Topics in Stochastic Control with Applications to a Tubular Reactor - Harris, James Thomas (My University, 1980)
This thesis represents part of an ongoing study on the modelling and control of a pilot scale packed bed tubular reactor carrying out the hydrogenolysis of n-butane. The use of time series modelling and stochastic control to analyze and develop control strategies for this process was investigated.
The mass and energy balances describing the hydrogenolysis of n-butane in this tubular reactor are a set of nonlinear partial differential equations in time and two spatial co-ordinates. In spite of their complexity, an analytical solution to these equations exists for certain linear combinations of the reaction species. These linear combinations, known as reaction invariants, define the reaction stoichiometry.
A dynamic model of the process suitable for on-line computer control had previously been developed from the material and energy balances. This dynamic model, and a stochastic model for the inherent process disturbances, were used to investigate the optimal location of thermocouples along the central axis of the reactor. The results of this analysis indicated that good state estimation and control of the temperature profile, and effluent concentrations, could be achieved when one or two thermocouples were located in the vicinity of the hot spot (maximum) temperature. The location of the thermocouples was insensitive to the statistical properties of the disturbances. A canonical variate anlaysis of the reactor temperatures using this model indicated that the variation of the hot spot temperature and average temperature had significant predictable components. Other linear combinations of the axial temperatures were essentially white noise processes, and therefore unpredictable. Control of the hot spot temperature and average temperature would control most of the predictable variation in the temperature profile, and as a result, most of the predictable variation in the effluent concentrations.
Univariate stochastic controllers designed for processes with deadtime have some very unusual spectral characteristics. The spectral characteristics of these controllers depend on the process deadtime and the structure and parameters of the stochastic disturbance model.
A number of univariate self-tuning regulators were implemented to control the hot spot temperature. The self-tuning controller gave good control over the hot spot temperature when compared to digital propotional plus integral type controllers. This algorithm quickly tuned the controller parameters and was robust to the assumption in its derivation.
Linear quadratic controllers designed for stochastic disturbance are identical to those designed to compensate for an 'equivalent' class of deterministic disturbances. When the controller structures are identical, it is the manner in which the state variables are reconstructed that determines how well a control strategy will perform. Although controllers can be readily designed to compensate process subject to deterministic and stochastic disturbances, reconstruction of the state variables in such instances is complicated by the presence of both type of disturbances.
Keywords: Chemical Engineering; Chemical Engineering