Design of delayed PID-type controllers for high-order recycling systems with time delays using model reduction

In even the simplest recycling system with a first-order plus dead time model for the direct and recycling paths, the characteristic equation for the open-loop transfer function contains an infinite number of poles. This is due to the presence of time delays in the internal dynamics. The task of designing a controller is therefore challenging from the perspective of control. This paper considers the problem of stabilising a high-order delayed recycling system (with a possible unstable direct path) through the use of a reduced model in conjunction with a new PID (proportional-integral-derivative)-type delayed controller. We state the condition under which the stability of the closed-loop system is guaranteed and determine the sets of stabilising control parameters. The performance of our proposed strategy is illustrated using several numerical simulations of industrial processes, including an industrial quench column, two continuous stirred tank reactor systems with recycling and a reactor–separator process.