Abstract
This paper focuses on the problem of fractional controller P I stabilization for a first-order time-delay systems. For this reason, we utilize the Hermite–Biehler and Pontryagin theorems to compute the complete set of the stabilizing P I λ parameters. The widespread industrial utilization of PID controllers and the potentiality of their noninteger order representation justify a timely interest in P I λ tuning techniques. Step responses are calculated through K p , K i , l a m b d a parameters inside and outside stability region to prove the method efficiency.
Highlights
Time delay usually appears in many real-time engineering systems in the state, the measurements, or the control input [1, 2]
In order to examine the accuracy of the stability region and the efficiency of our tuning method, step responses are calculated on either side of the stability region
It is clear that the closedloop system has a convergent stable dynamic when the controller parameters choose within the internal limit of the stability region, and it has a divergent unstable dynamic when the controller parameters choose from the outer limit of the stability region
Summary
Time delay usually appears in many real-time engineering systems in the state, the measurements, or the control input [1, 2]. Podlubny has proposed a generalization of the classic PI and PID controllers defined as PIλ and PIλDμ where the order integrator λ and the order differentiator μ assumed real noninteger values. He proved that these types of fractional controllers are the best for dynamics systems control [7, 8]. We develop analytical characterization of the stabilizing set of fractional controllers for first-order systems with time delay.
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