DEVELOPMENT OF ROBUST H∞ CONTROL FOR ACTIVE SUSPENSION OF HALF CAR MODEL WITH
GENETIC ALGORITHM
BY
MOHAMMED KALEEMULLAH
A dissertation submitted in fulfilment of the requirement for the degree of Master of Science (Mechatronics Engineering)
Kulliyyah of Engineering
International Islamic University Malaysia
MAY 2014
ii
ABSTRACT
Better ride comfort and controllability of vehicles are pursued by automotive industries by considering the use of suspension system which plays a very important role in handling and ride comfort characteristics. Comprehensive comparison on half car model was conducted to analyze the effect of active suspension system, namely, Robust H-infinity and LQR controller on the model. Passive suspension system is also compared with active suspension technique for the purpose of benchmarking.
Parametric uncertainties were also considered to model the non-linearities associated in the system. Sprung mass vertical acceleration and pitch acceleration responses were analyzed for measurements of ride quality and road handling. Suspension deflection and tire deflection responses were analyzed to identify any compromise in other aspects of vehicle dynamics. Results show that the Robust and LQR controller successfully controlled the active suspension, improving both the ride quality and handling of the vehicles without compromising the rattle-space requirement and road holding performance of the vehicles. Comparison of all models also shows that in spite of adding uncertainties in the system, the designed Robust H-infinity controller achieved better settling time than the traditional passive suspension system.
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ثحبلا ةصاخ
ى ذخااب تارايسلا ةعانص ى فده امئاد ناك تابكرما ى مكحتلاو ةحار رثكاا بوكرلا رثكاا بوكرلا تافصاوم لوانت ى ةيماا ةياغ ى ارود بعلي ىذلا قيلعتلا ماظن رابتعاا ىلع ةضيفتسم ةنراقم.ةحار اجاا قيلعتلا ماظن رثا ليلحتل هلوانت م ةرايس فصن جذوم
دق ىلسلا قيلعتلا ماظن اضيا.ىئانث ىطخ مظنم و يئاه ا قفأ وذ ملقأتم مكحتم مادختساب اضيأ ايرمارابلا تاديكأتلا مدع.تبثتلا ضرغل اجأا قيلعتلا ةقيرطب هتنراقم و هلوانت م جذوم لمعل رابتعأا نم تذخأ ةيسأرلا ةلجعلا ةباجتسأ .ماظنلل ةبحاصما تايطخا رغل
لوانتو بوكرلا ةدوج ىدم سايقل اهليلح م ةلئاما ةلجعلا كلذكو مسجا ةلتكل ىلع تارثأت ىا ةفرعم هليلح م دق تاراطأا فارحا كلذكو قيلعتلا فارحا ةباجتسأ.قيرطلا ةيكمانيدل ىرخأا هجوأا جئاتنلا .ةبكرما
مادختساب مكحتلا كلذكو ملقأتما مكحتلا نا نبت
بوكرلا ةدوج نم لك نسحتب ,حاجنب م دق اجأا قيلعتلا ماظنل ىئانث ىطخ مظنم تابث و ءادا ىلع كلذكو قيلعتلا ماظن فارحا تابلطتم ىلع رثأتلا نود ةبكرما لوانتو نا نبت ,كلذك ,جذامنلا لك ةنراقم .قيرطلا ىلع تابكرما رابتعاا اميف ذخأا نم مغرلاب ه
هميمصت م ىذلا اجأا مكحتلا ماظن ,ىئاهالا قفأل ملقأتما مكحتلا ى ةيدكأتلا مدع
هيلع فراعتما ىلسلا قيلعتلا ماظن نم لضفا توبث تقوب زيمتي
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APPROVAL PAGE
I certify that I have supervised and read this study and that in my opinion; it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Master of Science in Mechanical Engineering.
………. Waleed Fekry Faris
Supervisor
………. Md Mahbubur Rashid
Co-Supervisor
I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Master of Science in Mechatronics Engineering.
………. Mohammad Abdel Rahman
Examiner (Internal) ……….
Hishamuddin Jamaluddin Examiner (External)
This dissertation was submitted to the Department of Mechatronics Engineering and is accepted as fulfilment of the requirement for the degree of Master of Science in Mechatronics Engineering.
………. Md Raisuddin Khan
Head, Department of Mechatronics Engineering
This dissertation was submitted to the Kulliyyah of Engineering and is accepted as fulfilment of the requirement for the degree of Master of Science in Mechatronics Engineering.
