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[25 Marks) Problem 1 Given the below block diagram of a system. Assume that x(t) is:...
5) (1pt) Assume x(t) with Fourier Transform X(w) shown below (where 1X(15)1-3 and 1X(4511e1). Assume x(t)...
5) (1pt) Assume x(t) with Fourier Transform X(w) shown below (where 1X(15)1-3 and 1X(4511e1). Assume x(t) is the input to a system with |H(w)| shown below. Let yt) be the output of the system and Y(w) be its Fourier Transform. Sketch IYwll. Make sure to mark the most significant points in the graph for full credit IX(w) IY(w) -60 0 60 w IH(w)l 45 -15 0 15 45 X,(w) X,(w) ?6) (1pt) Assume two signals x1(t) and x2(t) have Fourier...
3. The system represented by the block diagram below modulates the message signal x(t) with a carrier wave c(t) to yield -(). The signal y(t) is generated by multiplying z() by the carrier wave c(t)....
3. The system represented by the block diagram below modulates the message signal x(t) with a carrier wave c(t) to yield -(). The signal y(t) is generated by multiplying z() by the carrier wave c(t). c(t) c(t) y(t) z(t) The output signal,y(t), can be written as y(t)-C() × X() x C(t). Using the properties of a) Fourier Transforms, write Yi) in terms of Cjo) and Yj). [2 points] The Fourier Transform of x(t) is illustrated below. 0.9 0.8 0.7 0.6...
Problem 1: Steady-state error analvsis (a) A block diagram of a feedback control system is given ...
The Class Name is: MAE 318 System Dynamics and Control I
Problem 1: Steady-state error analvsis (a) A block diagram of a feedback control system is given below. Assuming that the tunable constant Khas a value that makes this closed-loop system stable, find the steady-state error of the closed-loop system for (a a step reference input with amplitude R, r(t)- R u(t) (ii) a ramp reference input with slope R, r(t) = Rt-us(t) R(s) Y(s) (s+2)(s +5) (b) A block...
Given the block diagram for an audio processing system with mit) as the input. the frequency...
Given the block diagram for an audio processing system with mit) as the input. the frequency spectrum of met) is given as: Mif) TokHz I Yok het lokHzT -lo kHъ Block diagram: 2 cos(Wot) Lpf mit) Zit) O-SKHZ LPF -o-20kHz xet) 2 cos(wot) yet) if wo= 10,ooolT radssec, graphically draw the freaveny domain for the signal X(t), y(t), (4), also express the expressions for x (t), get), z (t) and XC4), YCf), Z(f)
Alinear system has the block diagram: x(t) yệt) *h(t) x(t) is the input to the system...
Alinear system has the block diagram: x(t) yệt) *h(t) x(t) is the input to the system and h(t) is the impulse response of the system: x(t) = cos(2 nt) - cos(3 tt) h(t) = 4 sinc(2t) cos(2 st) Find the output signal y(t). Explain how you calculated the output to get the full credit. Partial credits will be given for X(jw) and H(jw).
Problem 2. (35 marks) Time-Domain Analysis of Systems (a) (10 marks) x(t) = u(t – 3)...
Problem 2. (35 marks) Time-Domain Analysis of Systems (a) (10 marks) x(t) = u(t – 3) – u(t – 5) and h(t) = E=-1 8(t - k). Determine y(t) = x(t) * h(t). (b) (25 marks) An LTID system is specified by the following equation: 2y[n + 1] – 3y[n] + y[n – 1] = 4.x[n + 1] – 3x[n]. i) [8 marks] Draw a schematic diagram for the LTID system in terms of delay compo- nents "D". ii) [12...
asap Problem 1) (25 Pts.) C(s) a) Simplify the below block diagram to find the overall...
asap
Problem 1) (25 Pts.) C(s) a) Simplify the below block diagram to find the overall system transfer function G(s)R Show your work including all intermediate block diagrams you may require. b) Given input r(t) is a unit step, find output time response c(t). (Hint: By MATLAB might be easiest).
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spr...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
Question 3 The block diagram of a digital control system is given in Fig. 2. R(Z)...
Question 3 The block diagram of a digital control system is given in Fig. 2. R(Z) + VT CZ 0.52 0.24(2 +0.5) (2-0.4) (z-1) Fig. 2 (a) Write an expression for the closed-loop z-transfer function of the system, C(z)/R(z). Given that one of the poles is located at z=0.235, complete a pole-zero diagram for the system. [8 marks] (b) Using a sampling interval, T = 0.5 s, map the poles and zeros onto the primary strip in the s-plane. [8...
