This paper extends the concept of the discrete describing function proposed previously for the analysis of sector type nonlinear sampled data control systems. The previously defined functions were only applicable to the signals which have sub-harmonics of sampling frequencies. We remove the restriction on frequencies and make it possible to apply to an arbitrary frequency. All frequencies less than a half of the sampling frequency are divided into many groups.
For frequencies that belong to the same group, the evaluation of the discrete describing function provides the same region on the complex-plane. Practically, it is enough to consider a few shapes of these regions. Drawing the inverse Nyquist diagram of linear part of the system on the same complex-plane, limit cycles are predicted by the well-known. graphical method.
To clarify the description, a few examples are given. The simulation results show that our proposed method is useful for predicting limit cycles which have a period not equal to the sampling period multiplied by an integer.