………. Md.Noor B. Salleh
Dean, Kulliyyah of Engineering
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DECLARATION
I hereby declare that this dissertation is the result of my own investigations, expect where otherwise stated. I also declare that it has not been previously or concurrently submitted as a whole for any other degrees at IIUM or other institutions.
Mohammed Kaleemullah
Signature:……… Date:………
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@#
INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
DECLARATION OF COPYRIGHT AND AFFIRMATION OF FAIR USE OF UNPUBLISHED RESEARCH
Copyright © 2014 by International Islamic University, Malaysia. All rights reserved.
DEVELOPMENTOFROBUSTH∞CONTROLFORACTIVE
SUSPENSION OF HALF CAR MODEL WITH GENETIC ALGORITHM
No part of this unpublished research may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without prior written permission of the copyright holder except as provided below.
1. Any material contained in or derived from this unpublished research my only be used by others in their writing with due acknowledgement.
2. IIUM or its library will have the right to make the transmit copies (print or electronic) for institutional and academic purposes.
3. The IIUM library will have the right to make, store in a retrieval system and supply copies of this unpublished research if requested by other universities and research libraries.
Affirmed by Mohammed Kaleemullah
……….. ………..
Signature Date
vii
To my beloved father, Ahmedullah and mother, Asma Begum To my brother and sisters
For their love, prayers and patience
To my nephews and nieces
For being my stress buster and biggest motivator Not to forget my future wife
May Allah bless and grant mercy upon them
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ACKNOWLEDGEMENTS
First and foremost, all thanks to Allah the most Merciful and most Compassionate for helping me to complete this work. I would like to express my deep appreciation and gratitude to my research supervisor, Prof. Dr. Waleed Fekry Faris. He has been the biggest influence on this dissertation background with motivation, valuable advice, support, and constant guidance & encouragement throughout the work. I am really thankful to have worked under him. I would also like to thank my co-supervisor, Dr.
Md Mahbubur Rashid for his motivation and guidance in keeping me going with the work.
I wish to thank all my lecturers for making themselves available to help me whenever needed. Not to forget my colleagues, Fareed Hasbullah, Zohir Benlahcene, Ahmed Fadhil, and Mohammad Hasan at the Vehicle Dynamics Lab, for their help and making a pleasant work place. I am grateful to all my friends for offering unconditional support, care and for being there to listen, discuss and help through all the challenges faced emotionally and socially throughout the time.
Special thank to the Government of Malaysia and International Islamic University Malaysia for providing the Research Grant without which this work would have not been possible.
I owe my greatest debt of gratitude to my beloved parents, siblings, nieces and nephews for their prayers, love, care, patience, moral support and sacrifices throughout this study. They were the biggest motivator to keep me going. I hope to make up for all the lost time we have not spent together.
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TABLE OF CONTENTS
Abstract ... ii
Abstract in Arabic ... iii
Approval Page ... iv
Declaration ... v
Declaration of Copyright ... vi
Acknowledgement ... viii
List of Table ... xi
List of Figure ... xii
CHAPTER 1: INTRODUCTION ... 1
1.1 Background ... 1
1.2 Problem Statement And Its Significance ... 3
1.3 Research Objective... 3
1.4 Research Methodology... 3
1.5 Scope of Research ... 4
1.6 Dissertation Outline ... 5
CHAPTER 2: LITERATURE REVIEW ... 6
2.1 Introduction ... 6
2.2 Ride Evaluation Criteria ... 6
2.2.1 Vibration Evaluation Guide ... 7
2.2.2 Fatigue-Decreased Proficiency Boundary ... 7
2.2.3 Exposure Limit ... 9
2.2.4 Reduced Comfort Boundary ... 9
2.3 Vehicle Suspension ... 9
2.3.1 Passive Suspension System ... 10
2.3.2 Semi-Active Suspension System ... 12
2.3.3 Active Suspension System ... 14
2.4 Suspension Control Technique ... 15
2.4.1 Robust Control ... 15
2.4.2 Linear Quadratic Regulator ... 20
2.4.3 Other Controls ... 24
2.5 Summary ... 31
CHAPTER 3: SYSTEM AND DISTURBANCE MODELLING ... 33