Q2. The block diagram of an LTI system is given below. x[n] - h[n] = a[n+...
Q2. The block diagram of an LTI system is given below. x[n] - h[n] = a[n+ 2] - a[n - 2] h2[n] = 8[n - 1] y[n] a) Represent the overall impulse response h[n] in terms of hi[n] and h2[n]. b) If the input is x[n] = 8[n], sketch y[n]. c) If the input is x[n] = u(n + 1] - u[n -2], sketch y[n].
5) (1pt) Assume x(t) with Fourier Transform X(w) shown below (where 1X(15)1-3 and 1X(4511e1). Assume x(t) is the input to a system with |H(w)| shown below. Let yt) be the output of the system and Y(w) be its Fourier Transform. Sketch IYwll. Make sure to mark the most significant points in the graph for full credit IX(w) IY(w) -60 0 60 w IH(w)l 45 -15 0 15 45 X,(w) X,(w) ?6) (1pt) Assume two signals x1(t) and x2(t) have Fourier...
3. The system represented by the block diagram below modulates the message signal x(t) with a carrier wave c(t) to yield -(). The signal y(t) is generated by multiplying z() by the carrier wave c(t). c(t) c(t) y(t) z(t) The output signal,y(t), can be written as y(t)-C() × X() x C(t). Using the properties of a) Fourier Transforms, write Yi) in terms of Cjo) and Yj). [2 points] The Fourier Transform of x(t) is illustrated below. 0.9 0.8 0.7 0.6...
The Class Name is: MAE 318 System Dynamics and Control I
Problem 1: Steady-state error analvsis (a) A block diagram of a feedback control system is given below. Assuming that the tunable constant Khas a value that makes this closed-loop system stable, find the steady-state error of the closed-loop system for (a a step reference input with amplitude R, r(t)- R u(t) (ii) a ramp reference input with slope R, r(t) = Rt-us(t) R(s) Y(s) (s+2)(s +5) (b) A block...
Given the block diagram for an audio processing system with mit) as the input. the frequency spectrum of met) is given as: Mif) TokHz I Yok het lokHzT -lo kHъ Block diagram: 2 cos(Wot) Lpf mit) Zit) O-SKHZ LPF -o-20kHz xet) 2 cos(wot) yet) if wo= 10,ooolT radssec, graphically draw the freaveny domain for the signal X(t), y(t), (4), also express the expressions for x (t), get), z (t) and XC4), YCf), Z(f)
Alinear system has the block diagram: x(t) yệt) *h(t) x(t) is the input to the system and h(t) is the impulse response of the system: x(t) = cos(2 nt) - cos(3 tt) h(t) = 4 sinc(2t) cos(2 st) Find the output signal y(t). Explain how you calculated the output to get the full credit. Partial credits will be given for X(jw) and H(jw).
Problem 2. (35 marks) Time-Domain Analysis of Systems (a) (10 marks) x(t) = u(t – 3) – u(t – 5) and h(t) = E=-1 8(t - k). Determine y(t) = x(t) * h(t). (b) (25 marks) An LTID system is specified by the following equation: 2y[n + 1] – 3y[n] + y[n – 1] = 4.x[n + 1] – 3x[n]. i) [8 marks] Draw a schematic diagram for the LTID system in terms of delay compo- nents "D". ii) [12...
asap
Problem 1) (25 Pts.) C(s) a) Simplify the below block diagram to find the overall system transfer function G(s)R Show your work including all intermediate block diagrams you may require. b) Given input r(t) is a unit step, find output time response c(t). (Hint: By MATLAB might be easiest).
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
Question 3 The block diagram of a digital control system is given in Fig. 2. R(Z) + VT CZ 0.52 0.24(2 +0.5) (2-0.4) (z-1) Fig. 2 (a) Write an expression for the closed-loop z-transfer function of the system, C(z)/R(z). Given that one of the poles is located at z=0.235, complete a pole-zero diagram for the system. [8 marks] (b) Using a sampling interval, T = 0.5 s, map the poles and zeros onto the primary strip in the s-plane. [8...
Q2. The block diagram of an LTI system is given below. x[n] - h[n] = a[n+ 2] - a[n - 2] h2[n] = 8[n - 1] y[n] a) Represent the overall impulse response h[n] in terms of hi[n] and h2[n]. b) If the input is x[n] = 8[n], sketch y[n]. c) If the input is x[n] = u(n + 1] - u[n -2], sketch y[n].
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