H∞ and µ-synthesis Design of Quarter Car Active Suspension System

Table of Contents

CHAPTER 1 INTRODUCTION

1.1 Background

1.2 Statement of the Problem

1.3 Objective of the Study

1.3.1 General Objective

1.3.2 Specific Objective

1.4 Contribution of the thesis work

1.5 Methodology

1.6 Scope and Limitation

1.7 Outline of the Thesis

CHAPTER 2 LITRATURE REVIEW

2.1 Background

2.2 Review on H∞ and μ− synthesis Controller Design of Car Active Suspension System

CHAPTER 3 MATHIMATICAL MODEL

3.1 Active Suspension System Mathimatical Model

3.2 Hydraulic Actuator System Mathematical Model

3.3 Road Disturbance Input Signals

3.3.1 Bump Road Disturbance

3.3.2 Random Road Disturbance

3.3.3 Sine Pavement Road Disturbance

3.3.4 Harmonic Road Disturbance

CHAPTER 4 CONTROLLER DESIGN

4.1 Uncertainty Modeling

4.1.1 Active Suspension System Uncertainity Modeling

4.1.2 Hydraulic Actuator System Uncertainity Modeling

4.2 The Effect of Stiffness Ratio on the Performance of the Active Suspension System

4.3 The Proposed Controller Design

4.3.1 Weighting Functions

4.3.2 H∞ Controller with Matlab

4.3.3 H∞ Norm

4.3.4 H∞ Robust Performance

4.3.4.1 Lower Bound

4.3.4.2 Upper Bound

4.3.4.3 Critical Frequency

4.3.5 H∞ Robust Stability

4.3.5.1 LowerBound

4.3.5.2 UpperBound

4.3.5.3 Critical Frequency

4.3.6 H∞ Worst Case Gain

4.3.6.1 Lower Bound

4.3.6.2 Upper Bound

4.3.6.3 Critical Frequency

4.3.7 The Effect of Stiffness Ratio on the H∞ Controller

4.3.8 μ−synthesis Controller with Matlab

4.3.9 μ−synthesis Norm

4.3.10 μ−synthesis Robust Performance

4.3.11 μ−Synthesis Robust Stability

4.3.12 μ−synthesis Worst Case Gain

4.3.13 The Effect of Stiffness Ratio on the μ−synthesis Controller

4.4 H2 Optimal Control of Active Suspension System

4.4.1 H2 Optimal Controller

4.5 Mixed H2/H∞ with Regional Pole Placement Control of Active Suspension System

4.5.1 Pole-Placement Region

4.5.2 Mixed H2/H∞ Controller Design

4.6 H∞ Mixed-Sensitivity Synthesis Method for Robust Control Loop Shaping Design of Active Suspension System

4.6.1 H∞ Mixed-Sensitivity Controller

4.7 Numerically Robust Pole Placement Algorithm of Active Suspension System

4.7.1 Robust Pole Placement Gain

4.8 H∞ Loop Shaping Design Using Glover McFarlane Method Control of Active Suspension System

4.8.1 H∞ Loop Shaping Controller Design

CHAPTER 5 RESULT AND DISCUSSION

5.1 Analysis of the Active Suspension System with H∞ Controller

5.1.1 H∞ Worst Gain Responce

5.1.2 Analysis of the Active Suspension System with H∞ Controller Closed-loop System with K1

5.1.3 Impulse and Step Responce of Active Suspension System with H∞ Controller

5.1.4 Robust Performance of the Active Suspension System with H∞ Controller Analysis using Nyquist Diagram

5.1.5 Robust Stability of the Active Suspension System with H∞ Controller using Nichols Chart

5.1.6 Openloop Gain Responce of the Active Suspension System with H∞ Controller for Road Disturbance and Actuator Force

5.2 Analysis of the Active Suspension System with μ−synthesis Controller

5.2.1 μ−synthesis Worst Gain Responce

5.2.2 Analysis of the Active Suspension System with μ-synthesis Controller Closed Loop System with Kdk

5.2.3 Impulse and Step Responce of Active Suspension System with μ−synthesis Controller

5.2.4 Robust Performance of the Active Suspension System with μ-synthesis Controller using Nyquist Diagram

5.2.5 Robust Stability of the Active Suspension System with μ-synthesis Controller using Nichols Chart

