Studies in robust estimation and control

Effective monitoring and tight control of chemical, petrochemical and biochemical processes are often hindered by the absence of frequent measurements of important process variables that are related to product quality, the presence of process-model mismatch, unmeasureable disturbances, measurement noise, and highly nonlinear process dynamics. This dissertation presents new methods of nonlinear estimation and control in the presence of such practical problems. Simulation and real-time implementation are used to show the capability and the ease of implementation of the developed estimation and control methods. The inadequacy of the standard notions of detectability and observability to ascertain robust state estimation is shown. To address this inadequacy, the notions of integral detectability and integral observability are defined. A method of robust, nonlinear, multi-rate, state estimator design is developed. It can be used to improve robustness in an existing estimator or to design a new robust estimator. Real-time implementation of such a robust estimator on a polymerization reactor, in DuPont's Marshall Laboratory, Philadelphia, PA, shows that the estimator calculates robust continuous estimates of monomer concentration, and polymer weight-average and number-average molecular weights from their infrequent and delayed measurements and frequent temperature measurements. An expression is developed to calculate an upper bound on the maximum sampling period and time delay of infrequent measurements, such that estimation error does not exceed a desired limit. The upper bound depends directly on process time constants, and inversely on disturbance magnitude, process-model mismatch and measurement noise. For a class of free-radical polymerization reactors that exhibit multiple steady states, a nonlinear output feedback control law (which includes an input-output linearizing state feedback, and a reduced-order nonlinear state observer) is presented. For this class of processes, the global asymptotic stability of the closed-loop system is proven. A robust multi-rate nonlinear controller, comprising a mixed error- and state-feedback controller and the robust estimator, is derived and used for tight control of temperature and weight-average molecular weight in a polymerization reactor under different measurement scenarios. Superior performance is demonstrated as compared to that of conventional multi-rate controllers.