Frequency Shaping of the Sampled-Data System Based on Division Points

This study proposes a frequency shaping method for sampled-data systems considering intersample behavior. Since there are two types of times for sampled-data systems (continuous- and discrete-time), it is necessary to unify the time to obtain frequency response. However, intersample behavior cannot be considered if the plant is discretized by focusing only on the sampling points. Therefore, this study determines the number of divisions for intersample response and obtains the frequency response at the division points to address this issue. This approach enables plotting Bode and Nyquist diagrams, including intersample behavior. Furthermore, applying the generalized Kalman-Yakubovich-Popov lemma as a frequency shaping method, the frequency domain inequality at the division points can be converted into equivalent linear matrix inequality. This method allows for the design of control systems in a straightforward yet rigorous manner.