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The discrete-time equivalent of an analogue controller by a compensated approach

A new approach is presented to convert an analogue controller to its corresponding counterpart for the discrete-time system. Based on the trapezoidal integration of the continuous-time response, an extra geometric area is considered, so that the discrete-time transformation is reasonably compensated. In the transformation of the proposed method there is a flexible parameter n which can be tuned in accordance with the controller and the sampling period. Thus a suitable n in our proposed transformation can be found to make effective compensation for a sampled-data system. Since our aim is the improvement of the bilinear transformation, the discrete system obtained by the proposed transformation has a better performance. This can be demonstrated from the simulation results.