Robust nonlinear control of a thermal mixing process

The paper describes the application of a combination of feedback linearization, backstepping and sliding mode control concepts to the robust control of a thermal mixer. The mixer consists of a mixing chamber, hot and cold fluid valves, and an exit valve. The commanded positions of the three valves are the available control inputs, while the controlled variables are total mass flow rate, chamber pressure and the density of the mixture inside the chamber. The three controlled outputs are required to accurately track reference commands while the system remains stable regardless of source pressure variations and unknown energy losses between the chamber and the environment. The model is a 5th order nonlinear system with three inputs and three outputs, with unmatched uncertainties. Feedback linearization is used to specify virtual controls that produce desired dynamics and disturbance rejection properties. Sliding variables are defined as the difference between actual and desired virtual controls. The control law is obtained from requiring that the sliding variables reach zero in finite time and remain zero indefinitely, regardless of uncertainties. The usefulness of the technique is illustrated with a simulation.