Robust constrained regulator problem for linear uncertain continuous-time systems: application to a pH-process

The regulator problem for linear uncertain continuous-time systems having control constraints is considered. Necessary and sufficient conditions of positive invariance of polyhedral domains are extended to the case of continuous-time uncertain systems. Robust constrained regulators are then derived. An application to the control of a stirred tank pH is then achieved. First, the process is modeled as models studied hereafter, then a robust constrained regulator is calculated. Simulation results show that this control law is easy to implement and guarantees robust asymptotic stability and control admissibility.