Process controllability analysis using linear programming
Steve Walsh (Imperial College)
Abstract
Controllability analysis is concerned with determining the limitations
on achievable dynamic performance. This seminar proposes the use of
linear programming to determine the best linear controller and
corresponding dynamic performance for problems of the form:
min_{K,u0} J(K,u0) such that c(K,u0,w) <= 0 for all w in W
That is, a controller, K, and a reference operating point,
u0, are selected to minimise a specified objective, J, while
ensuring feasibility for all disturbances, w, within a specified
set, W. When K is a linear time invariant (LTI) controller and the
objective function J and the constraints c can be expressed as
linear functions then the above problem can be solved by linear
programming, by making use of the Q-parameterisation.
This formulation encompasses a wide range of problems ranging from
minimising the maximum deviation in the regulated outputs subject to
disturbances of magnitude less than one (the l1 optimal control
problem) to optimising the expected value of a linear economic
objective (the Optimal Linear Dynamic Economics - OLDE - problem). A
highly flexible framework for addressing typical process performance
requirements through appropriate selection of J, c and W is
presented.
The feasibility of the proposed approach is demonstrated on an
industrial reactor example. The needs for further work are discussed.