Extremum-seeking control for steady-state performance optimization of nonlinear plants with time-varying steady-state outputs

Extremum-seeking control is a useful tool for the steady-state performance optimization of plants for which the dynamics and disturbance situation can be unknown. The case when steady-state plant outputs are constant received a lot of attention, however, in many applications time-varying outputs characterize plant performance. As a result, no static parameter-to-steady-state performance map can be obtained. Recently, we proposed an extremum-seeking control method that uses a so-called dynamic cost function to cope with these time-varying outputs. We showed that, under appropriate conditions, the solutions of the extremum-seeking control scheme are uniformly ultimately bounded in view of bounded and time-varying external disturbances, and the region of convergence towards the optimal tunable plant parameters can be made arbitrarily small. In this technical report, a proof of the local stability result is presented

Second-order reset elements for stage control design

In dealing with inherent limitations during stage control design, the possibilities of a second-order reset element (SORE) are studied, in particular, a second-order low-pass filter with reset. Inducing significantly less phase lag, which follows from describing function analysis, SOREs allow for a significant increase of bandwidth in comparison to linear second-order elements. Being part of a reset control design procedure, loop-shaping of the linear feedback loop with a reset element will be based on a describing function description of this element. For the reset control system, closed-loop stability will be verified by solving linear matrix inequalities. The validity and predictive value of the control design procedure (both in terms of stability and performance) will be demonstrated by means of (measurement) results obtained from an industrial wafer stage system

Extremum-seeking control for steady-state performance optimization of nonlinear plants with time-varying steady-state outputs

\u3cp\u3eExtremum-seeking control is a useful tool for the steady-state performance optimization of plants for which the dynamics and disturbance situation can be unknown. The case when steady-state plant outputs are constant received a lot of attention, however, in many applications time-varying outputs characterize plant performance. As a result, no static parameter-to-steady-state performance map can be obtained. In this work, an extremum-seeking control method is proposed that uses a so-called dynamic cost function to cope with these time-varying outputs. We show that, under appropriate conditions, the solutions of the extremum-seeking control scheme are uniformly ultimately bounded in view of bounded and time-varying external disturbances, and the region of convergence towards the optimal tunable plant parameters can be made arbitrarily small. Moreover, its working principle is illustrated by means of the performance optimal tuning of a variable-gain controller for a motion control application.\u3c/p\u3