1. (15 pts.) Consider a cruise controller that is turned on and set to 30 m/s when a car is moving at 26 m/s. The car's velocity then increases at a constant rate. After 10 seconds, the current velocity is 29 m/s. (a) Given the history provided, what would the desired value of a PID controller input u be at this moment in time if the controller gains are kp=4, kd=2, and k=3? (b) What would the value of the input u if there is a saturation limit at 100? (c) What are the pole(s) and zero(s) for a PID controller with the gains given in part (a)? (d) Would this PID controller stabilize the following plant? G(s)= 1 s-7s+12