1. For the LTI ODE x(t) + 3x(t) +9x(t) + 14x(t) = u(t) a) Derive the transfer function if y(t) = 2x(t) + 3x(t) b) Based on the transfer function you derived, find the poles and zeros of the transfer function c) Use the initial value theorem to find the instantaneous change in y if a step input u = 1 is applied to the system at rest at t = 0 d) Use the final value theorem to find the steady-state value of y if a step input u = 1 is applied to the system at rest at t = 0 e) Convert the LTI ODE into state space in Matlab f) Use step to confirm your answers in parts (c) and (d) g) Use ss2tf to confirm your answer to part (a) h) Use roots on your results from ss2tf to confirm your answer to part (b) i) Also use eig to confirm the poles in part (b)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. For the LTI ODE x(t) + 3x(t) +9x(t) + 14x(t) = u(t)
a) Derive the transfer function if y(t) = 2x(t) + 3x(t)
b) Based on the transfer function you derived, find the poles and zeros of the transfer function
c) Use the initial value theorem to find the instantaneous change in y if a step input u = 1 is applied to the
system at rest at t = 0
d) Use the final value theorem to find the steady-state value of y if a step input u = 1 is applied to the system
at rest at t = 0
e) Convert the LTI ODE into state space in Matlab
f) Use step to confirm your answers in parts (c) and (d)
g) Use ss2tf to confirm your answer to part (a)
h) Use roots on your results from ss2tf to confirm your answer to part (b)
i) Also use eig to confirm the poles in part (b)
Transcribed Image Text:1. For the LTI ODE x(t) + 3x(t) +9x(t) + 14x(t) = u(t) a) Derive the transfer function if y(t) = 2x(t) + 3x(t) b) Based on the transfer function you derived, find the poles and zeros of the transfer function c) Use the initial value theorem to find the instantaneous change in y if a step input u = 1 is applied to the system at rest at t = 0 d) Use the final value theorem to find the steady-state value of y if a step input u = 1 is applied to the system at rest at t = 0 e) Convert the LTI ODE into state space in Matlab f) Use step to confirm your answers in parts (c) and (d) g) Use ss2tf to confirm your answer to part (a) h) Use roots on your results from ss2tf to confirm your answer to part (b) i) Also use eig to confirm the poles in part (b)
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