Symbolic computations: an overview and application to controller design

Conventional `numerical´ simulation programs fail to provide, in explicit form, the necessary and/or sufficient stability conditions for a system. In addition, these programs require more time for performing simulations than do the `symbolic´ ones. It is shown in this paper that engineers can apply in a systematic manner, a general computer algebra system like MAPLE V(R) to control system investigations. Applications of symbolic computation will not only provide explicit equations but also excellent numerical simulations, enhanced accuracy, performance and precision. The methodology for controller design using symbolic algebra is explained with the help of a PID controller and a second order plant. The entire analysis is carried out using the MATLAB symbolic algebra toolbox that supports MAPLE V(R). Stability conditions in explicit form have been obtained for the controller gains K_p, K_d and K_i. As an application of the design methodology, an example of the design of a controller for a synchronous generator feeding power to a power system is considered. Further, eigenvalue sensitivity to the system parameters has also been investigated