Velocity Control of a Counter-Flow Heat Exchanger

In this paper we consider a nonlinear tracking regulation problem for a counter-flow heat exchanger using velocity control. The methodology is based on a variation of our earlier work on design of feedback laws for regulation of distributed parameter systems based on the geometric theory of output regulation. In previous work we developed a technique, referred to as the β-iteration method, that has been successfully applied to regulate a wide variety of linear and nonlinear control system applications. We demonstrate that a modification of the β-iteration method can be successfully applied to a problem of thermal regulation for a counter-flow heat exchanger using velocity control. In particular, the thermal regulation of the cold (or hot) fluid is achieved by changing the speed of the hot (or cold) fluid. In this example, the β-iteration method produces a nonlinear control input operator that strongly depends on the state of the system. We provide two numerical examples where the goal is to track a time dependent reference signal. These examples illustrate the rapid convergence of the method and we observe that two iterations are often sufficient to achieve very accurate practical regulation.