Bitstream based Generalised Predictive Control for Linear Systems 

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Objectives of the Thesis

Although considerable success has been achieved and reported in the use of bit-stream for signal processing applications [48, 49], its application for controller implementation in very limited. Moreover, due to only classical controllers such as P, PI and PID being implemented in bit-streams for various applications [17, 11, 49, 21, 50, 51, 52, 53], there remains several open problems and practical issues that need more attention. Therefore, the main objective of the thesis is to investigate if bit-streams can be considered as a viable alternative to multi-bit implementation of sophisticated controllers. In an attempt to address these issues, existing bit-stream theory, predictive control algorithms and system identification tools will be employed to achieve the following objectives:
• To study the various features of bit-stream functional elements and to test and implement bit-streams on real plants.
• Investigate the performance of generalised predictive controller using bit-streams for linear systems and systems with time delay.
• Investigate the performance of bit-streams for unstable systems.
• Develop new methods of designing generalised predictive controllers for nonlinear system represented by polynomial nonlinear auto regressive moving average with exogenous input (NARMAX) models.
• Investigate the feasibility of a new type of nonlinear generalised predictive controller using polynomial NARMAX representation in bit-streams.

Outline of the Thesis

The organisation of the thesis proceeds in accordance with the objectives mentioned above. Following the introduction, Chapter 2 describes the various functional elements, such as bitstream converters, adders, subtractors, multipliers, tapped delay et cetera, which are the basic building blocks of a bit-stream system.
Chapter 3 focuses on the design and implementation of generalised predictive controller for linear systems in bit-stream considering two benchmark examples. The general guidelines for successful implementation of bit-stream GPC are presented. The methods of obtaining optimal tuning parameters using genetic algorithm are discussed.
After designing and implanting GPC for stable linear systems, Chapter 4 designs and implements in bit-stream, various types of controllers such as feedback linearising controller, state space based model predictive controller and generalised predictive controller for an unstable magnetic levitation system.
The next objective of the research has been to design and implement nonlinear GPC for nonlinear systems. The first step of this design process is to obtain a nonlinear model of the system. In this study, a nonlinear system is modelled by a polynomial NARMAX model. Therefore, Chapter 5 proposes a new structure selection algorithm to select significant terms of the model using evolutionary programming.
In Chapter 6, a novel GPC is designed for a class of nonlinear systems which are represented by polynomial NARMAX model. This controller is designed and implemented in bit-stream considering
several examples of complex nonlinear systems. The conclusions and future work are presented in Chapter 7.

Analogue and Digital Conversion in Bit-stream

The theory of bit-streams has been in existence for many years, but only with recent technological advances in semiconductor devices has their use become widespread [64]. The introduction of bit-stream signal processing for control purposes is a relatively new concept [11]. This type of encoding may be found under several names: Bit-streams, Sigma-Delta conversion, modulation and 1-bit processing. To understand how bit-stream can be used to represent signals, it is important to first understand the relationship between analogue and digital domains.

1 Introduction 
1.1 Motivation and Rational
1.2 Objectives of the Thesis
1.3 Outline of the Thesis
2 Bit-Streams – An Introduction 
2.1 Analogue and Digital Conversion in Bit-stream
2.2 The Concept of Bit-streams
2.3 Bit-Stream Functional Elements
2.4 Bit-stream Simulation of Linear and Nonlinear Systems
2.5 Conclusions
3 Bitstream based Generalised Predictive Control for Linear Systems 
3.1 Introduction
3.2 Generalised Predictive Control
3.3 Investigation Procedure
3.4 Case Study 1: Design of GPC for Speed Control of a D.C. Motor
3.5 Case Study 2: Design of GPC for Temperature Control of a Thermal System
3.6 Conclusions
4 Bit-stream based Controller for an Unstable Magnetic Levitation System 
4.1 Introduction
4.2 Mathematical Model of Magnetic Levitation System
4.3 Design of Feedback Linearising Controller
4.4 Linearised Model of Magnetic Levitation System .
4.5 Generalised Predictive Controller for Magnetic Levitation System
4.6 Conclusions
5 Structure Selection of Polynomial Nonlinear Systems 
6 Generalised Predictive Control for Nonlinear Systems 
7 Conclusion

Control of Linear and Nonlinear Systems Using Bit-Streams

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