Abstract
Presented is a method of continuous sliding mode control design to provide for the second-order sliding mode on the selected sliding surfaces in a three-loop control system, where two outer-loop virtual control signals must be smooth enough to be tracked in the inner loops. The control law in the vicinity of the sliding surface is a nonlinear dynamic feedback that in absence of unknown disturbances provides for finite-time convergence of the second-order reaching phase dynamics. The controller with a second-order disturbance observer in a combination with the proposed continuous dynamic feedback attracts the system trajectories to boundary layers around two sliding surfaces of the outer control loops with the second-order sliding accuracy in presence of unknown disturbances and the discrete-time control update.
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