ME_132_Fa23_Homework_6

pdf

School

Yale University *

*We aren’t endorsed by this school

Course

6

Subject

Mechanical Engineering

Date

Oct 30, 2023

Type

pdf

Pages

3

Uploaded by AgentCaterpillarMaster481

Report
ME 132 Homework 6 Integral Control and Discrete-time Systems Due Sunday, October 22, 2023, 11:59 PM Instructions 1. Submit your solutions to Gradescope by the due date above. Reserve time to upload your files. Late submissions will NOT be accepted. 2. Clearly handwrite or type your answers and show all relevant work. Partial credit may be awarded for incomplete solutions. Please box your final answers. 3. Begin each problem on a separate page. 4. Be sure to credit sources you consult, and other students you work with on this assign- ment. Problem 0 Honor Code and Credit 1. Please copy and sign the following statement: ”All solutions in this file are my own work. I have given credit to any external sources and other students I have worked with.” 2. Please list other students who you have worked with on this assignment. Problem 1 Finding Transfer Functions (a) Find the transfer function from u to y of the following cascade connection. y (2) + 3 y (1) + 10 y = v (1) 5 v 100 v (1) + v = u 1
ME 132 Dynamic Systems and Feedback Homework 6 (b) Find the transfer function from u to y of the system shown below. It may be easier to draw a block-diagram first. ¨ y + 3 ˙ y + 5 y = ˙ v + v ˙ w + 4 w = ˙ y y ˙ z + 4 z = y v = u + w + z (c) Find the differential equation relating the input u and the output y for part (b) above. Problem 2 Free Response — Analytically find the free response of each of the following differential equations. In each case plot (using matlab ) the solution for 0 t 10. Note: Yes, we know this one is a bit tedious. Sorry, it’s important to build intuition. (a) ˙ y ( t ) + y ( t ) = u ( t ), subject to the initial conditions y (0) = 4. (b) ¨ y ( t ) + 1 . 2 ˙ y ( t ) + y ( t ) = u ( t ), subject to the initial conditions ˙ y (0) = 4 , y (0) = 2. (c) y (3) ( t )+ ( 1 + 10 2 ) ¨ y ( t )+ ( 100 + 10 2 ) ˙ y ( t )+100 y ( t ) = 100 u ( t ), subject to the initial conditions ¨ y (0) = ˙ y (0) = 0 and y (0) = 1. Problem 3 Stability Analysis — For each of the following differential equations, determine if they are stable or unstable. If they are unstable, determine the number of poles in the closed right half complex plane. (a) y (2) + 7 y (1) + 22 y = u (b) y (2) + 25 y = u (c) y (5) + y (4) + 2 y (3) + y (2) + 2 y (1) + 3 y = u Problem 4 Proportional Control, Routh Test — Is it possible to design a proportional controller u = K 1 r + K 2 ( r y ) to stabilize the plant y = s 2 1 s 3 2 s 2 + 3 s + 4 u ? Due Sunday, October 22, 2023, 11:59 PM Page 2 of 3
ME 132 Dynamic Systems and Feedback Homework 6 Conclusion Hooray! You’re done! Feel free to leave any feedback on this assignment on this Google form . Be sure to submit to Gradescope before the deadline, and credit all sources and other students you worked with. Due Sunday, October 22, 2023, 11:59 PM Page 3 of 3
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

Browse Popular Homework Q&A

Q: Which of the following ways is the best way to provide an MLA in-text citation? O O 00 O "Turn what…
Q: Companies formed conglomerates in the Gilded Era. Describe the difference of how they developed and…
Q: Depth-first search (DFS) is an algorithm for traversing or searching a tree, tree structure, or…
Q: Question 1: Magnetic forces due to currents Two long, straight wires are parallel and 10 cm apart.…
Q: DO STYROFOAM CUPS HOLD HOT OR COLD LIQUIDS BETTER? WHAT WILL BE YOUR CONTROL GROUP ? WHAT WILL BE…
Q: we learned that the pituitary gland produces hormones; these hormones are essential to the proper…
Q: Company K operates in a jurisdiction that levies an income tax with the following rate structure:…
Q: Let y=5x2y=5x2.Find the change in y, Δy when x=3 and Δx=0.2   Find the differential dy when x=3 and…
Q: Seawolf class nuclear submarines have a crush depth of approximately d = 715 m. The density of…
Q: Find the derivative of y = 5x²sec 1(2x-3). O y'= 10x sec-¹(2x-3) + O y'= 10x sec-¹(2x-3) + O y'=…
Q: For the chemical reaction,   2NaOH+H2SO4⟶Na2SO4+2H2O2NaOH+H2SO4⟶Na2SO4+2H2O   what mass of…
Q: Problem 1) The cumulative distribution function of random variable X is: 0 x 1/2]. b) Find P[-1/2 <…
Q: Given the array of size 17, and the hashing function h(x) = x%17, at which array location would data…
Q: "While British bombers hit German cities by day, American bombers hit them by night."  Group of…
Q: What is office politics?
Q: What are some benefits that come with sexual reproduction? Please select all correct answers. a.…
Q: What changes did Eisenhower's republicanism bring?
Q: A stationary 1.57-kg potato is struck by a stick, delivering a horizontal force of F(t) = at — bt²…
Q: Calculate the values of L and C in part A. Make it clear how you found them
Q: Draw a free body diagram for the bolded object in the given scenario. Label each force with both its…
Q: What is the name of the compound shown here? F A) fluorobenzene B) o-fluorotoluene C)…
Q: a sample od copper  has mass of 2.45 mg and avolume of 2.733* 108 cubic micro meter. calculate the…