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

Master's Thesis , 2020 , 172 Pages

Engineering - Automotive Engineering

To improve the road handling and passenger comfort of a vehicle, a suspension system is provided. An active suspension system is considered to be better than the passive suspension system. In this thesis, 2 degrees of freedom of a linear quarter car active suspension system is designed, which is subject to different disturbances on the road. Since the parametric uncertainty in the spring, the shock absorber, mass and the actuator has been considered, robust control is used. In this thesis, H∞ and µ− synthesis controllers are used to improve the driving comfort and the ability to drive the car on the road. For the analysis of the time domain, using a MATLAB script program and performed a test using four disturbance inputs of the road (bump, random, sinusoidal and harmonic) for the suspension deflection, the acceleration of the body and the body travel for the active suspension with the H∞ controller and active suspension with µ− synthesis controller and the comparative simulation and reference results demonstrate the effectiveness of the presented active suspension system with µ− synthesis controller.

In addition, in this thesis, comparison have been made between the active suspension system with µ−synthesis controller and 5 different robust controller for suspension deflection, body acceleration and body travel tests using bump, random, sinusoidal pavements and harmonic road disturbances. Body accelerations comparison of the active suspension system with µ−synthesis controller with VW (Volkswagen) Passat B5 passenger car is done for a bump road input disturbance and the result shows that there is a 50% reduction in body acceleration for the active suspension system with µ− synthesis controller.

Inhaltsverzeichnis (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

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

The primary aim of this thesis is to design H∞ and μ-synthesis controllers for an active suspension system to enhance the vehicle's ride comfort and road handling. This is accomplished by implementing robust control techniques that effectively mitigate the impact of uncertainties in the system's parameters, such as spring stiffness, damping coefficients, mass, and actuator dynamics. By comparing these controllers under various road disturbances, the thesis explores their performance in reducing suspension deflection, body acceleration, and body travel.

• Robust Control Design: The thesis focuses on the use of H∞ and μ-synthesis controllers, which are robust control techniques explicitly addressing uncertainties in system parameters and disturbances.
• Active Suspension System Design: The research investigates the effectiveness of active suspension systems in improving ride comfort and road handling compared to passive suspension systems.
• Performance Evaluation: The thesis analyzes the controllers' performance in minimizing suspension deflection, body acceleration, and body travel under various road disturbances, including bump, random, sinusoidal, and harmonic profiles.
• Controller Comparison: The research compares the performance of the H∞ and μ-synthesis controllers, as well as the μ-synthesis controller with other robust control methods, to determine the most effective approach for active suspension system control.

Zusammenfassung der Kapitel (Chapter Summaries)

Chapter 1 introduces the concept of active suspension systems and the motivation for designing robust controllers to address uncertainties. It outlines the thesis objectives, methodology, and scope. Chapter 2 provides a comprehensive literature review on H∞ and μ-synthesis control methods applied to active suspension systems. It highlights relevant studies and identifies existing gaps in the field that this thesis aims to address.

Chapter 3 details the mathematical modeling of the quarter car active suspension system, including the hydraulic actuator and road disturbances. It provides a clear understanding of the system dynamics and the inputs that influence the suspension performance. Chapter 4 focuses on the controller design, including the proposed H∞ and μ-synthesis controllers. The chapter explores the uncertainty modeling and analysis techniques used to ensure the robustness and stability of the designed controllers.

Chapter 5 presents the simulation results and discussion of the different controllers. The time and frequency domain analyses are presented, demonstrating the effectiveness of the μ-synthesis controller compared to other robust controllers. The study highlights the reduction in body acceleration achieved by the μ-synthesis controller compared to the benchmark data from a VW Passat B5 passenger car. Chapter 6 summarizes the key findings and provides recommendations for future research on active suspension systems.

Schlüsselwörter (Keywords)

This research focuses on the application of robust control techniques to design an active suspension system that effectively manages uncertainties and improves passenger comfort and vehicle handling. The key terms and concepts explored in the study include:

• Quarter car active suspension system
• H∞ controller
• μ-synthesis controller
• Robust controller
• H2 optimal controller
• Uncertainties modeling
• Road disturbances
• Body travel
• Body acceleration
• Suspension deflection

• College: Jimma University College of Agriculture and Veterinary Medicine
• Author: Mustefa Jibril (Author)
• Publication Year: 2020
• Pages: 172
• Catalog Number: V515112
• ISBN (eBook): 9783346146038
• ISBN (Book): 9783346146045
• Language: English
• Tags: design, quarter, active, suspension, system