Control of general time delay systems using Matlab toolbox

Abstract

The aim of this paper is to show an application of Matlab toolbox "Robust Control Toolbox for Time Delay Systems with Time Delay in Numerator and Denominator". The solved problem is robust control of time delay system with time delay in numerator and denominator of the controlled plant. This type of problem is usually solved in the ring of retarded quasipolynomial (RQ) meromorphic functions. This approach can solve the task for nominal plants but it is not easy to apply this technique if the plant has uncertain time delays. In this paper, the plant is defined as a system with uncertain time delays which can vary in predefined intervals. A method handling this problem in the robust sense is derived and implemented using both the D-K iteration and algebraic approach. The D-K iteration is a standard method in the structured singular value framework. However, some remaining issues are present, such as nonzero steady-state error and the necessity of approximation of the resulting controller with low order system due to its high complexity. A solution the algebraic approach combining the structured singular value, algebraic theory and global optimization method can give. Here, Differential Migration is used providing high efficiency in finding the global extreme and reliable results.