Robust control with reduced knowledge of unmodeled dynamics using sliding mode: application to robot manipulators

The variable structure control (VSC) is based on switching functions of the state variables used to create a “sliding mode”. The purpose is to force the system dynamics to correspond to the one defined by the surface equation. When the state is maintained on this surface, the system dynamics become insensitive to parameter variations of the plant, and to unmodeled nonlinearities. This paper is the follow up work on the controller design for two axis robot arm using a variable structure model reference adaptive controller. It addresses the design of sliding mode controllers for perturbed systems characterized by the presence of the switching element imperfections (delay, small time constants, and the unmodeled dynamics). It is shown that its specific reaching conditions are satisfied for the reduced-order models and an additional condition is met, then the reaching conditions are also satisfied for the full-order model (take into account unmodeled dynamics, small time constants, switching delays, etc.). In this note the sliding mode control law is considered for the reduced-order model, and a composite control is implemented on the full-order model. Further, in sliding mode the controller system design can be reduced into a lower-order and free system. Advantages of such a control law appear from the following viewpoints: methodology-the control law can be easily implemented in an online computer as a classical control law (PID, RST...); robustness to unmodeled dynamics (the plant dimension is higher than the one of the model); quality of tracking trajectory