A Linear Programming Approach to Constrained Multivariable Control

Efficient operation of a process often means operation at or near constraints on the process inputs and/or outputs. At a constraint there is a loss in degrees of freedom which can cause serious degradation in the performance of control systems designed by classical single-loop or non-interacting design methods. We present a linear programming approach for dealing with linear inequality constraints on combinations of the process inputs and outputs. The approach is based on the strategy of estimating the effect of disturbances on the process outputs by subtracting from the measured outputs the effect of the control effort on the outputs. This is done with the aid of a process model. The inevitable mismatch between the process model and the real plant is accounted for by limiting the desired speed of response of the control system in a manner similar to that used by Model Algorithmic Control. Control system performance is demonstrated with the aid of several examples including multivariable systems with significant dead times and modeling errors.