On the extraction of dead-time controllers and estimators from delay-free parametrizations

Abstract

A novel approach to control design for dead-time (DT) systems is proposed. The underlying idea is to treat the DT element not as a part of the generalized plant, but rather as a (causality) constraint imposed upon the controller (estimator). This enables one to use well-understood parametrizations of all delay-free controllers in the DT design. In particular, DT controllers can be extracted from such delay-free parametrizations. In this paper the extraction procedures are developed in both H 2 and H 1 settings. It is shown that the proposed approach yields simple solution procedures and new transparent and intuitively appealing structures for the resulting controllers and estimators.

H/sup /spl infin// control of systems with multiple I/O delays via decomposition to adobe problems

“…Following [10] and [8], we exploit this fact to reduce the four-block problem with multiple delays to an equivalent one-block problem with multiple delays. To this end, we first need the standard solution, i.e., the solution for the situation when there are no delays.…”

“…The latter consists of a finite-dimensional system with a feedback/feedforward part that, though infinite dimensional, can be easily implemented owing to the fact that its components may be chosen to be FIR. This structure is reminiscent of that of the single-delay dead-time compensators proposed in [9] and [10], though the presence of feedforward interchannel interconnections is unique to the multiple delay situation. It is worth stressing in this respect that there appears to be no natural generalization of single-delay Smith predictor (deadtime compensator) schemes to the case of multiple delays; see, e.g., the discussion in [11].…”

“…Borrowing from [10] we define the completion operator , which "analytically completes" the impulse response of an -delay system to a delay-free system. Informally, see the following figure:…”

On the Dead-Time Compensation from<tex>$L^1$</tex>Perspectives

“…3. Expression (6), which splits the closed-loop system into two parts having impulse responses with disjoint supports, is similar to (3). Furthermore, when the regulated signal z is scalar, the arguments of Section II are directly applicable, so that…”

“…Since then, many of its modifications have been studied in the control literature [2], [3] and successfully implemented in practice. A remarkable property of DTC's, revealed in the last decade, is that generalized Smith predictors intrinsically result from some analytic design methods, such as the Youla parametrization and the H 2 and H 1 optimizations [4], [5], [6]. This property is important, both practically (as it makes implementation of infinite-dimensional controllers feasible) and conceptually (as it justifies the DTC configuration).…”