Interior point control of a heat equation using zero dynamics design

In this work the authors show how the zero dynamics design methodology, developed in a series of papers for boundary control of distributed parameter systems, can be extended to include interior point control for tracking problems and disturbance rejection for a one dimensional heat equation. In particular we demonstrate how simple control laws can be obtained for solving MIMO set-point control problems using co-located interior point control and actuation. The results apply also to a much wider class on one dimensional problems and also to some interesting nonlinear problems. In this conference work we restrict to the case of the heat equation and present two examples. In the first example we consider a problem with two interior controls. The tracking problem consists of a set-point control at one interior point while tracking a sinusoid at another interior point. In our second example we consider a multivariable set-point control problem