5.3 Active Suspension System Control Targets Simulation Output Specifications

5.4 Time Domain Comparison of the Active Suspension System with H∞ and μ−synthesis Controllers

5.4.1 Simulation of a Bump Road Disturbance

5.4.2 Simulation of a Random Road Disturbance

5.4.3 Simulation of a Sine Pavement Input Road Disturbance

5.4.4 Simulation of a Harmonic Road Disturbance

5.5 Time Domain Comparison Result of Active Suspension System with H∞ and μ−synthesis Controllers

5.5.1 Body Travel

5.5.2 Body Acceleration

5.5.3 Suspension Deflection

5.6 Frequency Domain Comparison of the Active Suspension System with H∞ and μ−synthesis Controllers

5.6.1 Body Travel

5.6.2 Body Acceleration

5.6.3 Suspension Deflection

5.7 Frequency Domain Comparison Result of Active Suspension System with H∞ and μ−synthesis Controllers

5.8 H∞ and μ−synthesis Controllers Comparison Results

5.9 Comparison of Robust Performance and Stability for the H∞ and μ−Synthesis Controllers

5.10 Comparison of the Active Suspension System with μ−synthesis and H2 Optimal Controller

5.10.1 Simulation of a Bump Road Disturbance

5.10.2 Simulation of a Random Road Disturbance

5.10.3 Simulation of a Sine Pavement Input Road Disturbance

5.10.4 Simulation of a Harmonic Road Disturbance

5.10.5 Time Domain Comparison Result of Active Suspension System with μ−synthesis Controller and H2 Optimal Controller

5.10.5.1 Body Travel

5.10.5.2 Body Acceleration

5.10.5.3 Suspension Deflection

5.11 Comparison of the Active Suspension System with μ−synthesis and Mixed H2/H∞ Controller

5.11.1 Simulation of a Bump Road Disturbance

5.11.2 Simulation of a Random Road Disturbance

5.11.3 Simulation of a Sine Pavement Input Road Disturbance

5.11.4 Simulation of a Harmonic Road Disturbance

5.11.5 Time Domain Comparison Result of Active Suspension System with μ−synthesis Controller and Mixed H2/H∞ Controller

5.11.5.1 Body Travel

5.11.5.2 Body Acceleration

5.11.5.3 Suspension Deflection

5.12 Comparison of the Active Suspension System with μ−synthesis and H∞ Mixed Sensitivity Controller

5.12.1 Simulation of a Bump Road Disturbance

5.12.2 Simulation of a Random Road Disturbance

5.12.3 Simulation of a Sine Pavement Input Road Disturbance

5.12.4 Simulation of a Harmonic Road Disturbance

5.12.5 Time Domain Comparison Result of Active Suspension System with μ−synthesis Controller and H∞ Mixed Sensitivity Controller

5.12.5.1 Body Travel

5.12.5.2 Body Acceleration

5.12.5.3 Suspension Deflection

5.13 Comparison of the Active Suspension System with μ−synthesis and Numerically Robust Pole Placement Controller

5.13.1 Simulation of a Bump Road Disturbance

5.13.2 Simulation of a Random Road Disturbance

5.13.3 Simulation of a Sine Pavement Input Road Disturbance

5.13.4 Simulation of a Harmonic Road Disturbance

5.13.5 Time Domain Comparison Result of Active Suspension System with μ−synthesis Controller and Numerically Robust Pole Placement Controller

5.13.5.1 Body Travel

5.13.5.2 Body Acceleration

5.13.5.3 Suspension Deflection

5.14 Comparison of the Active Suspension System with μ−synthesis and H∞ Loop Shaping Controller

5.14.1 Simulation of a Bump Road Disturbance

5.14.2 Simulation of a Random Road Disturbance

5.14.3 Simulation of a Sine Pavement Input Road Disturbance

5.14.4 Simulation of a Harmonic Road Disturbance

5.14.5 Time Domain Comparison Result of Active Suspension System with μ−synthesis Controllers and H∞ Loop Shaping Controller

