Control Systems Design for Nonlinear Multivariable Systems
The Linearising Transformation technique developed for single-input, single output systems has been extended to multivariable systems. However this technique was found to be impractical for general nonlinear multivariable systems because of the complexity involved, and the fact that you cannot always guarantee a transformation. As a result, two alternative, more practical, controller design techniques have also been developed for nonlinear multivariable systems. The first technique termed External Systems Restructuring is designed primarily for state-space models, and uses the concept of a structural modifier to design a controller with desirable features for the linearized process model. The second technique, termed Direct Synthesis theory for linear systems. This technique is designed primarily for transfer function models, and allows the pre-specification of a desired closed-loop process response; the controller required to achieve this response is then synthesized. The resulting direct synthesis controller is seen to be structurally similar to a multivariable-Pl-type controller. Different compensation options have also been developed for use with this controller. These controllers achieve decoupling of the system variables, compensate for both measurable and unmeasurable disturbances, and, most importantly, take into account the unavoidable discrepancies between actual plant response and model prediction. The control laws are practical in that they are easy to understand, design and implement. The effectiveness of these techniques in controlling nonlinear multivariable processes is demonstrated by simulation.