Multivariable Proportional-Integral-Plus (PIP) control of time delay systems.

Although it is able to exploit the full power of optimal state variable feedback within a Non-Minimum State Space (NMSS) setting, the Proportional-Integral-Plus (PIP) controller is a logical extension of conventional PI/PID controllers, with additional dynamic feedback and input compensators introduced automatically by the NMSS formulation of the problem when the process has second or higher order dynamics or pure time delays greater than one sampling interval. Furthermore, under certain pole assignment conditions, the PIP controller is directly equivalent to the ubiquitous digital Smith Predictor (SP) control system, so allowing SP controllers to be considered within the context of optimal NMSS state variable feedback control. The present paper applies the PIP methodology to the multivariable Shell heavy oil fractionator simulation, a highly coupled linear model with time delays that illustrates some of the control problems associated with a typical industrial plant and demonstrates the ability of PIP control to overcome these problems.