Consider the second-order linear time-invariant system given by the transfer fun
ID: 1796926 • Letter: C
Question
Consider the second-order linear time-invariant system given by the transfer function H(s) = PA(s)/Pomega(s) = K /s2 + 2zetaomegans + Let K 2, and omegan = 2pi5 rad/sec. Plot the unit impulse responses of PA(t) in one figure for the undamped case (zeta = 0, dashed line), underdamped case (choose zeta = 0.707, solid line), and overdamped case (choose xi = 1.8, dotted line). You should end up with one figure with three separate curves. Label the axes. Plot the responses from 0 to 0.7 seconds every 0.005 seconds (suggested MATLAB code example: time_vector=0.0:0.005:0.7;). Plot the unit step responses of PA(t)in one figure for the undamped case (zeta = 0, dashed line), underdamped case (choose zeta = 0.707, solid line), and overdamped case (choose zeta = 1.1, dotted line) cases. Label the axes. Consider the model in Eq. (9) of the notes entitled "Respiratory Mechanics Model v1" on the class ICON site. For this assignment consider Eq. (9) to represent the relationship between airway pressure at the mouth (P ) and alveolar pressure (PA) where gas exchange actually occurs. Assume that R=0.5 cm H2O s L-1, L=0.01 cmH2O s2 L-1, and C=0.1 L cmH2O in the model in Eq. (9). Calculate the natural frequency omegan and the damping ratio zeta in terms of R, L, and C. Plot the step and impulse responses on the same figure. Is this system undamped, underdamped. or overdamped? Simulate the case in which there is no damping in the system. What parameter must change in your model to produce the "no damping" condition? What is the damping ratio in this case? Plot this case. Simulate the case in which the system is overdamped in the system. What parameter must change in your model to produce the "overdamped" condition? What is the damping ratio in this case? Plot this case. Suppose that you wanted to model a slower breathing rate. What parameter(s) change could model this case? What is the natural frequency change after you alter one (or more) of the parameters? Plot this case.Explanation / Answer
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