State space control system design based on non-minimal state-variable feedback: further generalization and unification results

This paper shows how proportional-integral-plus linear-quadratic (PIP-LQ) c ontrol, based on non-minimal state space (NMSS) control system design, can be constrained to yield exactly the same control algorithm as both generali zed predictive control (GPC) and standard, minimal state, linear quadratic gaussian (LQG) design methods. However, while NMSS includes these other app roaches as special cases, it is less constrained and so more flexible in ge neral terms: for example, while PIP-LQ has the simplicity of GPC, it is for mulated like LQG in the powerful context of state variable feedback (SVF) c ontrol, which allows for ready access to modern robust control methods. Fur thermore, the paper suggests that the NMSS approach provides the greater de sign freedom, with a wider range of possible LQ solutions than its minimal state space equivalent.