7.9 Figure P17.9 depicts the Bode diagrams of an unknown process. (a) If this process is controlled with a P controller with positive gain kc, determine the range of values of the controller gain for which the closed-loop system is stable. What will be the offset (as a function of kc ) for a unit step change in the set point? (b) If this process is controlled with a P controller with gain kc=1, determine the phase and gain margins. (c) If this process is controlled with an ideal PD controller with positive gain kc and derivative time D=25, sketch the Bode diagrams of the corresponding loop transfer function and then determine the range of values of the controller gain kc for closed-loop stability. 7.9 Figure P17.9 depicts the Bode diagrams of an unknown process. (a) If this process is controlled with a P controller with positive gain kc, determine the range of values of the controller gain for which the closed-loop system is stable. What will be the offset (as a function of kc ) for a unit step change in the set point? (b) If this process is controlled with a P controller with gain kc=1, determine the phase and gain margins. (c) If this process is controlled with an ideal PD controller with positive gain kc and derivative time D=25, sketch the Bode diagrams of the corresponding loop transfer function and then determine the range of values of the controller gain kc for closed-loop stability