An Interactive Software for Designing Nonlinear Controllers Based on Feedback Linearization Technique

he nonlinearities of nonlinear dynamic systems have been traditionally handled in the literature by the use of classical linear control methods, which rely on linearized models approximating the dynamic system’s equations. These methods are just valid in a small operation range. When the required operation range has to be larger, the linear controller is likely to perform poorly. Nonlinear controllers, however, may handle the nonlinearities in large range operations directly. The nonlinear control considered here is based on the feedback linearization technique (static and dynamic) which gives a good solution for tracking control problems. Several accessible references describing its constructions are now available ([1] to [4]] as examples). This well-known nonlinear control technique has been successfully applied to the control of dynamic systems, even those with high nonlinearities in their model. However, this technique needs an extensive knowledge of differential geometry which provides a very useful framework for the analysis of nonlinear control systems. Differential geometric objects (Lie brackets, Lie derivatives, etc.) are not easily manipulated by hand. In order to facilitate this process, many new CAD tools appeared in the last decade (AISYS, AP_LIN, SCILAB, CONDENS, REDUCE, PROPAC etc.). They offer the possibility of designing and/or simulating nonlinear dynamic systems. In the real-time applications, the main problem encountered with these nonlinear control techniques is that they need an important calculation time which makes implementation impossible on a general use microprocessor. Fortunately, a new class of digital signal processors (DSPs) is making this implementation possible. The software presented in this paper (NLSoft) is developed in order to design nonlinear controllers, to simulate the closed-loop systems and to give useful information for the real-time implementation considering real DSPs characteristics (TMX320F2812, ADMC401 etc.). Furthermore, it is capable to inform us about the stability of the zero dynamics if they exist. NLSoft uses several subsystems expressed as classes which permit the design of nonlinear controllers and the plotting of the results obtained from the simulation of the closed-loop system.