Symbolic algebra tools for control teaching

The paper describes various interactive facilities implemented in Mathematica, which have been used for several years in the teaching of Advanced Control to final year undergraduates in the Department of Electrical Engineering and Electronics at UMIST. The first facility, known as the LinModels Package, is a symbolic algebra package, which provides the various transformations needed to manipulate linear system models from one form to another. In particular, system models can be readily transformed between any of the following standard forms; state-space, transfer-function (matrix), left or right matrix-fraction form, and Rosenbrock´s system matrix in state-space or polynomial form. In the case of transformation from transfer-function to state-space form, a simple yet reliable minimal realization algorithm is automatically invoked. Similarly, with transformations to matrix-fraction form the resulting system models are least-order. The second facility, known as the Analysis Package provides a range of well-established analysis tools which provide the following features; the Kalman tests for controllability and observability, Rosenbrock´s input and output decoupling zeros tests for models in state-space or polynomial matrix form, the Smith form of a polynomial matrix, the McMillan form of a rational polynomial matrix, and Bristol´s Relative Gain Array for system sesitivity analysis