1. If GcKc,Gp=2s+15,Gy and Gm=1 for what values of Ke the system will be stable? 2. If Gm=es and everything else are the same; use a first-order Pade approximation and find the range of Kc values for which the closed-loop system is stable. 3. Compare the result in (2) with the result in part (1) 4. Consider changing the controller to a PD controller, Gc=Kc(1+tD) where D=0.2, for the system in (2). Find the new range of Kc values required for closed-loop stability and compare this with the results in part (2). 5. Show analytically that the system in part (4) suffers from a steady-state offset for a unit step change in setpoint irrespective of the value of the derivative time constant tD or the proportional gain Ke