Adaptive VS/SM controller based on robust fixed point transformations

The great advantage of the Variable Structure - Sliding Mode controllers is their simplicity, and that they can efficiently work in the possession of a very rough model of the system to be controlled. Instead investing any effort into identifying the precise analytical model of this system they apply well timed bang-bang type control signals in order to drive the “error metrics” near zero during finite time. The effects of modeling errors and unknown external perturbations are compensated by the application of great amplitude for this fluctuation often induce chattering that can be obviated by smoothing these signals normally at the cost of degraded precision of trajectory tracking. The recently proposed adaptive control based on robust fixed point transformations drives the system nearby the kinematically arbitrarily prescribed trajectories by the use local basins of attraction in an iterative learning control also abandoning the identification of the precise model of the system. By the combination of these different approaches efficient adaptive VS/SM controller can be developed that more precisely can trace the desired trajectory kinematically prescribed by the usual relaxation of the error metrics. Chattering can be evaded by decreasing the amplitude of the fluctuating control signal without degrading the tracking precision. This statement is substantiated by simulation results obtained for a simple paradigm.