Structural and predictive aspects of proportional-integral-plus (PIP) control

Abstract

The Proportional-Integral-Plus (PIP) controller is based on the definition of a special Non-Minimal State (NMSS) form in which the state vector consists only of measured variables. PIP allows for the implementation of powerful state variable feedback control designs without resort to state reconstruction by a Kalman Filter or observer. A previous application has demonstrated the structural equivalence between PIP controller design in this manner and the Generalized Predictive Controller (GPC) as well as the direct equivalence between GPC and standard minimal state Linear Quadratic Gaussian (LQG) designs. To complete the link, this paper establishes the conditions for the full equivalence between PIP, GPC, and minimal LQ designs. In so doing, it reveals the advantages of the NMSS-based PIP approach in relation to these other design procedures. Show more