Multiple order models in predictive control
Predictive control has attracted much attention from both industry and academia alike due to its intuitive time domain formulation and since it easily affords adaption. The time domain formulation enables the user to build in prior knowledge of the operating constraints and thus the process can be controlled more efficiently, and the adaptive mechanism provides tighter control for systems whose behaviour changes with time. This thesis presents a fusion of technologies for dealing with the more practical aspects of obtaining suitable models for predictive control, especially in the adaptive sense. An accurate model of the process to be controlled is vital to the success of a predictive control scheme, and most the of work to date has assumed that this model is of fixed order, a restriction which can lead to poor controller performance associated with under/overparameterisation of the estimated model. To overcome this restriction a strategy which estimates both the parameters and the order of a linear model of the time-varying plant online is suggested. This Multiple Model Least-Squares technique is based on the recent work of Niu and co-workers who have ingeniously extended Bierman's method of UD updating so that, with only a small change to the existing UD update code, a wealth of additional information can be obtained directly from the U and D matrices including estimates of all the lower order models and their loss functions. The algorithm is derived using Clarke's Lagrange multiplier approach leading to a neater derivation and possibly a more direct understanding of Niu's Augmented UD Identification algorithm. An efficient and robust forgetting mechanism is then developed by analysing the properties of the continuous-time differential equations corresponding to existing parameter tracking methods. The resulting Multiple Model Recursive Least-Squares estimator is also ported to the δ-domain in order to obtain models for predictive controllers that employ fast sampling. The MMRLS estimator is then used in an adaptive multiple model based predictive controller for a coupled tanks system to compare performance with the fixed model order case.