Robustness analysis of digital control systems

In recent years the advances made in microcomputer and microprocessor industry have infused digital control systems into the human life. One of the most important requirements in the performance of control system is stability. This is true whether the system has continuous data, digital data or a combination of the two kinds of signal. Routh-Hurwitz criterion, the Nyquist criterion, the Bode plot and the Nichols plot are the most famous and well-known methods of stability analysis for continuous systems. All these methods can be used for stability analysis of digital control systems with some little changes. Much of the material being taught in a first course on automatic control appears to have changed little over the last two decades. While the basic theories on classical control remain unchanged, there have been many new developments in the field of control theory in recent years. One such topic is the relatively recent development in methods to analyse systems with parametric uncertainty. The goal of this thesis is to investigate some methods of the robust stability analysis of digital control systems with parametric uncertainties. It is well known that the uncertainties in the physical systems are an unavoidable fact. Therefore, taking uncertainties into account while analysing control systems gives some advantages. In this thesis, the methods related to robust stability of digital control systems with parametric uncertainty are studied. This thesis presents additional results in this direction and the work can be divided into three main parts. The first part presents the digital control systems, which has the simplest definition of its subtitles. The second part of this thesis deals with the parametric uncertainties of interval systems. Some new approaches used for the stability analysis of digital control systems with parametric uncertainty are investigated in this section. The robust stability of interval transfer functions are discussed using value set and frequency domain stability analysing techniques such as Nyquist, Bode and Nichols diagrams. Some required software programs have been prepared in the MATLAB environment. The results developed in these research work, have potential features to be used for practical applications. It is also possible to extend these results to other uncertainty structures. IV The last part is about the design of digital proportional-integral-derivative (PID) controllers. Some specifications have been discussed about the controller design and some examples have been done for intensifying the subject. KEYWORDS : Automatic Control, Digital Control, Kharitonov Theorem, Edge Theorem, Stability, Value Set, Parametric Uncertainty, Nyquist Diagram, Bode Diagram, Nichols Diagram, Digital Interval Polynomials, Digital PID Controller.