Frequency characteristics of Levant's differentiator and adaptive sliding mode differentiator

Sliding mode control has been used for the control of industrial processes. The usual controller designed requires the estimates of state variables which are given by the derivatives of the output. Levant's sliding mode differentiator has been found effective to estimate derivatives of signals. Its accuracy depends, however, on the choice of the differentiator parameters determined by the Lipschitz constant of the derivative of the signal. The effect of the improper choice of the parameters is analyzed through the frequency characteristics. Since the Lipschitz constant is usually not known accurately beforehand, this article proposes to use an adaptive mechanism of the differentiator parameters’ online adjustment. The adaptive differentiator is found to have the better characteristics of the frequency response in simulation. The adaptive differentiator is also realized using digital signal processor

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