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Designing a Proportional-Integral-Derivative (PID) controller for pure integrator with time delay and unstable first order plus time delay systems by extending the method proposed by Mikhalevich et al. (Mikhalevich SS, Baydali SA, Manenti F. Development of a tunable method for PID controllers to achieve the desired phase margin.  J Process Control 2015;25:28–34). In this paper, the same method is applied for pure integrating systems with time delay and achieved good response for servo problem. Later the method is applied to unstable systems by stabilizing the unstable system in inner loop with proportional controller and tuning a PID controller for the stabilized system in the outer loop. The servo and regulatory performance of the designed controllers is compared with the recently reported literature methods for various transfer function models.

Tuning of PID controllers for pure integrating and unstable time delay systems