Do you know how to do control lab report?

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Uxn12345

Engineering

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I have Control system lab and I already did it and wrote the report, so I need some one good at electrical engineering specially in Control system to paraphrased the report and do the math part by typing and everything should be in Word document as well.

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Introduction to Control System and Applications Objective: To design a closed-loop response of a system. Required Software: MATLAB, Simulink, and the Control System Toolbox. Part 1 a. We evaluate the closed loop transfer function of the above system using block diagram reduction: K* 20.83/(pi*(s+100)*s*(s+1.71)+ K*20.83). b. Let K=1000. Then the transfer function is: 20830/(pi*(s+100)*s*(s+1.71)+ 20830) 1 syms s sys=tf([20830*pi],[pi pi*101.71 pi*171 20830]); step(sys) S=stepinfo(sys) RiseTime: 0.1361 SettlingTime: 7.4187 SettlingMin: 1.0625 SettlingMax: 5.6890 Overshoot: 81.0860 Undershoot: 0 Peak: 5.6890 PeakTime: 0.3871 c. If we replace the power amplifier with a transfer function of unity, we get 208.3/ (pi*s^2+ pi*1.71*s + 208.3)=( 208.3/pi)/(s^2 +1.71s +208.3/pi) 2 Then: omega_n= 8.14 Zeta = 0.105 We use the following formulas: Peak time: T_p= pi/(omega_n x sqrt (1—zeta^2)=0.388 seconds Settling time: T_s=4/(zeta*omega_n)=4.68 seconds Percent overshoot: %OS=e^(-zeta*pi/sqrt (1-zeta^2))x100= 71.78%. d. The Laplace transform of the step response of the system in c. is found by multiplying the transfer function 208.3/pi/(s^2 +1.71s +208.3/pi)=66.3/(s^2 +1.71s+66.3) by 1/s, which is a unit step input. This new transfer function can be expressed as 66.3/(s*(s^2 +1.71s+66.3))=(1/s)--(s+1.71)/(s^2+1.71s+66.3)=1/s— ((s+0.855)+0.106(8.097))/((s+0.855)^2+(8.097)^2) Which yields the analytical solution for the step response as : y(t)=1—e^(-0.855t()(cos 8.097*t+0.106sin8.097t). Using the Simulink and the Linear System Analyzer, we get the following graph of the step response of the system in c.: e. zeta =-ln (% OS/100)/sqrt(pi^2+ln^2(%OS/100)) For 15% overshoot, zeta =0.517 Then omega_n=1.71/(2*zeta)= 1.65. Since Kx0.2083/pi= omega_n , K= 1.65*pi/0.2083=24.93 3 Part 2: We use the Control System Toolbox of MATLAB to analyze the system below. The figure shows the block diagram of a possible cascade control scheme for a hybrid vehicle driven by a dc motor. We develop a Simulink model for the system above. We set the reference signal input r_v(t=4u(t), as a step input with zero initial value, a step time as 0 seconds, and a final value of 4 volts. We use the X-Y graph to display over the period of 8 seconds (1) change in car speed, (2) car acceleration and (3) the motor armature speed: 4 Change in car speed (m/s) 5 Car acceleration (m/s^2) 6 Motor armature current (A) Lessons learned and Conclusion : By making small changes at the system, by adding or removing some elements, we can get results to satisfy different specifications. 7 Part 1 Objective To Design a closed-loop response of a system Minimum Required Software Packages MATLAB, Simulink, and the Control System Toolbox Given the antenna azimuth position control system shown below, do the following a. Find the closed-loop transfer function using block diagram reduction. Use Simulink to verify your solution. b. Use the control tool box to evaluate the closed-loop peak time, percent overshoot, and settling time for 𝐾 = 1000. c. Replace the power amplifier with a transfer function of unity and, using hand calculations, evaluate the closed-loop peak time, percent overshoot, and settling time for 𝐾 = 1000. Verify your results using Simulink and the Linear System Analyzer. d. For the system of d, derive the expression for the closed-loop step response of the system. Verify your solution using Simulink and the Linear System Analyzer . e. For the simplified model in e, find the value of the preamplifier gain K to yield 15% overshoot. Part 2 The following figure shows the block diagram of a possible cascade control scheme for a hybrid vehicle driven by a dc motor. In this problem the following notations are used: 𝐾𝐴 is the power amplifier gain; 𝐾𝑡 is the motor torque constant; 𝐽𝑡𝑜𝑡 is the sum of the motor total inertia; 𝑅𝑎 is the resistance of the electric motor; 𝑘𝑓 is the coefficient of the viscous friction; and 𝑘𝑏 is the back emf constant. Let the speed controller 𝐺𝑆𝐶 (𝑠) = 100 + 40 𝑠 , the torque controller and the power 6 amplifier 𝐾𝐴 𝐺𝑇𝐶 (𝑠) = 10 + , the current sensor sensitivity 𝐾𝐶𝑆 = 0.5, the speed sensor 𝑠 1 sensitivity 𝐾𝑆𝑆 = 0.0443. Also 𝑅 = 1; 𝜂𝑡𝑜𝑡 𝐾𝑡 = 1.8; 𝑘𝑏 = 2; 𝐷 = 𝑘𝑓 = 0.1; 𝐽 𝑎 0.0615; and 𝜌 𝐶𝑤 𝐴𝑣0 𝑖 𝑟 𝑡𝑜𝑡 = 0.6154. 1 𝑡𝑜𝑡 1 = 7.226; 𝑖 𝑟 𝑡𝑜𝑡 = a. Substitute these values in the block diagram and hand calculate the transfer function , 𝑇(𝑠) = 𝑟 𝑉(𝑠)⁄𝑅(𝑠) using block-diagram reduction. [Hint: Start by moving the last 𝑖 block to the 𝑡𝑜𝑡 right past the pickoff point.] b. Develop a Simulink model for the original system shown above. Set the reference signal input 𝑟𝑣 (𝑡) = 4 𝑢(𝑡), as a step input with zero initial value, a step tome = 0 seconns, and a final value of 4 volts. Use the X-Y graphs to display (over a period of 8 seconds) the response of the following variables to the step input: (1) change in car speed (𝑚/𝑠), (2) car acceleration (𝑚/𝑠 2 ), and (3) motor armature current (A). To record the time and the above three variables (in array format), connect them top four Workspace sinks, each of which carry the representative variable name. After the simulation ends, utilize MATLAB plot commands to obtain and edit the three graphs of interest. Deliverables Your report should include the following: 1. 2. 3. 4. 5. 6. The lab objectives The hand calculation for each problem The Simulink implementations for each problem A comparison between your hand calculations and the simulation results The MATLAB code and graphs for problem 2 part b Lessons learned and conclusion
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Explanation & Answer

