On the Optimal Digital State Vector Feedback Controller With Integral and Preview Actions

Abstract

A digital state vector feedback controller with integral and preview actions, which can be called a proportional plus integral plus derivative plus preview (PIDP) controller, is derived based on linear quadratic optimal control theory. The preview action is a generalization of the feedforward concept which has been exercised in many process control situations. Preview of future system disturbance inputs is shown to be effective to improve the performance of the control system.

Robust servomechanism with preview action for polytopic uncertain systems

“…Kojima and Ishijima [12] derived an H controller with preview action for a continuous-time system based on the state-space H control theory for in"nite-dimensional systems. Choi et al [13] considered the H control of a discrete-time system with previewable disturbance based on the technique due to Tomizuka and Rosenthal [2].…”

Biped walking pattern generation by using preview control of zero-moment point

“…In 1969, Hayase and Ichikawa worked on the same concept and solved a linear quadratic (LQ) optimal servo controller with preview action [17]. A digital version of LQ optimal preview controller was developed by Tomizuka and Rosenthal in 1979 [18] and was completed as the controller for MIMO system by Katayama et.al in 1985 [19].…”

Restricted structure predictive optimal control

“…Combining the state equations for the reference, plant, and noise obtain the total augmented system as The total observations signal now follows as The augmented system and the feedback/tracking control problem are illustrated in Figure 1. The equation for the future outputs to be costed in the criterion may be written in terms of the state vector XðtÞ; using (6), as…”

“…Future setpoint information has been used in a number of linear quadratic (LQ) optimal control problems [6,7] and summarized in the seminal work of Bitmead et al [8]. The use of state-space models for GPC was proposed by Ordys and Clarke [9] and extended by Ordys and Pike [10].…”