Question 6 λω, A Proportional plus Integral (PI) controller is designed for the control of an underdamped second order p

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Question 6 λω, A Proportional plus Integral (PI) controller is designed for the control of an underdamped second order plant of the form Gp(s) = s?+25wns+w Which of the following s-plane diagrams (with zeros and poles) relates to the closed loop transfer function of the plant with PI controller? Im(s) Im(s) Im(s) Im(s) x Rels) Rels) Re(s) Re(s) + х (a) (b) ) (c) (d) s-plane diagram (d) Os-plane diagram (a) s-plane diagram (b) s-plane diagram (c)
Question 7 The dynamics of a mass-spring-damper system can be modelled using the following transfer function: y(s) 0.65 F(S) S2 +0.912s +0.325 = where y(s) and F(s) are the output displacement and input force respectively. Which of the following plots shows the correct response from this system to a unit step input? 2.5 3.5 (i) (ii) 3 2 2.5 1.5 2 y 91.5 1 1 0.5 0.5 0 0 0 5 5 10 20 25 30 0 5 on 10 20 25 30 15 t(s) 15 t(s) 3 2 (iii) (iv) 2.5 1.5 2 1.5 y 1 y 1 0.5 0.5 0 0 0 0 5 10 20 25 30 5 10 20 25 30 15 t(s) 15 t(s) OL. Plot (1) O II. Plot (10) O III. Plot (ili) IV. Plot (iv)
A Moving to another question will save this response. Question 8 What is the equivalent transfer function Y(S) U (S) of the following block diagram? K и H2 y H 1 OA Y(s) = U(S) H (K+H) 1+H H K+H OB. Y(S) U(S) I+H,H2 1 OC Y(s) U (S) 2 H. (1+KH,) 1+H H H/(1+H) -H 1+KH H, OD. Y(s) U(s) =
Question 9 A system's response to a unit step input is shown in the figure below. Which of the following transfer functions models the dynamics of this system? 1.2 1 0.8 0.6 у 0.4 0.2 0 0 1 2 3 4 5 6 7 8 t(s) O y(s) 5 s+2 u(s) O y(s) u(s) s +5 Sa+3s +5 Oy(s) u(s) 5 $2+3s +2 O y(s) 5 s+3s +5 u(s)
Question 10 The transfer function relating the input displacement, u(s), to the output displacement, x(s), for a mass-spring-damper system can be expressed as: x(s) u(s) ki ms? + C2s + (ki + k) The parameter values for this system are as follows: m = 2 kg, k1 = 4 N/m, k2 = 4 N/m and C2 = 8 Ns/m. What is the steady-state value of x(t) in response to a step input with magnitude 2.3m? x(t) is measured in metres but you do not need to include units in your answer.