Robustification of nonlinear control systems vis-à-vis actuator dynamics: An immersion and invariance approach

Abstract In this brief note we pose, and solve, the problem of robustification of controller designs where the actuator dynamics was neglected. This situation is very common in applications where, to validate the assumption that the actuator dynamics can be neglected, a high-gain inner-loop that enforces a time-scale separation between the actuator and the plant dynamics is implemented. Of course, the injection of the high-gain has well-known deleterious effects. Moreover, a stability, and robustness, analysis of such a control configuration is usually unavailable. Our first main contribution is to provide an alternative to such a scheme, with provable robust stability properties. The second contribution is to, applying this result, propose a robustification procedure to the industry standard field-oriented control of current-fed induction motors, which is usually implemented neglecting the actuator dynamics, with no rigorous proof of stability available to date. Finally, we propose the first solution of smooth, time-invariant regulation of the dynamic model of a class of nonholonomic systems, that includes the widely popular unicycle example. Simulation examples prove the superior performance of the proposed controller compared with the existing switching and/or time-varying alternatives reported in the literature.