Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 13, Problem 9RQ
What method for finding the inverse z-transform immediately yields the values of the time waveform at the sampling instants?
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Use the standard list of Laplace Transform and determine the following:
a) L{1+ 2t
–t*}
3
b) L{5e2t – 3e¬t}
Determine the inverse Laplace transform of the function:
F (s)
7s-41s+84
(s 1)(s2 4s+13)
5
4. The Laplace transform
²2+4s +6
can be expressed as
L{e²¹[qssin(q6t) + q7cos(** t)]}
Chapter 13 Solutions
Control Systems Engineering
Ch. 13 - Prob. 1RQCh. 13 - Name three advantages of using digital computers...Ch. 13 - Name two important considerations in...Ch. 13 - Prob. 4RQCh. 13 - Prob. 5RQCh. 13 - Prob. 6RQCh. 13 - Prob. 7RQCh. 13 - 8. What method for finding the inverse z-transform...Ch. 13 - What method for finding the inverse z-transform...Ch. 13 - In order to find the z-transform of a G(s), what...
Ch. 13 - Prob. 11RQCh. 13 - Prob. 12RQCh. 13 - Prob. 13RQCh. 13 - Prob. 14RQCh. 13 - Prob. 15RQCh. 13 - Prob. 16RQCh. 13 - Prob. 17RQCh. 13 - Prob. 18RQCh. 13 - Prob. 19RQCh. 13 - Prob. 20RQCh. 13 - Prob. 21RQCh. 13 - Prob. 1PCh. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4PCh. 13 - Prob. 5PCh. 13 - Prob. 6PCh. 13 - Prob. 7PCh. 13 - Prob. 8PCh. 13 - Prob. 9PCh. 13 - Prob. 10PCh. 13 - Prob. 11PCh. 13 - Prob. 13PCh. 13 - Prob. 14PCh. 13 - Prob. 15PCh. 13 - Prob. 17PCh. 13 - Prob. 21PCh. 13 - Prob. 22PCh. 13 - Prob. 23PCh. 13 - Prob. 24PCh. 13 - Prob. 29PCh. 13 - Prob. 31PCh. 13 - Prob. 32PCh. 13 - Prob. 33PCh. 13 - Prob. 36PCh. 13 - Prob. 37PCh. 13 - Prob. 38PCh. 13 - Prob. 39PCh. 13 - Prob. 40P
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- find the inverse leplace transform of 20/(s-1)(s+4)arrow_forwardCompute theresponse x(t) for the following driven, undamped oscillator using the Laplace transform method. *(t)+4x(t) = sin(2t) x(t) = 0 *(t) = 0arrow_forwardCompute the Laplace Transforms of the following time domain functions from the Laplace Transformation definition a) f(1) =r" b) f(t) =tcos(wt)arrow_forward
- The Inverse Laplace Transform for 5/3S - 2/ ((3(s+3)) is *arrow_forwardFind the Laplace transform of the given function; b iş a real constant. f(t) = cos(bt) Your answer should be an expression in terms of b and s. NOTE: Your answer must be fully simplified. It cannot contain i. L{f(t)}(s) = F(s)arrow_forwardProblem-3. Consider the closed loop transfer function from R(s) to C(s) as given below as given below. 85 H(s) = (s+5)(s? + 2s +17) MATLAB gives the partial fraction values of the Laplace transform C(s) to the unit step input as follows: Num: Denom: -0.5313 -5.0000 -0.2344 + 0.3906i -1.0000 + 4.0000i -0.2344 - 0.3906i -1.0000 - 4.0000i 1.0000 d) Find the overshoot and peak time by using the reduced-order transfer function Hint:Tp = e-(n{//1-§2 %OV = Wn V1- 2)arrow_forward
- 4 Problem Find the Laplace transform fraction for the following function and rearrange it such that X(s)/F(s) is the only term on the left-hand-side: x(t) + 25wx (t) +w²x(t) = f(t) Assume the initial conditions are all zero, x(to) = x(to)= (to) = x (to) = 0 with initial time to = 0. Hint: Use the differentiation theorem.arrow_forwardQ5 Hydraulic power actuators were used to drive the dinosaurs of the movie Jurassic Park. The motions of the large monsters required high-power actuators requiring 1200 watts. One specific limb motion has dynamics represented by: y = [0 1] Design the state feedback gain matrix using the Ackermann's formula method. Where the new closed loop poles to be placed at s1,2 =-17j3.arrow_forwardK m fv fy- 0 J M A Figure 1 Find the Laplace transform and transfer function for the system in Figure 1. f(t)arrow_forward
- Find the transform of the given function of s. 3s + 8 F (s) = s2 + 8s + 20 A) f (t) = e 4t (3 cos 2t - 2 sin 2t) (B) f = e 4t (-2 cos 2t + 3 sin 2t) (c) =e-2t (3 cos 4t - 2 sin 4t) D There is no correct answer among the choices. E) f e -4t (3 cos 2t - 2 sin 2t)arrow_forwardMatch the transfer function with correct Bode phase plots. s+10 G(s)=(s+100) s+ 100 G(s)= s(s+10) G(s) = (s+10) (s+100) s(s+10) G(s) = (s+100) s(s+100) G(s)= (s+10) G(s) = (+10) (+500) S A. 180 deg- 90 deg 0 deg 90 deg 180 deg- 90 deg 00 00 0 deg C. 90 deg+ 90 deg+ 0 deg -90 deg D. 180 deg F. 90 deg 0 deg 90 deg -180 deg 90 deg 0 deg 90 deg -180 deg 90 deg 0 deg -90dex+ -180 deg 00arrow_forwardKnowing that u c(t) it is the unit step function, the inverse Laplace Transform of the function F(s)= e-s(s-2)/s2 - 4s +3 is: a) f(t) = u1(t) e2(t-1) cosh(t - 1) b) f(t) = u1(t) e2(t-1) cosh(t) c) None of the answers d) f(t) = u2(t) e2(t-1) cosh(t - 1) e) f(t) = u2(t) e2(t-1) cosh(t - 2)arrow_forward
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