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

Multivariable proportional-integral-plus (PIP) control of the ALSTOM nonlinear gasifier simulation

“…This contrasts with minimal state space models that represent the same system in a less intuitive manner, requiring each state to be formed from various, often rather abstract, combinations of the input and output signals. In this manner, the non-minimal formulation provides more design freedom than the equivalent minimal case, as discussed by [2].…”

“…Consider in the first instance, a PIP controller based on TF models obtained from open-loop experiments at the 100% load operating condition. By first converting the TF models given by Tables 1 and 2 into MFD form (1), it is a straightforward exercise to develop the equivalent 24th order linear NMSS representation (2). Solution of the LQ cost function (8), subsequently yields a fixed gain PIP control agorithm (6), suitable for implementation in the forward path form of Fig.…”

“…The PIP controller can be interpreted as a logical extension of conventional PI/PID algorithms, but with inherent model-based predictive control action [1,2]. Here, multivariable Non-Minimal State Space (NMSS) models are formulated so that full state variable feedback control can be implemented directly from the measured input and output signals of the controlled process, without resorting to the design of a deterministic state reconstructor (observer) or a stochastic Kalman filter.…”

A Refined Iv Method for Closed-Loop System Identification

“…The control system used in the illustrative example considered later in section 4 is based on the discrete-time Proportional-Integral-Plus (PIP) control system design methodology (see e.g. Young et al [1987], Taylor et al [2000] and the prior references therein).…”

“…The PIP-LQ control system is implemented in the forward path form, with a diagonal cost function weighting matrix having weights of 100 on the integral-of-error state and unity on the other non-minimal state variables (past values of the input and output signals): see Taylor et al [2000]. In all cases, the PIP control system is designed on the basis of the discrete-time equivalent of the continuous-time model at the selected sampling interval.…”