Ga-based digital redesign by balancing magnitude and phase response with compensation of computational and sampling delays

In this study, three topics of digital redesign problems, wideband system digital modeling, digital filter redesign, and digital controller redesign, are investigated. Since most of real life systems belong to the continuous-time domain, it is necessary to transform the continuous-time model into discrete-time model for the digital applications. Direct conversion by using some linear transformations like impulse invariant transform (IIT) or nonlinear transformations like bilinear transform (BT) might be acceptable for narrowband applications, though they may cause aliasing and distortion problem, respectively. But for wideband systems, aliasing and distortion can be real problems. Furthermore, sampling and computational delays occur in the discrete-time systems. Such delays have great influences on the digital redesign of controllers where delays can decrease the phase margin of the closed-loop system and hence decrease the relative stability, and even lead to instability of the closed-loop system. In order to resolve the aforementioned problems, a genetic-algorithm- based digital redesign is proposed, which can adaptively balance on the replication of either "magnitude" or "phase" response, or even any particular frequency segment and compensate for sampling and computational delays. The desired frequency response of the analog system is the design goal of this genetic redesign algorithm. Its magnitude and phase are used as the major variables in the performance index, and some modifications are made in the index to compensate for the delays in the controller design. A real-coded Genetic algorithm is proposed to find the numerical solution of the digital redesign.