PID controller design for a one-dimensional heated rod using orthogonal collocation

This paper presents the design of PID-type controllers for a one-dimensional, distributed heat conduction system starting from the parabolic partial differential equation modelling the system. The partial differential equation modelling the system was lumped using the orthogonal collocation method resulting in third-order lumped model. This lumped model was then used for the controller design based on a method of PID controller design previously developed for higher-order systems by the authors. The results of closed-loop simulations demonstrate the superior performance of the PID-type controllers so designed. The approach presented is quite general and may be used to carry out PID-type controller designs for other single-input, single-output distributed parameter systems.Keywords: Distributed parameter system, heat conduction, partial differential equation, early lumping, orthogonal collocation, PID controller design, Closed loop simulatio