Eigenvalue Assignment via the Smith Predictor based IMC-PID the Matrix Lambert W function for Control of Time-delayed Process Systems

摘要

In a process modeled using delay differential equations (DDEs), we investigate performance and stability of the FOPDT (first-order plus time delay) process system. In this paper, we design two feedback controllers via eigenvalue assignment for the two most common process systems. In the first approach, an Equivalence of the Smith Predictor based on the desired eigenvalue with IMC (Internal Model Controller) for the System is proposed. Analytical expressions for proportional-integral-derivative (PID) controllers based on IMC structure are derived. In the second approach, proportional-integral (PI) controllers are designed by obtaining solution to the system in terms of the matrix Lambert W function. The controller designed using the presented approach can improve the system performance, illustrated by simulation examples and successfully stabilize it. This provides insight into the work of bringing these techniques together to process control system design.