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 the 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 robustness. By taking a new approach in parameterizing the motor dynamics, we reduce the number of adapted parameters by a factor of two relative to the standard approach. This new parameterization and the unique periodic property of the motor enable us to find conditions on exogenous signals which guarantee persistency of excitation. As with many challenging control applications, the adaptive motor linearization problem raises new and fundamental theoretical questions. For example, we develop a new robustness result which, roughly speaking, shows that the allowable model perturbation does not decrease in size as the adaptation rate is slowed. This is accomplished with a unique dual-Lyapunov-function technique. Also, the kind of perturbations we consider include nonlinear dependence on state and parameter error. Finally, this nonlinear adaptive control scheme has been successfully implemented. Experimental results demonstrate over 30 db reduction in torque ripple.