Synthesis of PI Controller with a Simple Set-Point Filter for Unstable First-Order Time Delay Processes and Integral plus Time Delay Plant

  • Radmila Gerov
  • Zoran Jovanovic
Keywords: Pole assignment, PI controllers, Time delay, Unstable FOPTD processes, Integral plus time delay plant.


The paper describes PI controllers tuning for unstable first order time delay processes and integral plus time delay plant. The suggested method for designing a PI controller is based on the pole assignment method. Conditions for selecting the PI controller parameters in the function of the desired poles and parameters of the plant are met by using the features of the Lambert W function. The system stability in feedback is guaranteed by selecting the desired poles of the pre-defined range. The determined scope for pole selection includes the condition that this controller operates without integral gain, merely as proportional. The overshoot is reduced by using the simple first-order set-point filter. The manner of selecting the initial matrix which is used in a LambertW_DDE toolbox has been proposed. The illustrations of the simulation have been provided. Performances of the system regulated with a suggested PI controller are compared with the results received from other methods wherefrom it may be seen that this method yields better results in terms of the system settling time, rise time and IAE, ISE for set-point and good results in term of IAE, ISE for load disturbance and for the robustness on the uncertain changes expressed by the process parameter change of 10 %.