Carefully read each statement below and identify it as True or False and, for each answer, explain your reasoning briefly in 1-2 sentences. 1. The smaller the phase margin in a 2nd-order system, the larger the peak gain at the resonant frequency for the closed-loop system. True or False? Why? 2. The larger the slope of the magnitude curve of the loop transfer function at the gain crossover frequency, the smaller the overshoot in the step response of the closed-loop system. True or False? Why? 3. A gain margin smaller than one (i.e., negative gain margin in dB) will always indicate closed-loop instability. True or False? Why? 4. An LQR full-state feedback regulator can lead to an unstable closed-loop system if the open-loop system is itself unstable. True or False? Why? 5. As a pole of a 2nd-order continuous-time system moves away from the real axis in the s-plane, while its real part remains constant, the settling time in the step response will increase. True or False? Why? 6. As a pole of a 2nd-order discrete-time system moves away from the origin in the z-plane, while its phase remains constant, the damped oscillation frequency in the step response will remain constant. True or False? Why? 7. A loop transfer function has 3 zeros and 2 poles on the Right Hand Plane. If its Nyquist plot encircles the -1 point two times in the counter-clockwise direction, the associated closed-loop system will be stable. True or False? Why? 8. Given the magnitude of a stable, minimum-phase transfer function, one can uniquely calculate its phase. True or False? Why? 9. A Type 1 system can track a ramp reference input with zero steady-state error. True or False? Why? 10. Using any of the bilinear transform, matched pole-zero, or impulse invariance tech- niques in converting a continuous-time system to a discrete-time system will always preserve the system stability. True or False? Why