Adaptive stabilization and command following using a Prandtl-Ishlinskii/NARMAX controller

We investigate a NARMAX controller structure involving hysteretic nonlinearities. A weighted combination of backlash nonlinearities constitutes a Prandtl-Ishlinskii hysteresis model. The rationale for using a Prandtl-Ishlinskii NARMAX (PIN) controller is due to the fact that the describing function of a backlash nonlinearity has both gain and phase shift. By combining backlash nonlinearities into a NARMAX control law it is reasonable to expect that arbitrary gain and phase shift can be attained by adaptively updated controller coefficients.