Nonlinear adaptive torque-ripple cancellation for step motors

The modeling of torque-ripple in hybrid step motors and its cancellation using adaptive linearization control are discussed. Although the nonlinear adaptive control of this problem can fit into a general framework, a representation of the torque-ripple which reduces the number of adapted parameters per torque-ripple harmonic by half is used. By doing so, it is possible to prove conditions on exogenous signals to guarantee the persistency of excitation of the regressor, and hence the exponential stability of the unperturbed system. It is shown that the adaptive system is robust to a class of state- and parameter-dependent modeling errors and disturbances even when the adaptation gain and convergence rate of the unperturbed system become small. The adapted parameter errors are proved to converge to a neighborhood of zero whose radius can be made small by slow adaptation. The proposed control scheme is verified in an experiment in which a 32-dB reduction in torque-ripple component at the rotor pole frequency is observed