ADAPTIVE LINEARIZATION OF HYBRID STEP MOTORS - STABILITY ANALYSIS

The adaptive linearization of step motors is an attractive method for improving motor performance at relatively low cost. However, due to th e lack of robustness, a direct application of a standard approach does not work well. In this paper we present a new adaptive linearization scheme for torque-ripple cancellation and establish stability and robu stness. By taking a new approach in parameterizing the motor dynamics, we reduce the number of adapted parameters by a factor of two relativ e to the standard approach. This new parameterization and the unique p eriodic property of the motor enable us to find conditions on exogenou s signals which guarantee persistency of excitation. As with many chal lenging control applications, the adaptive motor linearization problem raises new and fundamental theoretical questions. For example, we dev elop a new robustness result which, roughly speaking, shows that the a llowable model perturbation does not decrease in size as the adaptatio n rate is slowed. This is accomplished with a unique dual-Lyapunov-fun ction technique. Also, the kind of perturbations we consider include n onlinear dependence on state and parameter error. Finally, this nonlin ear adaptive control scheme has been successfully implemented. Experim ental results demonstrate over 30 db reduction in torque ripple.