Problem Statement:
1. Derive the Laplace Transform of a time-shifted function with deadtime theta.
2. Determine the Ziegler-Nichols ultimate controller gain and period for of a first order system with dead time of 0.1 s, time constant of 1 s, and gain of 1. Simulate the closed-loop response of this system using the corresponding Ziegler-Nichols PI controller parameters.
3. Repeat D2 using the Smith-Corripio ITAE open-loop tuning method.
