Project README

Overview

This project focuses on designing and implementing industrial control systems, specifically aimed at accurately identifying, modeling, and controlling a given system with inherent time delays. Using MATLAB and Simulink, the project performs system identification, controller design, and simulation to achieve optimal performance. Various PID tuning methods, such as Ziegler-Nichols, modified Ziegler-Nichols, and Smith Predictor, are evaluated for their effectiveness in handling time-delay effects and improving system stability.

Table of Contents

1. Introduction
2. Problem Definition
3. System Identification
   • Three-Element Model Identification
   • Four-Element Model Identification
   • MATLAB Identification (ident command)
4. Response Comparison
5. System Final State Parameters
   • Relay Feedback Application
   • Final Parameter Determination
6. PID Controller Design
   • Ziegler-Nichols (Time Domain)
   • Ziegler-Nichols (Frequency Domain)
   • Extended Ziegler-Nichols
   • Lambda Tuning Method
7. Smith Predictor Implementation
   • Complete System Dynamics
   • Design with Identified Models
     • Three-Element Model
     • Four-Element Model
     • ident Command Model
8. Analysis and Comparison

Project Structure

1. Introduction

This section provides a foundational understanding of industrial control methods and the significance of accurate system identification in designing effective controllers.

2. Problem Definition

The given system is characterized by a first-order denominator with a time delay. The project aims to identify the system using both three- and four-element models and to design various controllers based on these models.

3. System Identification

Using MATLAB and Simulink, the system's characteristics are identified:

• Three-Element Model: Estimation of parameters such as final value, time constant, and delay.
• Four-Element Model: Enhanced modeling through computation-intensive methods and non-linear equation solving.
• MATLAB ident Command: For further accuracy, identification is performed with and without time delay considerations.

4. Response Comparison

All models’ responses are plotted for comparison, with the four-element model generally providing the most accurate behavior.

5. System Final State Parameters

Relay feedback is applied to determine the system's final point parameters, using amplitude and oscillation period to extract system details crucial for controller tuning.

6. PID Controller Design

PID controllers are designed using different methods:

• Ziegler-Nichols (Time Domain): Provides baseline PID values but may exhibit slow settling time.
• Ziegler-Nichols (Frequency Domain): Improves response speed and overshoot compared to the time domain.
• Extended Ziegler-Nichols: Modified tuning for enhanced stability.
• Lambda Tuning Method: Based on a predefined λ, optimizing stability and control accuracy.

7. Smith Predictor Implementation

The Smith Predictor compensates for system delays, achieving an ideal response by moving the delay out of the feedback loop:

• Complete System Dynamics: The Smith Predictor is applied to the original system.
• Identified Models: Implemented with each model (three-element, four-element, and ident-based) to evaluate model accuracy and stability.

8. Analysis and Comparison

The project evaluates various controller designs and their impact on system stability, precision, and response time. The Smith Predictor method, combined with an accurate model, provided optimal delay compensation, resulting in the most stable and responsive control.

Conclusion

This project demonstrates the effectiveness of combining MATLAB’s computational capabilities with robust control design techniques to achieve precise and stable control of time-delay systems in an industrial context.