Semi-Active Suspension Control Design for Vehicles - 1st Edition - ISBN: 9780080966786, 9780080966793

Semi-Active Suspension Control Design for Vehicles

1st Edition

Authors: Sergio Savaresi Charles Poussot-Vassal Cristiano Spelta Olivier Sename Luc Dugard
eBook ISBN: 9780080966793
Hardcover ISBN: 9780080966786
Imprint: Butterworth-Heinemann
Published Date: 13th August 2010
Page Count: 240
Tax/VAT will be calculated at check-out
File Compatibility per Device

PDF, EPUB, VSB (Vital Source):
PC, Apple Mac, iPhone, iPad, Android mobile devices.

Amazon Kindle eReader.

Institutional Access


Semi-Active Suspension Control Design for Vehicles presents a comprehensive discussion of designing control algorithms for semi-active suspensions. It also covers performance analysis and control design. The book evaluates approaches to different control theories, and it includes methods needed for analyzing and evaluating suspension performances, while identifying optimal performance bounds. The structure of the book follows a classical path of control-system design; it discusses the actuator or the variable-damping shock absorber, models and technologies. It also models and discusses the vehicle that is equipped with semi-active dampers, and the control algorithms. The text can be viewed at three different levels: tutorial for novices and students; application-oriented for engineers and practitioners; and methodology-oriented for researchers. The book is divided into two parts. The first part includes chapters 2 to 6, in which fundamentals of modeling and semi-active control design are discussed. The second part includes chapters 6 to 8, which cover research-oriented solutions and case studies. The text is a comprehensive reference book for research engineers working on ground vehicle systems; automotive and design engineers working on suspension systems; control engineers; and graduate students in control theory and ground vehicle systems.

Key Features

  • Appropriate as a tutorial for students in automotive systems, an application-oriented reference for engineers, and a control design-oriented text for researchers that introduces semi-active suspension theory and practice
  • Includes explanations of two innovative semi-active suspension strategies to enhance either comfort or road-holding performance, with complete analyses of both
  • Also features a case study showing complete implementation of all the presented strategies and summary descriptions of classical control algorithms for controlled dampers


Research engineers working on automotive and ground vehicle systems; Automotive design engineers working on suspension systems; Control engineers; Graduate / postgraduate students in ground vehicle systems or control theory.

