8.12 Consider the system represented in state variableformX(t)=10-4 -50x(1) + [9]u(e)4y(t) = [ 10 ]x(t) + [0]u(t).(a) Determine the transfer function representation ofthe system. (b) Sketch the Bode plot.

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Answered: 8.12 Consider the system represented in…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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11. Find the zero of the following linear functions: (a) f(r) = x hint: don't overthink (b) f(x) = r - 6 (c) f(r) = x + 5 (d) f(r) = 5x – 25 (e) f(x) = -x +7 (f) f(x) = 23 –- x (g) f(x) = 37 + 23.r
Use EROS and backward substitution to solve the system Ax= b, where (三) (6) 21 1 and 1. -3 -1 What is the rank of A?
A single-input, single output system has the state variable representation a. b. C. d. where A = = L-₁0 B = 1 -10 -5. The transfer function of the system T(s) = Y(s)/U(s) is: a. T(S) c. T(S): = b. T(S) = d. T(S) = -50 5s²+5s+1 -100 s²+10s+100 -50 s²+5s+100 x = Ax + Bu y = Cx -100 s²+5s+10 =[] c C = [010]
Match b and a system representation to its corresponding difference equation y[n] = -1.46x[n] - 3.53x[n-1] + 3.93x[n-2] - 2.86y[n-1] - 4.1y[n-2] -0.65y[n-3] y[n] = -1.46x[n] - 3.53x[n-1] + 3.93x[n-2] + 2.86y[n-1] + 4.1y[n-2] + 0.65y[n-3] y[n] = 1.46x[n] + 3.53x[n-1] - 3.93x[n-2] + 2.86y[n-1] + 4.1y[n-2] + 0.65y[n-3] y[n] = -1.46x[n] - 3.53x[n-1] - 3.93x[n-2] + 2.86y[n-1] + 4.1y[n-2] + 0.65y[n-3] y[n] = 1.46x[n] + 3.53x[n-1] - 3.93x[n-2] - 2.86y[n-1] - 4.1y[n-2] -0.65y[n-3] 1. 2. 3. 4. 5. b = [-1.46 -3.53 3.93]; a = [1 2.86 4.1 0.65] b = [-1.46 -3.53 -3.93]; a = [1 -2.86 -4.1 -0.65] b = [-1.46 -3.53 3.93]; a = [1 -2.86 -4.1 -0.65] b = [1.46 3.53 -3.93]; a = [1 2.86 4.1 0.65] b = [1.46 3.53 -3.93]; a = [1 -2.86 -4.1 -0.65]
(5) Consider the family of systems 4 = (" Y (a) Identify all bifurcation values for this family. (b) Describe the bifurcations that occur as m increases.
Consider a dynamical system given by Xn+1 = ,which one of the following is X11? X11 = X11 = X11 = X11 = [a(1.09)" b(0.91)" [a(0.91) b(1.09)". [a(0.91)¹1 b(1.09)11 [a(1.09)11- b(0.91)¹1 0.91 0 0 1.09 Xn. Assuming that Xo = a b
2s Transfer function of a linear system is given as H(s) Find the output y(t) due s+6 to the input e-3tu(t).
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8.12 Consider the system represented in state variable form 01 -4 -5 y(t) = [ 10 ]x(t) + [0]u(t). (a) Determine the transfer function representation of the system. (b) Sketch the Bode plot. x(t) = x (t) +