Hello buddy! I have attached the answer in a word document for you. :) Let me know if you have any edits or have any questions.

Last Name 1

Name
Instructor's name
Course
Date
Control Lab Report
Objectives
The objectives of this lab include:
1. To Design a closed-loop response of a system
Materials
The software packages used are MATLAB, Simulink, and the Control System Toolbox
Data
Part 1: The antenna azimuth position control system shown below was given.

Part 2: The the block diagram of a possible cascade control scheme for a hybrid vehicle
driven by a dc motor is shown below:

Last Name 2

In this diagram the following notations are used:
𝐾𝐴 𝑖𝑠 𝑡ℎ𝑒 𝑝𝑜𝑤𝑒𝑟 𝑎𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑟 𝑔𝑎𝑖𝑛
𝐾𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑜𝑡𝑜𝑟 𝑡𝑜𝑟𝑞𝑢𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡;
𝐽𝑡𝑜𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑜𝑡𝑜𝑟 𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑒𝑟𝑡𝑖𝑎;
𝑅𝑎 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑚𝑜𝑡𝑜𝑟;
𝑘𝑓 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑣𝑖𝑠𝑐𝑜𝑢𝑠 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛;
𝑘𝑏 𝑖𝑠 𝑡ℎ𝑒 𝑏𝑎𝑐𝑘 𝑒𝑚𝑓 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡.
Let
the speed controller 𝐺𝑆𝐶 (𝑠) = 100 +

40
𝑠

,
6

the torque controller and the power amplifier 𝐾𝐴 𝐺𝑇𝐶 (𝑠) = 10 + 𝑠 ,
the current sensor sensitivity 𝐾𝐶𝑆 = 0.5,
the speed sensor sensitivity 𝐾𝑆𝑆 = 0.0443.
Also

1
𝑅𝑎

0.6154.

= 1; 𝜂𝑡𝑜𝑡 𝐾𝑡 = 1.8; 𝑘𝑏 = 2; 𝐷 = 𝑘𝑓 = 0.1;

1
𝐽𝑡𝑜𝑡

=

1

;

𝑟

7.226 𝑖𝑡𝑜𝑡

= 0.0615; 𝜌 𝐶𝑤 𝐴𝑣0

𝑟
𝑖𝑡𝑜𝑡

=

Last Name 3

Discussion
Part1: The following calculations are made:
The closed-loop transfer function using block diagram reduction as follows:
The feed-forward path transfer function:
100
0.2083
20.83𝐾
][
]=
𝐺1 (𝑠) = 𝐾 [
𝑠 + 100 𝑠 (𝑠 + 1.71)
𝑠(𝑠 + 100)(𝑠 ...


Anonymous
Excellent! Definitely coming back for more study materials.

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