MATHEMATICA AIDED TEACHING OF NONLINEAR CONTROL THEORY

摘要

During the last three years the authors of this paper have been using Mathematica to develop symbolic computing tools that, at their present stage of development, allow to: (1) Calculate and topologically classify the equilibrium points of nonlinear second order dynamical systems depending on two or three parameters [2], (2) Detect and classify Poincare-Andronov-Hopf (PAH) bifurcations [5], (3) Track the dependence of flows ws on system's parameters through sequences of phase portraits for prescribed sequences of values of the parameters, (4) Estimate basins of attraction with Lyapunov functions [1] and (5) design linear and nonlinear controllers and observers for nth order nonlinear control systems (NLCS) [3, 4, 6, 7]. Even though these tools were not originally developed as teaching aids, their use for such purposes might relieve students for a big amount of symbolic and graphical calculation by hand, allowing them to pay more attention to conceptual problems and to study more realistic models of physical phenomena. [References: 8]