3.1 Introduction ... 33
3.2 Vehicle Model ... 33
3.3 Half Car Model ... 34
3.4 Disturbance Model ... 37
3.4.1 Random Disturbance ... 37
3.4.2 Bump and Pothole Disturbance ... 41
3.5 Performance Criteria ... 42
3.6 Summary ... 44
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CHAPTER 4: CONTROLLER DESIGN ... 45
4.1 Introduction ... 45
4.2 Uncertainty Modelling ... 45
4.2.1 Model Uncertainty ... 46
4.3 Controller Design ... 48
4.3.1 H-Infinity Control Theory ... 48
4.4 Weighting Functions ... 51
4.5 LQR Control ... 52
4.6 Genetic Algorithm ... 53
4.6.1 Optimization Problem Formulation ... 55
4.7 Validation ... 56
4.8 Summary ... 58
CHAPTER 5: SIMULATION RESULTS ... 59
5.1 Introduction ... 59
5.2 Response to Bump Input ... 59
5.2.1 Sprung Mass Acceleration ... 59
5.2.2 Suspension Deflection ... 61
5.2.3 Tire Deflection ... 63
5.3 Response to Pothole Input ... 66
5.3.1 Sprung Mass Acceleration ... 66
5.3.2 Suspension Deflection ... 68
5.3.3 Tire Deflection ... 70
5.4 Response to Random Input ... 73
5.4.1 Sprung Mass Acceleration ... 73
5.4.2 Suspension Deflection ... 74
5.4.3 Tire Deflection ... 76
5.5 Summary ... 78
CHAPTER 6: CONCLUSION ... 79
6.1 Conclusion ... 79
6.2 Main Contribution ... 80
REFERENCES ... 81
APPENDIX A: STATE SPACE REPRESENTATION ... 88
APPENDIX B: WEIGHTING FUNCTION ... 91
APPENDIX C : SAMPLE MATLAB CODE ... 94
APPENDIX D: SAMPLE SIMULINK MODEL ... 105
LIST OF PUBLICATIONS ... 108
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LIST OF TABLES
Table No. Page No.
2.1 Values of Fatigue-Decreased Proficiency Boundary” for Vibration
Acceleration 8
2.2 Passive Q-car variable and description 11
2.3 Literature survey of Robust controller 301
3.1 State variables and input description for half car 36
3.2 Model parameters of half car 36
3.3 Values of Csp and N for PSD for various surfaces (Wong 2001) 398
3.4 ISO classification of road roughness 399
4.1 Perturbation uncertainty values 487 5.1 PTP response to bump input 654
5.2 Settling time for bump input (in seconds, s) 655 5.3 PTP response to pothole input 721
5.4 Settling time for pothole input (in seconds, s) 722
5.5 RMS value for random input 776
xii
LIST OF FIGURES
Figure No. Page No.
2.1 Fatigue-decreased proficiency boundary 8
2.2 Two DoF Passive Q-car Model 11
2.3 Two DoF Semi-active Q-car Model 13
3.1 Two DoF half car model 35
3.2 Power Spectral Density for various types of road and runways 38
3.3 Classification of road surface roughness by ISO 40
3.4 Random surface profile 40
3.5 Pothole disturbance input 42
3.6 Bump disturbance input 42
4.1 Robust controller K(s) 487
4.2 System with uncertainty 4950
4.3 Flow chart of the algorithm 54
4.4 Sprung mass acceleration response by (Shirdel et al. 2010) (top)
and reproduced result (bottom) 576
4.5 Suspension deflection response by (Shirdel et al. 2010) (top) and
reproduced result (bottom) 587
5.1 Sprung Mass Vertical Acceleration 598
5.2 Sprung Mass Pitch Acceleration 5960
5.3 PTP of sprung mass vertical acceleration 59
5.4 Settling time of sprung mass vertical acceleration 59
5.5 PTP of sprung mass pitch acceleration 610
5.6 Settling time of sprung mass pitch accleration 610
xiii
5.7 Front Suspension Deflection 621
5.8 Rear Suspension Deflection 621
5.9 PTP of front suspension deflection 632
5.10 Settling time of front suspension deflection 632
5.11 PTP of rear suspension deflection 632
5.12 Settling time of rear suspension deflection 632
5.13 Front Tire Deflection 643
5.14 Rear Tire Deflection 643
5.15 PTP of front tire deflection 654
5.16 Settling time of front tire deflection 654
5.17 PTP of rear tire deflection 654
5.18 Settling time of rear tire deflection 654
5.19 Sprung Mass Body Acceleration 676
5.20 Sprung Mass Pitch Acceleration 676
5.21 PTP of sprung mass acceleration 687
5.22 Settling time of sprung mass acceleration 687
5.23 PTP of sprung mass pitch acceleration 687
5.24 Settling time of sprung mass pitch acceleration 687
5.25 Front Suspension Deflection 698
5.26 Rear Suspension Deflection 698
5.27 PTP of front suspension deflection 69
5.28 Settling time of front suspension deflection 69
5.29 PTP of rear suspension deflection 69
5.30 Settling time of rear suspension deflection 69
5.31 Front tire deflection 710
5.32 Rear Tire Deflection 710
5.33 PTP of front tire deflection 721
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5.34 Settling time of front tire deflection 721
