Modern, continuous and discrete, control

This thesis considers various topics in modern control. With a view to microprocessor implementation, we shall first address finite word length problems in discrete control. We propose the use of an alternative operator (the delta operator) to the usual shift operator in order to improve finite word length properties. The use of the delta operator also allows a unified treatment of many topics in continuous and discrete systems theory. It also allows a unified treatment of parameter estimation and adaptive control. We give a unified global convergence proof for an adaptive pole assignment algorithm based on the above ideas. One confusing difference between continuous and discrete systems has existed with regard to the zeros of sampled continuous time systems. The sampling process often introduces extra zeros in the discrete time model which become unstable if the sampling rate is increased. In this thesis we show that these extra zeros can be ignored if rapid sampling is used and so discrete time model reference adaptive control is possible. In chapter 7 we consider the control of a particular type of non-linear system, namely a rigid link robot system. We show how linear parameter estimation may be used to give a globally convergent adaptive computed torque control scheme.