OPTIMAL LINEAR CONTROL OF DISTRIBUTED SYSTEMS MORTON M. DENN
University of Delaware, Newark, Del., 1977 1 The optimal controller for a linear-distributed system relative to a quadratic error criterion is shown to be a linear feedback-feedforward control system in which the gains may be entirely precomputed.
PTIMAL
control theory is generally of significance to prac-
0 tical controller design in the chemical process industries
only in those few situations in which the optimal policy may be precomputed as a feedback-feedforward system, where the only information needed is the present state and a measure of the disturbances entering the system. Several such results are well known for lumped linear systems and are discussed in texts on optimal control ( k h a n s and Falb, 1966). The extension of these important results of control theory to the control of dynamical systems which are spatially distributed has not been widely undertaken, however. I n this paper we extend one such classical result, control relative to a quadratic error criterion, to include linear distributed systems. Although arbitrary linear differential operators in the spatial variable can be treated, we limit ourselves for simplicity to the important class of hyperbolic systems, whose dynamical response to input variations is characterized by an initial pure time delay. System Equations
We assume that deviations from desired operating conditions are represented by the linear vector partial differential equation
bX
- + v -bX= at
br
AX
+ Biui + Gidi; 0 < t _< 6, 0
