For the following transfer functions: a. Study the stability of the system placed in a unitary feedback loop with Routh criterion. Select a value for K for stable behavior considering the Routh criterion only b. C. Obtain and locate the gain and phase margins with the Bode plot. d. Obtain and locate the gain and phase margins with the Nyquist plot. Verify that your system is stable with the Nyquist criterion. e. Plot the step response of the closed-loop system. f. Select a value of K for unstable behavior and draw the Bode plot and Nyquist plot. Conclude on the margins of an unstable system. Redo the analysis from a to f, with an integrator in the controller. Conclude on the effect of an integrator on the stability of the system. The grade will be based on the quality and the understanding of the figures. Your explanation about the stability of the systems will also be taken into account. 1. G(s): 2. G(s) = 3. G(s): = K s+1 K s+2s+10 K (s+1)(s+8)