PI controller design for a class of distributed parameter systems

In this paper, the regulation problem of convection governed dynamical processes described by linear distributed parameter models with position-independent inputs is addressed by combining the method of characteristics (MC) and the Malek-Zavarei and Jamshidi theorem. In this approach, the MC is used to transform the first order partial differential equations model of such processes into a set of time-delayed ordinary differential equations whose elements are used to generate certain matrices that satisfy linear matrix inequalities that render the proportional integral (PI) control parameters that guarantee the process stability. The performance of the proposed PI controller is tested via numerical simulations in the temperature regulation of a linear heat exchanger and compared to a tightly tuned classical PI controller. The application of the proposed controller is extended to regulate the outlet concentration in a nonlinear non-isothermal plug flow reactor. It is shown that the proposed controller is able to handle the infinite dimensional nature of the process model yielding smooth and unsaturated responses around the predetermined set-point trajectory in the face of load changes, time varying boundary conditions and set-point changes.

► A rather simple methodology is proposed to control spatially distributed convective processes that are described by First Order Partial Differential Equations.
► This Proportional-Integral control scheme was successfully applied in simulation runs to a linear heat exchange process and a nonlinear reacting process.
► The proposed control methodology is able to meet the control objectives despite the infinite dimensional structure of the mathematical model under the influence of load disturbances, time-varying boundary conditions and set-point changes.