On the relationship between discrete-time Bode plots and actual system response

Discrete-time Bode plots represent the frequency characteristics of digital control systems. However, discrete-time Bode plots do not correspond to the response of the actual discrete-time system. This study inputs sinusoidal sampled signals into a discrete-time system and compares their corresponding responses with those of the discrete-time Bode plots. Moreover, this study proposes three indices for characterizing the gain and phase difference output response of discrete-time systems to enable effective comparison. The indices for gain are maximum value, minimum value, and area ratio, and the indices for phase difference are maximum value, minimum value, and mean value. The results show that gain plots of the discrete-time Bode plots represent the largest amplitude of the actual system responses, and phase plots of the discrete-time Bode plots represent the mean value of the phase difference of the system responses. In the future, developing a design and system analysis method that considers the above characteristics of discrete-time Bode plots would be desirable.