Hidden oscillations in sampled-data control systems

Oscillations between sampling instants in the response of sampled-data control systems impose certain limitations on the z-transform method and other methods available for synthesis of such systems. It is shown that these oscillations appear in the response because of certain forms of the open-loop transfer function G(s). If the impulsive response of these functions is oscillatory then these oscillations occur in the response, and if the sampling period is larger or equal to half the period of these oscillations, the z-transform method fails to indicate their presence. The modified z-transform can be advantageously applied in these cases. This method is straightforward and simple in detecting the presence of these oscillations and indicating their values. Theorems relating to initial and final values of the response in the form of modified z-transform has been presented. Two examples have been discussed in which such oscillations occur and the modified z-transform method has been applied in their analysis.