The control of multivariable time-delayed processes and a generalized Smith predictor : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Production Technology at Massey University
In this thesis the description, analysis and control of time-delayed multivariable processes are investigated, particularly the descriptions of multivariable processes that facilitate a multivariable extension of the Smith predictor. Two new pseudo-commutativity results for matrix multiplication are presented. These results are used to show that a general time-delayed transfer function can be decomposed into three components representing input-delays, output-delays and the delay-free dynamics of the process. It is also shown that any such time-delayed transfer function can also be written in a form in which all the delays appear as output-delays. These time-delayed transfer functions are used in the development of a multivariable Smith predictor. It is also shown that the pseudo-commutativity results can be applied to non-delayed processes. In particular a new method, based on these results, for reformulating a transfer function description of a process as a state-space description is developed. A case study of a time-delayed process is investigated.