PROCESS CONTROLLABILITY ANALYSIS USING LINEAR-PROGRAMMING

Controllability analysis is concerned with determining the limitations on achievable dynamic performance. This paper proposes the use of lin ear programming to determine the best linear controller and correspond ing dynamic performance for problems of the form: min J(K, u(0))s.t.c( K, u(0), w) less than or equal to 0 For All w is an element of W. That is, a controller, K, and a reference operating point, u(0), are selec ted to minimise a specified objective, J, while ensuring feasibility f or all disturbances, w, within a specified set, W. When K is a linear time invariant (LTI) controller and the objective function J and the c onstraints c can be expressed as linear functions then the above probl em can be solved by linear programming. This formulation encompasses a wide range of problems ranging from minimising the maximum deviation in the regulated outputs subject to disturbances of magnitude less tha n one (the II optimal control problem) to optimising the expected valu e of a linear economic objective (the Optimal Linear Dynamic Economics (OLDE) problem). The relationship of this work to other approaches to controllability analysis is discussed. A highly flexible framework fo r addressing typical process performance requirements through appropri ate selection of J, c and W is presented. The relative merits of alter native approaches for defining the achievable closed loop transfer fun ctions based on the e-parameterisation are carefully discussed. The fe asibility of the proposed approach is demonstrated on an industrial re actor example. The needs for further work are discussed. (C) 1998 Else vier Science Ltd. Ail rights reserved.