In current industrial control, PID technology is firmly established as the standard. Often, however, high control loop performance can only be obtained within narrow limits around a given steady-state operating point. If perturbations introduced by any reference or load change are outside these limitations then the actuators will constrain the system inputs. Other operational limits may also be imposed by additional variables within the plant producing output constraints.

A typical method of dealing with input and output constraints, especially for PID control, has been the...