Model Order Reduction for Decentralized PID Control Design on TITO processes

The decentralized PID control design of multivariable processes is an appealing approach due to its practical applicability and the existence of a good theoretical basis. However, although industrial processes may be modeled using simple first order and second order models, in decentralized control, the models increase their complexity due to loop interaction, compromising the applicability of existing PID tuning rules. In fact, even inverse response behavior may appear due to loop interaction. The contribution of the article is twofold. First, we derive conditions to assess the inverse response behavior of reduced effective transfer functions. As a result, we know when tuning rules for first order and minimum phase second order models are suited for decentralized control tunning. Secondly, at the sight of matrix transfer function parameters, we derive simplified models in a straightforward way. The results are useful for decentralized MIMO process control design using simple tuning rules derived for first order and second order systems.