Evaluation of time delay requirements for closed-loop stability using classical and modern methods

Classical and modern methods are used for computing the maximum allowable time delay a closed-loop system can tolerate before destabilizing. Maximum allowable time delays are computed using both methods for three control systems previously designed for a simple process. The three control systems are proportional plus integral (PI), linear quadratic Gaussian (LQG), and linear quadratic Gaussian with loop transfer recovery (LQG/LTR). The allowable time delays computed using the modern technique yields conservative values in comparison with exact values computed using the classical method. Even though the LQG/LTR control system yields good performance and stability robustness, the closed-loop system is easily destabilized by small process time delay. The PI and LQG control systems can tolerate a significant amount of delay in the process control systems. Thus it appears that the design of a control system robust with regard to parameter variations, disturbance rejection, noise, and model uncertainty will not inherently be closed-loop stable when there is significant process delay