1. Given a Bode diagram of a dynamic system (a) Find the transfer function of the system G(s). (b) At what frequency the gain of the system |G (jw)| = 1 ? What is the phase of the system at this frequency? (c) At what frequencies is the phase of G (jw) equals –180°? What is gain at these frequencies? (d) Assuming that this system is in a unity feedback configuration, i.e. H(s) = 1 i. What is the steady state error of the closed-loop system to unit step input ? ii. What is the steady state error of the closed-loop system to unit ramp input ? iii. What is the steady state error of the closed-loop system to constant acceleration input r(t) = }t2? (e) What is the steady state response of the open-loop system G(s) to the input r(t) = 2 · sint+ 5 · sin10t

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1. Given a Bode diagram of a dynamic system
(a) Find the transfer function of the system G(s).
(b) At what frequency the gain of the system |G (jw)| = 1 ? What is the phase of the system at this
frequency?
(c) At what frequencies is the phase of G (jw) equals – 180°? What is gain at these frequencies?
(d) Assuming that this system is in a unity feedback configuration, i.e. H(s) = 1
i. What is the steady state error of the closed-loop system to unit step input ?
ii. What is the steady state error of the closed-loop system to unit ramp input ?
iii. What is the steady state error of the closed-loop system to constant acceleration input r(t) = t2?
(e) What is the steady state response of the open-loop system G(s) to the input
r(t) = 2· sint + 5· sin10t
Transcribed Image Text:1. Given a Bode diagram of a dynamic system (a) Find the transfer function of the system G(s). (b) At what frequency the gain of the system |G (jw)| = 1 ? What is the phase of the system at this frequency? (c) At what frequencies is the phase of G (jw) equals – 180°? What is gain at these frequencies? (d) Assuming that this system is in a unity feedback configuration, i.e. H(s) = 1 i. What is the steady state error of the closed-loop system to unit step input ? ii. What is the steady state error of the closed-loop system to unit ramp input ? iii. What is the steady state error of the closed-loop system to constant acceleration input r(t) = t2? (e) What is the steady state response of the open-loop system G(s) to the input r(t) = 2· sint + 5· sin10t
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Transcribed Image Text:80 -20 db/dec 60- O db/dec -20 db/dec 40 -60 db/dec 20 OF -40 db/dec -20 -20 db/dec -40 -60 102 10 10 10' 10 10 w (rad/sec) -20 -40 -60 -80 -100 -120 -140 -160 -180 -200 -220 102 10 10 10' 10 10 w [rad/sec] [6ap]b
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