PID Stabilization of Systems with Approximated Time-Delay

In this paper we deal with the problem of stabilizing time delay systems using proportional-integral-derivative (PID) controller. We describe a simple approach which can be used for stabilizing time delay system with transfer function of different order. Based on this approach, transfer function is decomposed into real and imaginary parts and then the set of controllers which will ensure stability for a constant value of proportional controller is determined. All stabilizing PID controllers are also determined. Pade approximation is used here which simplifies the analysis and design of time delay system and it is avoided from direct computation of the ischolar_mains of transfer function. It's worthy to note that stabilization of system with approximated time-delay term (using Pade approximation) does not guarantee that the original time-delay system will be also stabilized. Closed-loop step response is also used to show the correctness of the approach. Two examples are given to illustrate the approach which will be described in detail in continuation.