No abstract

Real

This paper presents an approach to the problem of nonlinear output feedback control. A nonlinear output feedback control law is derived within the framework of input-output linearization. It includes an input-output linearizing state feedback, a linear system describing the linear input-output closed-loop response under the state feedback, and a reduced order nonlinear state observer. The nonlinear output feedback control law is applied to a class of free-radical polymerization reactors that usually exhibit multiple steady states. For this class of processes, the global asymptotic stability of the closed-loop system is proven. The performance of the controller is shown by numerical simulation of a styrene polymerization reactor.Index Terms-Global asymptotic stability, input-output linearization, model-based control, nonlinear control, output feedback control, polymerization reactor control, state observer. NOMENCLATUREConcentration of initiator in the outlet stream, kmol m −3 . Concentration of initiator in the initiator inlet stream, kmol m −3 . Concentration of monomer in the outlet stream, kmol m −3 . Concentration of monomer in the monomer inlet stream, kmol m −3 . Monomer concentration set point, kmol m −3 . Concentration of solvent in the outlet stream, kmol m −3 . Concentration of solvent in the initiator inlet stream, kmol m −3 . Concentration of solvent in the solvent inlet stream, kmol m −3 .Heat capacity of the reacting mixture, kJ · kg −1 · K −1 . Observer error. Initiator efficiency. Flow rate of the monomer inlet stream, m 3 · s −1 . Flow rate of the initiator inlet stream, m 3 · s −1 . Flow rate of the solvent inlet stream, m 3 · s −1 . Rate constant for chain-transfer-to-monomer reactions, m 3 kmol −1 s −1 . Rate constant for chain-transfer-to-solvent reactions, m 3 kmol −1 s −1 . Dissociation rate constant for initiator, s −1 .

Real-time implementation of a robust multi-rate state estimator on a continuous stirred tank, free-radical, styrene polymerization reactor is presented. The estimator was designed on the basis of a first-principles model of the process. The estimtor had "integral action", which permitted robust estimation of polymer weight-average and number-average molecular weights, and monomer concentration. These were estimated from (a) on-line frequent measurements of the reactor temperature, and (b) off-line, infrequent and delayed measurements of polymer weight-average and numberaverage molecular weights and monomer concentration. Infrequent measurements of monomer concentration were obtained by gas chromatography and gravimetry, and those of weight-average and number-average molecular weights by gel permeation chromatography.

A comparative study of multi-rate control of a jacketed styrene polymerization reactor is presented. A multirate nonlinear control system is used to regulate weightaverage molecular weight of the polymer product and temperature in the reactor, by manipulating the flow rate of an initiator feed stream and the rate of heat input to the reactor jacket. The multi-rate control system consists of a multi-rate nonlinear state estimator and a mixed errorand statefeedback controller. The state estimator p r e vides continuous estimates of state variables of the p r e cess from (i) frequent measurements of the reactor temperature, the jacket temperature and the reacting-mixture density, and (ii) infrequent and delayed measurements of the leading moments of the molecular weight distribution of the dead polymer chains. The infrequent and delayed measurements have sampling periods of three hours and measurement delays of one hour. In the presence of processmodel mismatch and measurement noise, by numerical simulations the performance of the multi-rate nonlinear control system is shown and compared with those of a multi-rate, proportional integral (PI), parallel cascade, control system and a multi-rate, PI, completely decentralized, control system.