5.14.5.1 Body Travel

5.14.5.2 Body Acceleration

5.14.5.3 Suspension Deflection

5.15 Comparison Results of the μ−synthesis Controller with the Robust Controllers

5.16 Numerical Values of the Simulation Outputs

5.17 Body Accelerations Comparison of the Active Suspension System with μ−synthesis Controller with VW (Volkswagen) Passat B5 Passenger Car When the Car Crossed a Speed Bump

CHAPTER 6 CONCULUSION AND RECOMENDATION

6.1 Conculusion

6.2 Recomendation

Research Goals and Core Themes

The primary objective of this thesis is to design and evaluate H∞ and μ-synthesis controllers for a linear quarter car active suspension system to enhance passenger comfort and road handling. The research focuses on mitigating the effects of parametric uncertainties and various road disturbances by developing robust control models that outperform traditional passive suspension systems.

• Design of robust H∞ and μ-synthesis controllers for active suspension systems.
• Development of mathematical models for vehicle dynamics and hydraulic actuators.
• Simulation and comparative analysis under multiple road profiles (bump, random, sinusoidal, harmonic).
• Performance evaluation based on ride comfort, body acceleration, and suspension deflection.
• Benchmarking the proposed control strategies against traditional and other robust control methods (H2 optimal, pole placement, loop shaping).

Excerpt from the Book

Summary of Chapters

CHAPTER 1 INTRODUCTION: Outlines the motivation, problem statement, research objectives, and the scope of developing robust control strategies for active suspension systems.

CHAPTER 2 LITRATURE REVIEW: Provides a comprehensive overview of existing research and literature concerning the design of robust controllers for automotive active suspension systems.

CHAPTER 3 MATHIMATICAL MODEL: Details the mathematical modeling of the quarter car active suspension system, hydraulic actuator dynamics, and various road disturbance profiles.

CHAPTER 4 CONTROLLER DESIGN: Covers the design methodology for H∞, μ-synthesis, and other comparative robust control strategies using MATLAB/Simulink tools.

CHAPTER 5 RESULT AND DISCUSSION: Presents simulation results comparing the performance of different robust controllers across time and frequency domains under various road conditions.

CHAPTER 6 CONCULUSION AND RECOMENDATION: Summarizes the findings of the thesis and provides suggestions for future research in the field of active suspension control.

Keywords

Active suspension system, H∞ controller, μ-synthesis controller, Robust controller, H2 optimal controller, vehicle dynamics, road disturbance, hydraulic actuator, passenger comfort, road handling, MATLAB simulation, robust stability, robust performance, control theory.

Frequently Asked Questions

What is the primary focus of this thesis?

This thesis focuses on designing and testing advanced robust control strategies (H∞ and μ-synthesis) to improve the performance of a quarter car active suspension system, specifically targeting better ride comfort and road handling.

What are the central thematic fields covered?

The work integrates control theory, vehicle dynamics, mathematical modeling of hydraulic actuators, and numerical simulation of road surface disturbances.

What is the main objective or research question?

The main objective is to develop a control system that can effectively minimize vehicle vibrations and suspension deflection despite uncertainties in vehicle parameters and unpredictable road conditions.

Which scientific methods are applied in this research?

The research uses robust control theory, specifically H∞ and μ-synthesis, alongside pole placement algorithms, loop shaping, and H2 optimal control, implemented and validated via MATLAB scripts.

What topics are discussed in the main body?

The main body covers mathematical modeling of vehicle systems, formulation of uncertainty models, design of specific controllers, and an extensive comparative simulation analysis of the controllers under various road input signals.

Which keywords best characterize this work?

Key terms include active suspension, robust control, H-infinity, μ-synthesis, vehicle dynamics, road disturbance modeling, and passenger comfort optimization.

Why are multiple road disturbance types used in the simulations?

Using four different road types (bump, random, sinusoidal, and harmonic) allows for a comprehensive evaluation of how each controller handles different spectral characteristics and intensity levels of road irregularities.

What is the significance of the 50% reduction mentioned in the results?

The 50% reduction in body acceleration indicates the superior effectiveness of the designed μ-synthesis controller compared to a conventional passenger vehicle (VW Passat B5) when crossing speed bumps.