Homework 2: Answer the following questions Q: 1. Show the ode(t) regarding Y=GF for sys. A....

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Homework 2: Answer the following questions Q: 1. Show the ode(t) regarding Y=GF for sys. A. 2. Show the ode(t) regarding Y=feedback(K*G,1)*F for sys. B. 3. Show the ode(t) regarding Y=feedback(K*H*G,1)*F for sys. C. 4. Show the ode(t) of sys. C in state space form. 5. Realize sys A, B and C in Simulink (show slx diagram and scope(f, y) 6. Give ss_error= f(inf) - y(inf) & % overshoot Problem: Let the plant transfer function be MAE 376 23F HW 2 Y G(s) 100 = = U (s+1)(s+155+100) Let the forward (lead-lag) controller transfer function be H(S) = == E 5(s+z) s+p with unspecified pole(p) and zero(z). (1) (2) Consider the following three signal relations: one transfer function and two unit-feedback systems with the following block diagrams F ----- - [G] ---- Y System A F- -----+ ---- - [K] ---- [G] ---- --+ -Y + + System B - [K] -- [H] -- [G] ---+---- -Y F + ---- |- + System C Homework 2: Answer the following questions Q: 1. Show the ode(t) regarding Y=GF for sys. A. 2. Show the ode(t) regarding Y=feedback(K*G,1)*F for sys. B. 3. Show the ode(t) regarding Y=feedback(K*H*G,1)*F for sys. C. 4. Show the ode(t) of sys. C in state space form. 5. Realize sys A, B and C in Simulink (show slx diagram and scope(f, y) 6. Give ss_error= f(inf) - y(inf) & % overshoot Problem: Let the plant transfer function be MAE 376 23F HW 2 Y G(s) 100 = = U (s+1)(s+155+100) Let the forward (lead-lag) controller transfer function be H(S) = == E 5(s+z) s+p with unspecified pole(p) and zero(z). (1) (2) Consider the following three signal relations: one transfer function and two unit-feedback systems with the following block diagrams F ----- - [G] ---- Y System A F- -----+ ---- - [K] ---- [G] ---- --+ -Y + + System B - [K] -- [H] -- [G] ---+---- -Y F + ---- |- + System C