Abstract
The extremum seeking control (ESC) approach with a first-order sliding mode has been proposed for searching a setpoint by making a sliding mode occur, where a performance index tracks a reference signal to reach its extremum. The system dynamics is assumed to be much faster than the parameter updating rate determined by the ESC rule and thus is omitted in the stability analysis for the ESC system with a first-order sliding mode. As a result only a static optimization can be obtained. In this paper, an ESC approach with a second-order sliding mode is proposed with the consideration of the system dynamics such that the performance index can be optimized dynamically even if the system dynamics is not faster than the parameter updating rate for the extremum seeking. The asymptotic second-order sliding mode relay control algorithm is implemented to guarantee the asymptotic convergence to the second-order sliding mode without using the derivative of the performance index. Simulation results show that the second-order sliding mode can be reached asymptotically and the system converges to the setpoint on the second-order sliding mode in the speed determined by the reference signal.
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