Application of Model Order Reduction Techniques in PID controller Design

Doctoral Thesis / Dissertation , 2012 , 314 Pages , Grade: A

Engineering - General

The analysis and synthesis of higher order models are complicated and are not desirable on economic and computational considerations. To circumvent the difficulties, lower order model formulation techniques are utilized to find a lower dimensional approximant for the original higher order model. The obtained lower order model preserves the characteristics of the original higher order model.

Firstly, the linear time invariant single input single output continuous systems are considered to investigate the efficiency of the proposed lower order model formulation approach. For this, the given linear time invariant higher order system represented in the form of transfer function is adopted to get adjunct lower order transfer function and its coefficients are tuned suitably with the help of modified particle swarm optimization along with transient and steady state gain adjustments. The lower order model is formed on an error based criterion. Moreover, the formulated second order models are used to design the continuous PID controllers.

Secondly, the single input single output linear time invariant discrete systems are dealt for model order formulation with the help of proposed approach. Discrete PID controllers are designed by employing the proposed formulated lower order model and it retains the desired performance specifications. The lower order models minimize the computational complexities for the process of output stabilization compared with higher order models. The proposed approach is direct and simple in approach for linear time invariant discrete systems.

Thirdly, certain procedures are proposed for designing the state feedback controller and state space observer of linear time invariant continuous and discrete systems. Further, the lower order model formulation approach for single input single output systems is extended to multi input multi output linear time invariant continuous and discrete systems. The analysis of the discrete system is carried out directly without applying any linear or bilinear transformations, which reduces computational complexities. This approach guarantees an absolutely stable lower order model if the considered higher order system is stable in nature. The proposed methodology extracts a second order model which has a better approximation compared to models obtained due to other methods.

Algorithms are also presented for all the contributions provided in the thesis with illustrations and results.

Inhaltsverzeichnis (Table of Contents)

• Abstract
• Chapter 1: Introduction
  • 1.1 Introduction to Lower Order Model Formulation
  • 1.2 Motivation of the Work
  • 1.3 Literature Survey
  • 1.4 Organization of the Thesis
• Chapter 2: Lower Order Model Formulation for Single Input Single Output Linear Time Invariant Continuous Systems
  • 2.1 Problem Statement
  • 2.2 Existing Techniques of Order Reduction
  • 2.3 Proposed Lower Order Model Formulation Approach
  • 2.4 Design of Continuous PID Controllers
  • 2.5 Case Studies
• Chapter 3: Lower Order Model Formulation for Single Input Single Output Linear Time Invariant Discrete Systems
  • 3.1 Problem Statement
  • 3.2 Proposed Lower Order Model Formulation Approach for Discrete Systems
  • 3.3 Design of Discrete PID Controllers
  • 3.4 Case Studies
• Chapter 4: State Feedback Controller and State Space Observer for Linear Time Invariant Continuous and Discrete Systems
  • 4.1 Problem Statement
  • 4.2 State Feedback Controller Design
  • 4.3 State Space Observer Design
  • 4.4 Case Studies
• Chapter 5: Reliability Analysis of Lower Order Models for Linear Time Invariant Continuous and Discrete Systems
  • 5.1 Problem Statement
  • 5.2 Reliability Analysis for Continuous Systems
  • 5.3 Reliability Analysis for Discrete Systems
  • 5.4 Case Studies
• Chapter 6: Lower Order Model Formulation for Multi Input Multi Output Linear Time Invariant Continuous and Discrete Systems
  • 6.1 Problem Statement
  • 6.2 Proposed Lower Order Model Formulation Approach for MIMO Systems
  • 6.3 Case Studies
• Chapter 7: Conclusion

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This thesis aims to develop a comprehensive and effective algebraic approach for formulating lower order models of linear time-invariant systems. This approach is designed to circumvent the complexities and computational challenges associated with higher order models while preserving the essential characteristics of the original system.

• Lower Order Model Formulation for Linear Time Invariant Systems
• Comparison of Lower Order Model Formulation Techniques
• Design of Controllers using Lower Order Models
• Reliability Analysis of Lower Order Models
• Extension of Lower Order Model Formulation to Multi Input Multi Output Systems

Zusammenfassung der Kapitel (Chapter Summaries)

Chapter 1 introduces the concept of lower order model formulation, highlighting its significance and providing a comprehensive literature review. It also outlines the organization and structure of the thesis.

Chapter 2 delves into the application of the proposed lower order model formulation approach to single input single output linear time invariant continuous systems. It explores existing order reduction techniques, presents the proposed approach, and demonstrates its efficacy through case studies. The chapter also discusses the design of continuous PID controllers using the formulated lower order models.

Chapter 3 extends the proposed approach to single input single output linear time invariant discrete systems. It addresses the specific challenges of discrete system modeling and outlines the steps involved in designing discrete PID controllers based on the formulated lower order models.

Chapter 4 focuses on the design of state feedback controllers and state space observers for linear time invariant continuous and discrete systems. The chapter leverages the proposed lower order model formulation approach to simplify the design process and ensure robust performance.

Chapter 5 undertakes a thorough reliability analysis of the lower order models for linear time invariant continuous and discrete systems. The chapter compares the cost functions of optimal and sub-optimal control to evaluate the consistency and effectiveness of the proposed approach.

Chapter 6 generalizes the lower order model formulation approach to multi input multi output linear time invariant continuous and discrete systems. It emphasizes the advantages of the proposed approach for handling MIMO systems, showcasing its effectiveness through case studies.

Schlüsselwörter (Keywords)

This thesis explores the realm of lower order model formulation, particularly in the context of linear time-invariant systems. Key keywords and concepts include: lower order model formulation, order reduction, linear time-invariant systems, continuous systems, discrete systems, PID controllers, state feedback controllers, state space observers, multi input multi output systems, reliability analysis, and cost function.

• College: Anna University
• Grade: A
• Author: Dr G. Sugumaran (Author)
• Publication Year: 2012
• Pages: 314
• Catalog Number: V1164249
• ISBN (PDF): 9783346576477
• ISBN (Book): 9783346576484
• Language: English
• Tags: application, model, order, reduction, techniques, design