Control System Selection: a Measure of Control Quality Loss in Analytical Control

A question that often process control engineers face is for what class of processes one should use model predictive control that requires solving numerically a constrained optimization problem repeatedly on-line. The alternative is to use analytical control, such as P, PI, PID and differential geometric control, which do not require the on-line optimization. In other words, for what class of processes can analytical control provide control quality close to the optimal control quality that model predictive control (MPC) can provide? This work presents a measure that allows one to quantify the degradation in closed-loop performance when one implements analytical control instead of MPC. A special case of the measure is used to derive a simple test that can be used to check if a given input-constrained process can be controlled satisfactorily by analytical control. It is shown that processes that exhibit directionality greatly benefit from MPC. In other words, for input-constrained processes whose nonsingular characteristic (decoupling) matrix is independent of manipulated inputs and can be made diagonal by row or column rearrangements, control quality provided by analytical control can be adequate. The measure is used to see if four input-constrained process examples can be controlled satisfactorily by analytical control. Closed-loop responses are shown to confirm the usefulness of the measure.