5.35 PTP of rear tire deflection 721
5.36 Settling time of rear tire deflection 721
5.37 Sprung Mass Acceleration 732
5.38 Sprung Mass Pitch Acceleration 743
5.39 RMS value of vertical acceleration 743
5.40 RMS value of pitch acceleration 743
5.41 Front Suspension Deflection 754
5.42 Rear Suspension Deflection 754
5.43 RMS value of front suspension deflection 765
5.44 RMS value of rear suspension deflection 765
5.45 Front Tire Deflection 765
5.46 Front Tire Deflection 776
5.47 RMS value of front tire deflection 776
5.48 RMS value of rear tire deflection 776
xv
LIST OF SYMBOLS
ms sprung mass
mu unsprung mass
v vehicle velocity
τ time delay between two consecutive axle
infinity
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CHAPTER ONE INTRODUCTION
1.1 BACKGROUND
Much has been said about reducing the polluting emission from automobiles which affects the environment. Perhaps, toxic gases are not the sole type of pollution from vehicles. Noise is another form of pollution which has immense affects on passenger/s in the vehicle. There are many sources that can generate noise, such as, aerodynamic forces, engine, air ducts, and the vibrations transmitted to the car frame due to uneven road profile. In order to reduce engine noise level, work such as, sound proofing the engine compartment and the soft mounting the engine has been done earlier (Martin 1978) (van den Boom et al. 1980).
To improve ride comfort of the passengers and to reduce fatigue damage to the various vehicle components, the suspension system is equipped to the vehicle that acts like a cushion. The main objective of the suspension system is to provide superior handling performance, proper ride quality (passenger comfort) and increased road holding ability of the tires. A suspension system thus absorbs the energy exerted by the spring from road profile to the vehicle and dissipates it.
The road disturbance are broadly classified into two types, they are shock and vibration. Shocks are generally termed as suddenly applied inputs such as those from potholes. Potholes are described as discrete events with short duration but high power and vibrations are consistent excitation (Wong 2001).
The function of a suspension system is to provide sufficient force between the road and tires. Different types of forces such as tractive, cornering, and braking forces
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are induced by the tires while on motion depending on the wheel position and its motion. All of these forces are related to the vertical force acting between the road and the tires. When the suspension is under vibration, the magnitude of the vertical force varies. The road holding ability is assessed by the vibration of tires and it consequently affects the handling performance of the vehicle. The magnitude of the dynamic vertical force should not exceed that of the static load to avoid losing contact with the ground (Gillespie 1992).
Handling performance refers to vehicle steering command response to road profile input. Suspension is used to improve the feeling of ride by absorbing vibration of vehicle under uneven state of road surface (Son et al. 2001). Vehicle suspension is also necessary to keep tire contact with the ground, and to keep wheels in appropriate position on road surface (Du and Zhang 2009). This objective can be achieved by minimizing vertical car body acceleration using suspension system.
A suspension is normally divided into the following categories depending upon the operating principle: the passive suspension consists of springs and dampers, the semi-active suspension using a variable damper, the active suspension using hydraulic, air, or electric force actuator. Passive suspension is the simplest to design and economically advantage. The main drawback of passive suspension is its limit of suppressing the vibration occurring due to irregular road surface (Du and Zhang 2009). Semi active suspension gives freedom to vary the damper characteristics along with the road. An active suspension has the additional advantage of negative damping and larger range of force can be generated at low velocities (Lauwerys et al. 2004).
Another benefit of active suspension is that they offer dynamic compensation as compared to passive suspension and various techniques can be used to design control algorithm (Chantranuwathana and Peng 1999).
