Optimal Control of a Pilot Heat-Exchanger

Abstract

The first part of the paper gives a practical method for the synthesis of industrial control systems. The application of optimal control theory to industrial control problems is severely restricted by two considerations : It does not give true zero steady-state errors in the presence of step or ramp disturbances (or reference inputs) and the disturbances (or reference inputs) must be known a priori to apply the theory. These two drawbacks are successively considered : the first one is eliminated by the choice of a quadratic criteria which includes the plant'state vector and appropriate time integrals of the output. Optimizing this criteria yielis a regulator structure which includes additionnal open loop integrators, reorganizing this structure to get a classical unitary over-all feedback system leads to a practical control system where the added integrators appeared in front of the plant resulting thus in zero steady state errors control system. For this practical regulator, a predictive optimal command minimizing the transient errors is then applied. This predictive command is computed via the use of a Lyapunov matrix. It is shown that the predictive command depends linearly on the plant'state vector and on the reference input coefficients. The synthesis method is analytical and does not need the usual approximations required when treating this kind of problem via optimal tracking on a non-infinite time interval.The second part of the paper gives a description of the pilot heat-exchanger mathematical model. The pilot plant is counter-flow heat exchanger. The heat exchange process is described by a set of four non-linear partial differential equations where the variations of heat-transfer coefficients with respect to flow-rates and temperatures are considered. After linearization around a steady-state operating point a tedious analytical treatment gives a transfer matrix of transcendental Laplace transforms. The complexity of these transcendental functions being of little pratical use, from these expressions a program, based on parametric identification, computes the parameters of rationnal transfer functions approximating the transcendental model. The resulting transfer functions relate the cold outlet temperature to the hot-fluid flow-rate and to the disturbing cold-fluid flow-rate. The simplified model is made of first and second order transfer functions of the types given below : F1(s)=K1+TsandF2(s)=K(1+T3s)(1+T1s)(1+T2s)The third part of the paper displays experimental results of the pilot plant's control system. The control algorithm is computed via the use of the simplified transfer function, then programmed on a small process computer linked to the pilot heat-exchanger .