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Question 42127

posted 11 months ago

Consider the telecommunication radio tower example given in Problem Two. For a mobile phone moving away from the radio tower at a constant speed of v = 1 km/hr, the total energy (E) received over the travelled distance is given by:
E=\int_{S}^{F} \frac{P}{v} d x
where S and F are the distances from the radio tower, at which the mobile started moving and stopped moving, respectively.In other words, energy received is the area under the power curve between the S andF locations as shown in the Figure.
The objective is to determine the total energy, E, for the distance from S to F from the radio tower.
\text { a) Compute the total energy, } E, \text { from } S=2 \text { to } F=12 \mathrm{~km} \text {, using Simpson's rule for } h=
\Delta x=1
b) Write MATLAB statements to compute the total energy, E, from S=2 to F= 12 km,using the Trapezoidal rule for h-Ar = 1.

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Question 38536

posted 1 years ago

1: Design a double-dwell cam to move a follower:
Rise:0~25 mm in 90°
Dwell:at 25 mm in 45°
Fall:25-0 mm in 90°
Dwell:for the remainder
Set up appropriate boundary conditions and determine the coefficients C, for the 7th-degree polynomial
s=\sum_{i=0}^{7} C_{i}\left(\frac{\theta}{b}\right)^{n} \text { where } \theta \text { is the cam angle, } b \text { is the total angle of any segment, rise, fall, or dwell }
(b) Develop a MATLAB program to compute and plot svaj diagrams, assume the cycle takes 2 sec.Parameters: The mass of the follower is 1.0 kg. The spring has a rate of 10 N/m, a damping ratio of 0.10,and a preload of 1.0 N. Find the follower force over one revolution. If there is a follower jump, re-specify the spring rate and preload to eliminate it.

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Question 38537

posted 1 years ago

Problem 2: The figure shows a 4-bar linkage. Write a Matlab calculate and plot the angular displacements, angular velocities and angular accelerations of links 3 and 4, and x and y acceleration components of the coupler point P over the maximum range of motion possible. Given: w2 = 20rpm and az =0.program to

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Question 38538

posted 1 years ago

Problem 3: The offset crank-slider linkage has the dimensions given in the figure. Develop a MATLAB program to calculate and plot the accelerations AAand Ag in the global coordinate system for w 25 rad/sec CW and a2= 0rad/sec?.

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Question 34018

posted 1 years ago

5.6 Figure P6.6 shows a mechanical system driven by the displacement of the left end, x(1), which could be supplied by a rotating cam and follower (see Problem 2.2). The mechanical parameters are mass m =0.5 kg, b = 6 N-S/m, and k = 500 N/m, and the system is initially at rest. The displacement of the left endis x,() = 0.05 sin ot (in m), where o is the input frequency in rad/s. Using Simulink, obtain and plot the response x(t) for input frequency o = 20 rad/s (or, 10/x cycles per second = 3.183 Hz). Show the inputXin(t) on the same plot.

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Question 34019

posted 1 years ago

A series RL circuit with a nonlinear inductor is shown in Fig. P6.10. Recall that the following nonlinear function for inductor current was used in Problem 3.11 in Chapter 3
I_{L}(\lambda)=97.3 \lambda^{3}+4.2 \lambda \quad(\operatorname{amps}, A)
where i is the flux linkage. Use Simulink to obtain the dynamic response for current I1) if the source voltage is a 4-V step function, that is, ein(t) = 4U(t) V. The RL circuit has zero energy stored at time t =and the resistance is R = 1.2 2. Plot current /, vs. time.

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Question 34934

posted 1 years ago

Consider the following system:
\dot{x}=1+x-y^{2}, \quad \dot{y}=-1+6 y+x^{2}-5 y^{2}
1. Determine the Jacobian.
2. Draw up a table showing the coordinates of the fixed points, their relevant determinants, traces and discriminants and their type (stability). Full workings for at least two fixed points must be shown. 8:
3. Write an-lile and construct plots of the time response and the phase portrait.an
4. Comment on the dynamics of this system.

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Question 34935

posted 1 years ago

Consider the following system:
\ddot{q}-\zeta \dot{q}+\dot{q} q^{2}+q=0
where ( is a constant. Explore this system! Include your mlile in your report. You will be awarded marks for analysis that sheds light on the dynamics.

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Question 33940

posted 1 years ago

On February 18th, 2021, NASA's Mars 2020 Preserverance Rover is planned for landing on Mars.A landing animation video can be seen here http://bit.ly/PreserveranceThe Sky Crane, which is responsible for gracefuly landing the rover on the designated site, can be modeled as a rigid body with thruster forces being controlled by a gimbal to produce thrusta t angles 0 as shown.
a. (20%) Derive the equations of motion for the system (3 directions)The thruster angles and thrust forces are all independent input variables now.We wish to design a state-space controller to help the SkyCrane navigate to a desired position in space.
b. (30%) Linearize the system and put it in state-space form, then design a controller via pole placement to achieve the following transient response characteristics
- Ts = 2 s
-\omega_{d}=20 \mathrm{rad} / \mathrm{s}
c. (25%) Apply your controller on the nonlinear system (numerical integration)
d. (25%) In reality, there are limits to the inputs. The thrust can not be negative, and there is a minimum thrust once the engine is ignited. The thruster gimbal can only operate within a specific angular range. Repeat part c with the following saturation limits:
- Thrusts: 100N < F < 2000N
Gimbal Angle Range: -45° < 0 < 45°-

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Question 33938

posted 1 years ago

There are several ways to transfer the block diagram into state-space, but let's try to remodelthe state-space from the beginning.
Given the following block diagram, with
The sensor H(s) relates the state to the output: y = Cx-
а.(50%) Convert this system into state-space form, accounting for the multiple inputs and out-puts.
Note you already have the model of the system from the state-space, and this is a linear system.You can calculate the derivative and propagate the system directly.
- The feedback defines the control law: U(s) = G.(Gf * R(s) - Y(s)), which can be substituted intothe plant dynamics to find the closed-loop form.
G_{f}=10, G_{c}=20, G_{p 1}=\frac{2.0}{1.0 s^{2}+10.0 s+20.0}, G_{p 2}=\frac{5.0}{1.0 s^{2}+5.0 s+25.0}, H=1.0 s+6.0
\text { - The plant transfer functions give us the plant dynamics } \dot{x}=A x+B u \text { and } u=[u d]^{\wedge} T^{\prime \prime}
- Random Noise, normally distributed, zero mean with o = 2: d(t) = 2 * rand()
С.(50%) Simulate the response of the system using basic numerical integration. To a- Reference: r(t) = 5

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