Design of stable proportional-integral-plus controllers

There are a number of reasons why, in practical situations, implementation of an unstable dynamic controller may be undesirable. In particular, sensor failure can result in a forward path which is unstable and might severely damage the plant. As with many dynamic controller design techniques, the PIP design philosophy may produce controllers which stabilize the closed-loop system, but are themselves unstable. This paper builds upon the existing PIP design philosophy, introducing a design step which stabilizes the PIP controller. This design strategy not only stabilizes the controller, but also ensures that the equivalent closed-loop transfer function of the system remains identical (in the absence of model mismatch) to that of the original PIP closed-loop system.