Design of PID Controller with Filter for Distributed Parameter Systems

This paper presents a method for tuning simple controllers for distributed parameter systems in the process industry. These systems are usually described by partial differential equations (PDE), which are then simplified into lumped parameter systems represented by ordinary differential equations (ODE), providing low order transfer functions used for PID control design. The drawback of this approach is that the control system only performs well at low bandwidths and without disturbances, as relevant system dynamics, such as resonances lying at medium-high frequencies, are not taken into account, limiting the performance of the closed-loop system. This work proposes a method for SISO systems which uses a transfer function that models the resonances (obtained directly from the PDE) to tune a PID controller that incorporates a filter that is designed to fulfill control requirements.