An approach to control MIMO time-delay processes

This work develops an approach to control MIMO (Multiple Inputs Multiple Outputs) time-delay processes that can be represented by stable time-delay transfer matrices. A method to transform a time-delay transfer matrix into a delay-free one is also developed. Such a delay-free transfer matrix is used to obtain its state space representation in order to design a linear quadratic regulator controller. This controller is applied to the time-delay transfer matrix with the purpose of obtaining controlled outputs with the ability to follow arbitrary reference signals. Such outputs are also employed for an observer to estimate the state vector of the delay-free transfer matrix. The estimated vector is then employed to compute the controller. Two time-delay processes representing industrial distillation columns were used to demonstrate the validity of the design approach.