.2 Half Truck and MR Damper Model | p. 252 |
7.6.3 Road Damage Assessment | p. 255 |
7.6.4 Road Damage Reduction Algorithm | p. 255 |
7.6.5 Time Response | p. 256 |
7.6.6 Truck Response on Different Road Profiles | p. 258 |
7.6.7 Truck Response to Bump and Pothole | p. 262 |
7.6.8 Robustness Analysis | p. 264 |
7.6.8.1 Trailer Mass Variation | p. 266 |
7.6.8.2 Tyre Stiffness Variation | p. 267 |
7.6.8.3 MRD Response Time | p. 268 |
7.7 Conclusions | p. 270 |
References | p. 271 |
Bibliography | p. 283 |
Authors' Biographies | p. 289 |
Index | p. 291 |