Adaptive linearization of hybrid step motors: stability analysis

An adaptive linearization scheme for torque-ripple cancellation is presented, and the stability and robustness are established. By taking a new approach in parameterizing the motor dynamics, the number of adapted parameters is reduced by a factor of two relative to the standard approach. This parameterization and the unique periodic property of the motor enable the authors to find conditions on exogenous signals which guarantee persistency of excitation. The authors develop a 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. The kinds of perturbation considered include nonlinear dependence on state and parameter error. This nonlinear adaptive control scheme has been successfully implemented. Experimental results demonstrate over 30 db reduction in torque ripple