Mathematical model reduction for process simulation and controller design

Techniques of mathematical model reduction are applied to determine reduced models, which are then used for simulation and controller design of the original model. Both single input-single output (SISO) and multiple input-multiple output (MIMO) models are investigated. Numerous existing reduction methods are employed, as well as the development of new methodologies of model reduction. The use of the second order modes emerges as a potential criterion for the selection of the order of the reduced model. The resulting reduced models are evaluated in terms of simulation and controller design of the full model.

For the SISO models, the methods of model reduction are compared with the use of open loop simulations, calculation of the integral of the squared error between the full and reduced models. Bode plots, and PI controller design. From the three examples presented, the Cauer third form of continued fraction expansion is shown to be the best method for SISO model reduction. In the case of MIMO models, the reduction methods are compared using open loop simulations and multivariable PI controller design. Using three examples, the singular perturbation method is suggested for the reduction of MIMO models. For both the SISO and MIMO models the second order modes were found to be useful in selecting the order of the reduced model.

The characteristics of the full model that must be retained by the reduced model are shown to be very different. To circumvent this phenomenon, guidelines for the reduction of SISO and MIMO models are hypothesized. This research illustrates the many problems that may be encountered in model reduction and highlights several promising avenues of research.