Mathematical Modeling and Process Control of Distributed Parameter Systems. Case Study: The One-Dimensional Heated Rod
This paper illustrates the integration of applied mathematics and common classical control design techniques to improve the performance of distributed parameter systems. The case study deals with tracking a temperature set-point change at the end of a one-dimensional rod. A set of partial differential equations was first solved using the Laplace transform and was subsequently inverted using the residue theorem. A Proportional-Integral (PI) controller reduced the time constant of the process by 50 and 33% from 1.379.