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

Abstract

Shows how the non-minimal state space (NMSS)-based PIP-LQ control system design can be constrained to yield exactly the same control algorithm as both GPC and standard, minimal state, LQG design methods. However, while NMSS includes these other approaches as special cases, it is less constrained and so more flexible in general terms: for example, while PIP-LQ has the simplicity of GPC, it is formulated in the powerful context of state variable feedback (SVF) control, like LQG, which allows for ready access to modern robust control methods, including H∞ and associated risk sensitive optimal control. But, unlike conventional minimal state LQG controllers, the NMSS design does not require the introduction of an observer or Kalman filter, with the concomitant disadvantage of reduced robustness. Furthermore, the NMSS methodology is particularly appropriate for solving multi-objective optimisation problems.