You are designing the control system to regulate the thrust of a rocket engine. The engine exhibits first-order dynamics in thrust output with a time constant of 1 second, and based on the length of the plumbing to the fuel tank, a fixed deadtime (transport lag) of time T. The DC gain must be 40dB to meet steady-state error requirements; the loop gain for this system is then -Ts G(s) e 100 s+1 (4) You need to tell the plumbing team the maximum transport lag, T, your closed-loop system (unity feedback around G(s)) can withstand without going unstable. (a) (2 points) Find 7 by determining when the phase margin is reduced to zero. You may use MATLAB, but this problem can also be solved analytically without too much trouble. (b) (2 points) Using a first-order Pad approximation for the transport lag, -Ta 1- 1+ (5) calculate the critical lag T* by examining the closed-loop characteristic equation. Note that this will give an approximate answer, while the answer from part (a) is exact.