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1.2 PROBLEM STATEMENT AND ITS SIGNIFICANCE
Passive suspension is simple to design and implement but a compromise has to be made between ride comfort and vehicle handling. In order to achieve better ride comfort, it is preferable to have low damping allowing a large deflection. On the other hand, high damping will have better contact of tire on road surface at the expense of ride comfort. A passenger car which requires ride comfort and handling, active suspension is much needed off late which provides both the solution.
1.3 RESEARCH OBJECTIVE
1. To derive a mathematical model of a ½ car model using state space equation.
2. To implement Robust H∞ control for active suspension of half car model.
3. Use Genetic Algorithm for optimization of vehicle performance paramter.
4. To compare the performance of Robust H-infinity controller with LQR controller and passive suspension performance using three types of inputs namely, bump, pothole, and random excitation.
1.4 RESEARCH METHODOLOGY
The methodology of this research is as follows, 1. Review of relevant literature.
The literature of this research is divided into 3 different categories namely, ride evaluation criteria, vehicle suspension, and suspension control techniques.
2. Derivation of mathematical model of the system.
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Mathematical model of active and passive suspension system are developed and showed here.
3. Implementation of Robust H∞ controller.
Robust H-infinity controller is implemented for the active suspension controller.
4. Genetic Algorithm.
Optimization of the control performance using Genetic algorithm is introduced to find the best solution.
5. Simulation of the controller.
To ensure that the designed controllers are valid, it is simulated using Matlab and Simulink.
6. Result analysis.
The result of the system are analyzed and compared with each other according to performance criteria.
1.5 SCOPE OF RESEARCH
Most of the work carried out in Robust H∞ control is focused in Quarter car model.
The advantage of quarter car model is: simpler to analyze and model but it is limited to only being able to simulate vertical deflection of the car. Due to this, the effect of pitch and roll cannot be determined and analyzed.
The goal of this research is categorized into the following: vehicle control performance and passengers ride comfort. Robust H-infinity controller is designed to control the suspension system and to reduce the vibrations in the car and to improve handling. A half car model is considered in this research to study the effects in passenger owing to different road profiles. To the author’s knowledge, this is the first
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kind of work on Robust H-infinity controller with Genetic Algorithm on a half car model with different types of usually existing road disturbance. The investigation was carried out in time domain of the system. In this work, the dynamics of the actuator is not taken into account and the system is considered linear.
1.6 DISSERTATION OUTLINE
In chapter 2, related research work is presented. The review is grouped into three parts, namely ride evaluation criteria, vehicle suspension, and suspension control technique.
In chapter 3, vehicle ride model is presented and its equation of motion is derived. Different types of disturbance model used in this thesis are also shown.
Finally, performance criteria used is explained.
In chapter 4, design of two active controllers, namely Robust H-infinity control and LQR control are presented. Then optimization parameters for the controller are also discussed. At last, validation of the codes used throughout this work is presented.
In chapter 5, comparison of results between different road disturbances is presented. Sprung mass acceleration, pitch acceleration, suspension deflection and tire deflection of active controllers are compared along with passive system which is considered as a reference. In chapter 6, conclusion and main contribution of the work is presented.
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CHAPTER TWO LITERATURE REVIEW
2.1 INTRODUCTION
This chapter is divided into three sections excluding the introduction. In the first section, vehicle’s response to excitation is reviewed. In the following section, different types of suspension technique like passive, semi-active and active are explained.
Literature of active suspension control techniques and off-road vehicle suspension are reviewed in the last section.
2.2 RIDE EVALUATION CRITERIA
ISO 2631 was published in the year 1974 to give numerical values for limits of exposure for vibration transmitted from surfaces to human body in the frequency range of 1 to 80 Hz. After going through several revisions, the numerical values of the exposure limits were specified in 1985. These limits are given according to the three recognizable criteria: preserving comfort, working efficiency, and safety or health. For example, when the primary objective is to maintain the working efficiency of a vehicle driver, the fatigue decreased proficiency boundary would be used as the guiding limit in describing vibration specifications or to lay down vibration control measures. The four physical factors of primary importance in determining the human’s response to vibrations are vibration intensity, vibration frequency, direction of the vibration, and duration (exposure time) of the vibration.
7 2.2.1 Vibration Evaluation Guide
In ISO 2631, the limits for standards are applied to three criteria:
1. Fatigue decreased proficiency boundary.
2. Exposure limits.
3. Reduced comfort boundary.
The limits to these three criteria were given in a simple relationship such that for any vibration frequency, axis or duration
Exposure limits = 2 times fatigue decreased proficiency boundary
Fatigue-decreased proficiency boundary = 3.15 times reduced comfort boundary.
