An Analytical Design Method of PI and PID Controllers for Series Cascade Industrial Processes with Time Delay Under Robustness Constraints

  • Marko Bošković University of East Sarajevo, Faculty of Electrical Engineering
  • Ivan Prelić University of Belgrade, School of Electrical Engineering
  • Tomislav Šekara University of Belgrade, School of Electrical Engineering
Keywords: robustness; maximum sensitivity function; analytical controller design; cascade control;


In this paper, an analytical method is proposed to design PI and PID controllers for two stage series cascade industrial processes with transport delay under robustness constraints. The main rationale behind using series cascade control structure is that the disturbances in the inner loop are suppressed by the secondary controller before being transmitted to the outer loop. The presented design procedure has two steps: in the first one, the controller Cb(s) in inner control loop is designed, while in the second step one gets the controller Ca(s) in the outer control loop. The obtained controller is of PI or PID-type structure depending on the number of selected terms used in Maclaurin’s approximation of the transfer function of the high-order controller. By specifying the robustness constraints within design procedure one define values of adjustable parameters to achieve compromise between robustness and performance indicators. As the result, one achieves efficient load disturbance rejection which is evaluated by the Integral of Absolute Error (IAE). The step reference response can be additionally reshaped by using Two Degree of Freedom – 2DoF control structure via suitable selection of set-point weighting factor b, 0≤b≤1, which acts on the control signal through displaced proportional action of the controller. The proposed design method is analyzed with simulations on wide class of typical representatives of industrial processes including stable, integral and unstable processes with time delay. Comparison with recent studies is included to demonstrate effectiveness of the proposed tuning methodology for cascade industrial processes.

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