1. Review

2. Feedback Terminology In Block diagrams, we use not the time domain variables, but their Laplace Transforms. Always denote Transforms by (s)!

3. Deriving differential equations in state- variable form consists of writing them as a vector equation as follows: where is the output and u is the input State-Variable Form

4. Transfer Function

5. MEG 421 Chapter 35 (A) (B) (C) (D) The transfer function of the system shown is

6. (A) G1 alone (B) closed loop Num. and Denom. (C) closed loop Denom. alone (D) Gain K alone (E) The product K*G1(s) The transfer function of the system shown is The stability of the closed loop is determined by

7. (A) G1 alone (B) closed loop Num. and Denom. (C) closed loop Denom. alone (D) Gain K alone (E) The product K*G1(s) The transfer function of the system shown is The stability of the closed loop is determined by

8. The Steady-state error e ss of the closed loop to a unit step R(s) = 1/s is (A) e ss = 1/K (B) e ss = 1 (C) e ss = 0 (D) e ss 

9. The Steady-state error e ss of the closed loop to a unit step R(s) = 1/s is (A) e ss = 1/K (B) e ss = 1 (C) e ss = 0 (D) e ss 

10. (A) n = 0 (B) n = 1 (C) n = 2 (D) the number of integrators is not relevant. For tracking control (following a ramp reference) the minimum number of integrators in the control loop is

11. (A) n = 0 (B) n = 1 (C) n = 2 (D) the number of integrators is not relevant. For tracking control (following a ramp reference) the minimum number of integrators in the control loop is

12. (A) s=0, -1, -1 (B) s=0, -1/2, -1 (C) s=0, -2, -1 (D) s=0, -1 (E) s=0, 0.5, 1 The Root Locus Branches of the system shown originate for K =0 at

13. (A) s=0, -1, -1 (B) s=0, -1/2, -1 (C) s=0, -2, -1 (D) s=0, -1 (E) s=0, 0.5, 1 The Root Locus Branches of the system shown originate for K =0 at

14. (A) closed-loop poles (B) zero (C) infinity (D) Two branches terminate at infinity, one at zero (E) One branch terminates at infinity, two at zero The Root Locus branches of the system shown terminate for K  infinity at

15. (A) closed-loop poles (B) zero (C) infinity (D) Two branches terminate at infinity, one at zero (E) One branch terminates at infinity, two at zero The Root Locus branches of the system shown terminate for K  infinity at

16. The Root Locus exists on the real axis between (A) +inf>x>0 and 0>x>-2 and -3>x>-4 (B) -1>x>-2 and -3>x>-4 (C) +0>x>-2 and -3>x>-4 (D) +0>x>-1 and -3>x>-4 and -4>x>-inf (E) +0>x>-1 and -3>x>-4

17. The Root Locus exists on the real axis between (A) +inf>x>0 and 0>x>-2 and -3>x>-4 (B) -1>x>-2 and -3>x>-4 (C) +0>x>-2 and -3>x>-4 (D) +0>x>-1 and -3>x>-4 and -4>x>-inf (E) +0>x>-1 and -3>x>-4

18. The RLocus of an unstable system with transfer function is shown at left. We can stabilize the closed loop by XXX (A) adding poles on the negative real axis (B) adding a lead element on the negative real axis, with the zero between 0 and -4 (C) adding a lead element on the negative real axis, with the zero to the left of -4 (D) adding a lag element on the negative real axis, with the pole close to the origin. (E) the closed loop cannot be stabilized

19. The RLocus of an unstable system with transfer function is shown at left. We can stabilize the closed loop by XXX (A) adding poles on the negative real axis (B) adding a lead element on the negative real axis, with the zero between 0 and -4 (C) adding a lead element on the negative real axis, with the zero to the left of -4 (D) adding a lag element on the negative real axis, with the pole close to the origin. (E) the closed loop cannot be stabilized

20. The open-loop TF of the Root Locus plot shown at left is (A) (B) (E) none of the above

21. The open-loop TF of the Root Locus plot shown at left is (A) (B) (E) none of the above

22. For the given set of open loop poles and zeros, the correct root locus is (C) Neither (A) nor (B) are correct

23. For the given set of open loop poles and zeros, the correct root locus is (C) Neither (A) nor (B) are correct