2.2.2 Fatigue-decreased proficiency boundary
The fatigue-decreased proficiency boundary for vertical vibration as a function of frequency and exposure time for daily exposure time from 1 minute to 24 hours is shown in Figure 2.1. The values showing the boundary is in Table 2.1. These values defining the boundary are in terms of r.m.s value of pure sinusoidal single frequency vibration.
The boundary value specifies a limit, beyond which, vibration experience can be signified as risk of impaired working efficiency in tasks which are time dependent effects (fatigue) are known to worse performance, for instance, in vehicle driving. It is worth mentioning that the actual degree of task interference in any situation depends on many factors like individual characteristics as well as nature and difficulty of the task. However, the limits recommended by ISO 2631 show the interference of the frequency dependence and the time dependence that are commonly observed.
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Table 2.1 Values of Fatigue-Decreased Proficiency Boundary” for Vibration Acceleration
Center frequency of one third band
(Hz)
Acceleration (m x m/s) Exposure time
24 h 16 h 8 h 4 h 2.5 h 1 h 25 min 16 min 1 min
1.0 0.280 0.425 0.63 1.06 1.40 2.36 3.55 4.25 5.60
1.3 0.250 0.375 0.56 0.95 1.26 2.12 3.15 3.75 5.00
1.6 0.224 0.335 0.50 0.85 1.12 1.90 2.80 3.35 4.50
2.0 0.200 0.300 0.45 0.75 1.00 1.70 2.50 3.00 4.00
2.5 0.180 0.265 0.40 0.67 0.90 1.50 2.24 2.65 3.55
3.2 0.160 0.235 0.36 0.60 0.80 1.32 2.00 2.35 3.15
4.0 0.140 0.212 0.32 0.53 0.71 1.18 1.80 2.12 2.80
5.0 0.140 0.212 0.32 0.53 0.71 1.18 1.80 2.12 2.80
6.3 0.140 0.212 0.32 0.53 0.71 1.18 1.80 2.12 2.80
8.0 0.140 0.212 0.32 0.53 0.71 1.18 1.80 2.12 2.80
10.0 0.180 0.265 0.40 0.67 0.90 1.50 2.24 2.65 3.55
12.5 0.224 0.335 0.50 0.85 1.12 1.90 2.80 3.35 4.50
16.0 0.280 0.425 0.63 1.06 1.40 2.36 3.55 4.25 5.60
20.0 0.355 0.530 0.80 1.32 1.80 3.00 4.50 6.30 7.10
25.0 0.450 0.670 1.00 1.70 2.24 3.75 5.60 6.70 9.00
31.5 0.560 0.850 1.25 2.12 2.80 4.75 7.10 8.50 11.20
40.0 0.710 1.060 1.60 2.65 3.55 6.00 9.00 10.60 14.00
50.0 0.900 1.320 2.00 3.35 4.50 7.50 11.20 13.20 18.50
63.0 1.120 1.700 2.50 4.25 5.60 9.50 14.00 17.00 22.40
80.0 1.400 2.120 3.15 5.30 7.10 11.80 18.00 21.10 28.00
Figure 2.1, Fatigue-decreased proficiency boundary
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For humans, the most sensitive frequency is in the range of 4 to 8 Hz in vertical direction and that the tolerance of vibration decreases with increasing exposure time.
2.2.3 Exposure limit
The exposure limit as a function of frequency and exposure time is of the form as fatigue-decreased proficiency boundary but the levels are raised by a factor of 2 (6 dB higher). In other words, maximum safe exposure limit can be determined for any condition of frequency, duration, and direction by doubling the values of fatigue- decreased proficiency. The exposure limit recommended is set at approximately half of the considered threshold level of pain for healthy human subjects to vibrating seat.
2.2.4 Reduced comfort boundary
The reduced comfort boundary according to ISO 2631 lie approximately at one-third of the corresponding levels of the fatigue-decreased proficiency boundary, and it is assumed to have the same time and frequency dependency. These values are obtained from the corresponding values of the fatigue-decreased proficiency boundary by a reduction of 10 dB. Usually, the reduced comfort boundary is related to difficulties in carrying out operations such as eating, reading and writing.
2.3 VEHICLE SUSPENSION
Vehicle suspension systems are normally divided into passive, semi-active and active suspension system.
