Lets consider a system with inherent dead time. We will use only a proportional controller. The closed-loop characteristic equation is 1 + GcGp = 0. The process transfer function is Gp = 3e^-s /(4s+1).
a) If you approximate the dead-tim function with a first order Pade formula, use any analytical method of your choice to find the approximate range of proportional gain such that the system is stable.
b) show how you would find the exact ultimate gain with the direct substitution method
c) Repeat, using a Bode plot