Multi-rate suboptimal digital redesign of a cascaded continuous-time input time-delay system

This paper presents a new multi-rate control scheme for optimal digital-redesign approach of the input time-delay continuous-time cascaded system. It shows that the states of the multi-rate sampled-data system with the digitally redesigned control law closely match those of the original cascaded continuous-time closed-loop system with analogue control law at any instant between sampling periods. Moreover, the developed digital control law can be implemented using low-cost microcomputers with a relatively longer sampling period. Also, it utilizes the innovative one-duration description of input time-delay sampled-data system which is suitable for any value of input time delay, even larger than one sampling period. As a digitized continuous-time system with a very small sampling period may become an unstable and/or non-minimum phase model, even if the original system is stable and/or minimum phase. A new method, with different sampling rates, suboptimal digital-redesign of a cascaded continuous-time system with different input time delays is accessible in this paper. An illustrative example is presented to demonstrate the effectiveness of the proposed design methodology.