MEM355 HW6

pdf

School

Drexel University *

*We aren’t endorsed by this school

Course

355

Subject

Electrical Engineering

Date

Feb 20, 2024

Type

pdf

Pages

Uploaded by ProfessorCaribouMaster900

MEM355 HW#6 – Creating Bode Plot Experimentally <Homework submission instruction> - Create a SINGLE WORD or PDF file containing all descriptions, derivations, plots, tables and codes, and upload it to Blackboard. Submit the file using the following naming style: HW#_LastName_FirstName.docx (or PDF). - If you are scanning your handwriting homework for submission, please make sure the scanned document is readable. Problem 1 (50 points) (a)-(b) Consider a two-mass pendulum with a damper and a spring shown below. Mass M1 is connected to the ceiling via the damper C. Mass M2 is connected to the ceiling via the spring K. The system rotates about a pivot between the two masses. Assume that the system is in the static equilibrium when θ=0 (i.e., The pendulum is in the horizontal posture). Force F is applied to M2 in the vertical direction. Assume small angle of motion. Transfer function of this system is given, !(#) %(#) = ’ (( ! ) " + ( " ’ " )# " + ) " +# + ’ " , Where M1=3kg, M2=2kg, a=2m, b=3m, C=10N-s/m, and K=300N/m You want to see how the system gain - #(%&) ((%&) - (.. 0. , - )*+,*+ -.,*+ -) varies with different frequency force inputs (i.e. Frequency domain analysis). For this purpose, you add a force shaker underneath the mass M2 to apply sinusoidal force at a certain frequency as shown above. The force shaker moves up and down vertically and applies sinusoidal force input to the mass M2. The force generated by the force shaker is measured by a force transducer inside the force shaker. Maddie white

(a) (10points) It is desired to draw a bode diagram to see how the system gain changes for different input frequencies. 1) Use MATLAB function bode() to create the bode plot of the system and 2) Find a frequency that provides the highest gain (i.e. 2 . , natural frequency) and identify the gain at that frequency. (b) (40 points) In order to verify the bode plot created above, you will apply a sinusoidal force input with a certain frequency to the system. Consider three sinusoidal force inputs below in Table 1. Apply each sinusoidal force input in Table 1 one by one to the system. You can use function sin () and lsim () on MATLAB. Follow (1)-(5). ** Note: Show your plots in time from 0s to 10s (i.e. t=[0:0.01:10]. Put appropriate labels on the x-axis and y-axis. 1) Create plots for each signal (i.e. Three plots in total with input signal and output signal). You may need to zoom in the plots to clearly see the amplitude of the output signal. Use ‘data cursor’ to obtain the amplitude of the output signal. (*Note: Measure the amplitude when the response is in steady state) 2) Fill out the table below 3) Create a bode plot again (Problem1-(a)) and use ‘data cursor’ to obtain three gains(in dB) at three frequencies in Table 1. 4) Compare the value of the Gain (in dB) in the table above and the gain value corresponding to that frequency in the bode plot that you created in Problem1 – (a). Are these values similar to each other? 5) Explain what a magnitude plot (i.e. Gain vs Frequency) of the Bode diagram is. Based on its definition, explain how we can experimentally obtain a magnitude plot when the force shaker can only produce a single frequency at a time.

a 9 3 27 2 2 s 2 21101s 3 300 a 3 3052 40s 2700 2 Based on the bode plot the highest gain is 42 dB The frequency at that gain is 9 44 rad see 6 signal 1 Flt 10 sin 9.4.47 bode plot Amplitude 0715 Time 6.3 seconds Gain 201091.00715 42.91

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

signal 2 Fst to sin 12.447 Amplitude 0123 Gain 20 log 00123 58.2 dB 1 1 1 i 00123 signal 3 Fat to sin 6.447 Amplitude 019 Effff f 0019 20 log 00 9 54.42 dB

from plots 019 0019 54.42 6 4 The gain in part a was 42dB at 9.44 rad s All of the gain values for signals 1,2 and 3 are close They rose in magnitude with higher frequency The value for signal I got pretty close b 5 A magnitude plot of the Bode diagram shows how the amplitude of the output signal changes with different input frequencies The amplitude represents the gain which is on the y axis while the x axis holds values for the input frequency in logarithmic scale If your force shaker can only produce 1 input frequency at a time you could run multiple trials and set it to different frequencies for each trial Your experiment can produce gain results across a frequency range of your selection You can start at the lowest freque ney and gradually increase in small increments making sure to record the amplitude for each trial