Table of Contents

List of Figures

List of Tables

About the Authors




Chapter 1 Introduction and Motivations

1.1 Introduction and Historical Perspective

1.2 Semi-Active Suspensions

1.3 Applications and Technologies of Semi-Active Suspensions

1.4 Book Structure and Contributions

1.5 Model Parameter Sets

Chapter 2 Semi-Active Suspension Technologies and Models

2.1 Introduction to Suspension Modeling

2.2 Passive Suspension Systems

2.2.1 Coil Spring

2.2.2 Gas Spring

2.2.3 Ideal Damping Element in a Passive Suspension System

2.3 Controllable Suspension Systems: a Classification

2.4 Semi-Active Suspension Technologies

2.4.1 Electrohydraulic Dampers (EH Dampers)

2.4.2 Magnetorheological Dampers (MR Dampers)

2.4.3 Electrorheological Dampers (ER Dampers)

2.4.4 On “linearization” of Damping Characteristics

2.5 Dynamical Models for Semi-Active Shock Absorber

2.5.1 Classical Model for Semi-Active Shock Absorber

2.5.2 Control Oriented Dynamical Model

2.5.3 Simplified First-Order Model for Semi-Active Shock Absorber

2.6 Conclusions

Chapter 3 Suspension Oriented Vehicle Models

3.1 Passive Vertical Quarter-Car Model

3.1.1 Nonlinear Passive Model

3.1.2 Equilibrium Points

3.1.3 LTI Passive Models

3.1.4 Quarter-Car Model Invariance Properties

3.1.5 Numerical Discussion and Analysis

3.1.6 Remarks on the Simplified Quarter-Car Model

3.2 Passive Vertical Half-Vehicle Models

3.2.1 Pitch Oriented Model

3.2.2 Numerical Discussion and Analysis

3.3 Passive Vertical Full Vehicle Model

3.3.1 Assumptions and Kinematic Equations

3.3.2 Full Vertical Dynamic Equations

3.4 Passive Extended Half-Vehicle Model

3.4.1 Nonlinear Model

3.5 Semi-Active Vertical Quarter-Car Model

3.5.1 Nonlinear and LTI Models

3.5.2 Toward LPV Models

3.6 Conclusions

Chapter 4 Methodology of Analysis for Automotive Suspensions

4.1 Human Body Comfort and Handling Specifications

4.1.1 Comfort Specifications

4.1.2 Road-Holding Specifications

4.1.3 Suspension Technological Limitations: End-Stop

4.1.4 Quarter-Car Performance Specifications and Signals of Interest

4.2 Frequency Domain Performance Evaluations

4.2.1 Nonlinear Frequency Response Computation

4.2.2 Performance Index Computation

4.2.3 Numerical Discussion and Analysis

4.3 Other Time Domain Performance Evaluations

4.3.1 Bump Test

4.3.2 Broad Band White Noise Test

4.4 Conclusions

Chapter 5 Optimal Strategy for Semi-Active Suspensions and Benchmark

5.1 General Rationale of the Solution

5.1.1 Objective and Assumptions

5.1.2 Optimization: General Idea

5.2 Cost Function Definitions

5.3 Optimization Problem Constraint Definitions

5.3.1 Dynamical Equality Constraints

5.3.2 Actuator Inequality Constraints

5.4 Problem Formulation and Resolution

5.5 Numerical Discussion and Analysis

5.5.1 Nonlinear Frequency Response

5.5.2 Performance Index

5.5.3 Results Analysis and Methodology Discussion

5.5.4 Bump Test

5.6 Conclusions

Chapter 6 Classical Control for Semi-Active Suspension System

6.1 Comfort Oriented Semi-Active Control Approaches

6.1.1 Skyhook Control

6.1.2 Acceleration Driven Damper Control (ADD)

6.1.3 Power Driven Damper Control (PDD)

6.2 Road-Holding Oriented Semi-Active Control Approaches

6.2.1 Groundhook Damper Control (GH 2-States)

6.2.2 Groundhook Damper Control (GH Linear)

6.3 Performance Evaluation and Comparison

6.3.1 Comfort Oriented Strategies

6.3.2 Road-Holding Oriented Strategies

6.3.3 About the Trade-Off Comfort Versus Road-Holding

6.4 Modern Semi-Active Control Approaches

6.4.1 H∞ Clipped Control Approach

6.4.2 Predictive Approaches

6.4.3 Some Other Approaches

6.5 Conclusions

Chapter 7 Mixed SH-ADD Semi-Active Control

7.1 Mixed Skyhook-ADD: The Algorithm

7.2 The 1-Sensor-Mix Algorithm

7.3 The Frequency-Range Selector

7.3.1 First Interpretation: Single-Tone Disturbance

7.3.2 Second Interpretation: Broadband Disturbance

7.3.3 Sensitivity of Mixed Strategies with Respect to α

7.4 Numerical Time-Domain Simulations

7.4.1 Pure Tone Signal

7.4.2 Bump Test

7.5 Conclusions

Chapter 8 Robust H∞ “LPV Semi-Active” Control

8.1 Synthesis Model

8.1.1 System Model c

8.1.2 Actuator Model

8.2 “LPV Semi-Active” Proposed Approach and Scheduling Strategy

8.2.1 Basic Definition on LPV Polytopic Systems

8.2.2 Generalized LPV Plant g(ρ) and Problem Definition

8.2.3 Scheduling Strategy for the Parameter ρ

8.3 H∞ LMI Based “LPV Semi-Active” Controller Synthesis

8.3.1 Problem Feasibility and Controller Reconstruction

8.3.2 Numerical Issues and “LPV Semi-Active” Synthesis Algorithm

8.4 Controller Implementation and On-Line Scheduling

8.5 Controller Parametrization

8.5.1 Comfort Oriented Controller Parametrization (Controller 1)

8.5.2 Road-Holding Oriented Controller Parametrization (Controller 2)

8.6 Numerical Discussion and Analysis

8.6.1 Nonlinear Frequency Response

8.6.2 Performance Index

8.6.3 Bump Test

8.7 Conclusions

Chapter 9 Conclusions and Outlook

Appendix A Control Method Comparisons

A.1 Method Complexity Comparison

A.1.1 Skyhook 2-States and Skyhook Linear

A.1.2 ADD and PDD

A.1.3 Groundhook 2-States and Groundhook Linear

A.1.4 SH-ADD (and 1 Sensor Version)

A.1.5 LPV Semi-Active

A.1.6 (Hybrid) MPC Based

A.2 Conclusions

Appendix B Case Study

B.1 Description of the Actuator

B.2 Model of the Semi-Active Suspension System

B.3 Control Algorithms

B.4 Experimental Set-Up

B.5 Definition of the Test-Bench Experiments

B.6 Analysis of the Experimental Results




No. of pages:
© Butterworth-Heinemann 2011
eBook ISBN:
Hardcover ISBN:

About the Author

Sergio Savaresi

Affiliations and Expertise

Politecnico di Milano, dipartimento di Elettronica e Informazione, Italy

Charles Poussot-Vassal

Affiliations and Expertise

Systems Control and Flight Dynamics Department (DCSD) of ONERA, France

Cristiano Spelta

Affiliations and Expertise

Universita degli Studi di Bergamo, Italy

Olivier Sename

Affiliations and Expertise

Control Systems department of GIPSA-lab, France

Luc Dugard

Affiliations and Expertise

Control Systems department of GIPSA-lab, France