Generalised proportional-integral-plus control
This thesis is concerned with the True Digital Control (TDC) design philosophy and its practical embodiment in the non-minimal state space (NMSS) approach to control design, for systems described by discrete time transfer function models in the backward shift operator. This yields Proportional-Integral-Plus (PIP) controllers that are particularly easy to implement in practice, since the state variables are defined only in terms of the sampled input and output signals. The basic PIP algorithm is extended and enhanced in various ways to form a more sophisticated Generalised PIP controller. This includes an investigation into the importance of structure in PIP control design, the development of a command input anticipation technique and the introduction of two stochastic formulations of the problem, namely Kalman Filtering and risk sensitive optimal control. Finally, the thesis discusses the relationship between PIP and predictive control, in particular Generalised Predictive Control (GPC) and the Smith Predictor. The power of the approach is illustrated by the design of PIP controllers for a number of difficult applications also described in the thesis, including the control of a large horticultural greenhouse at Silsoe Research Institute; the control of carbon dioxide in crop growth experiments; the control of a Statistical Traffic Model simulation of interurban traffic networks; and, finally, the control of the multivariable Shell heavy oil fractionator simulation.