Model Reduction for Control of Stirred Tank Reactor Processes
Doctoral thesis, 2007
Models of chemical processes have a tendency of being far too complex for controller design. In many cases these models are also too complex for simulation together with other sub-systems, due to long simulation times and numerical problems. Therefore, simplistic models are often used for controller design and simulation with a weak justification of the simplifying assumptions.
In this thesis, a systematic method for development and evaluation of simplified models used in closed loop is presented. The method is applied to continuously operated tank reactor systems with a temperature dependent first order, A -> B, exothermic reaction. Both a non-ideally and an ideally stirred tank reactor are described by rigorous models. These detailed models are linearized and used as reference models when the simplified models are investigated. The simplified models are derived by physical approximations applied to the detailed models. Particular focus is on assumptions of constant densities and of constant specific heat capacities as well as on variations in some key parameters.
In the evaluation method controllers are developed for the simplified models. The resulting closed loop sensitivity functions are then compared to the sensitivity functions of the original detailed models in closed loop with the same controllers. Measures for these comparisons are suggested and successfully applied on both the non-ideally and on the ideally stirred tank reactor models.
A large number of sets of substances have been investigated by means of parameter variations. The evaluation of these sets has resulted in boundaries in the temperature dependent functions for the specific heat capacities and the densities. Within the boundaries the approximation of interest will not particularly affect the behaviour of the closed loop system.
A control strategy has also been developed for one of the tank reactor models. The control strategy is based on Quantitative Feedback Theory. The control is attractive since it uses only a small number of linear controllers for a large operating range.