Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
3. Consider the system shown below. The outputs of the system are the angular displacement of the upper gear (positive about the x-axis) and the Contact force between the upper and lower gear. Assume that the initial conditions for all state variables are zero and that the gears are massless. There are two inputs Ti(t) acting on the top gear and T2(t) acting on the rightmost disk. If you let • 9₁ denote the state variable for the spring 92 denote the state variable for the rightmost disk. u₁ denote T₁. • u₂ denote T₂. You should expect to get the following state space representation KR² [[讚]岛+[纛]問 TR and q= 3/2 0 Ti(t) 0₁ + 0 T₂(t) 82 03 140⁰ B Figure 3: System for problem 3 (a) Derive the state-space model (state equation and output equation) in vector form. (b) For the system parameters I = 8 kg m², k = 1 Nm,b=2 N s m/rad, R₁ = 1 m, and R₂ = 3 m: i. Use MATLAB to determine the transfer function matrix [G(s)]. ii. What is the characteristic equation AS of the system? iii. What are the values of the system poles? iv. What do the values of the system poles imply about the number and types of terms. (exponential, sinusoidal, constant, etc.) that should be expected in the system output? v. Use MATLAB to plot the system output for a unit step function input. vi. Use MATLAB to plot the system output for a unit impulse input. (c) For the system parameters I = 8 kg m², k = 1 Nm,b=2 N s m/rad, R₁ = 1 m, and R₂ = 2 m: i. Use MATLAB to determine the transfer function matrix [G(s)]. ii. What is the characteristic equation AS of the system? iii. What are the values of the system poles? iv. What do the values of the system poles imply about the number and types of terms (exponential, sinusoidal, constant, etc.) that should be expected in the system output? v. Use MATLAB to plot the system output for a unit step function input. vi. Use MATLAB to plot the system output for a unit impulse input.

3. Consider the system shown below. The outputs of the system are the angular displacement of the upper gear (positive about the x-axis) and the Contact force between the upper and lower gear. Assume that the initial conditions for all state variables are zero and that the gears are massless. There are two inputs Ti(t) acting on the top gear and T2(t) acting on the rightmost disk. If you let • 9₁ denote the state variable for the spring 92 denote the state variable for the rightmost disk. u₁ denote T₁. • u₂ denote T₂. You should expect to get the following state space representation KR² [[讚]岛+[纛]問 TR and q= 3/2 0 Ti(t) 0₁ + 0 T₂(t) 82 03 140⁰ B Figure 3: System for problem 3 (a) Derive the state-space model (state equation and output equation) in vector form. (b) For the system parameters I = 8 kg m², k = 1 Nm,b=2 N s m/rad, R₁ = 1 m, and R₂ = 3 m: i. Use MATLAB to determine the transfer function matrix [G(s)]. ii. What is the characteristic equation AS of the system? iii. What are the values of the system poles? iv. What do the values of the system poles imply about the number and types of terms. (exponential, sinusoidal, constant, etc.) that should be expected in the system output? v. Use MATLAB to plot the system output for a unit step function input. vi. Use MATLAB to plot the system output for a unit impulse input. (c) For the system parameters I = 8 kg m², k = 1 Nm,b=2 N s m/rad, R₁ = 1 m, and R₂ = 2 m: i. Use MATLAB to determine the transfer function matrix [G(s)]. ii. What is the characteristic equation AS of the system? iii. What are the values of the system poles? iv. What do the values of the system poles imply about the number and types of terms (exponential, sinusoidal, constant, etc.) that should be expected in the system output? v. Use MATLAB to plot the system output for a unit step function input. vi. Use MATLAB to plot the system output for a unit impulse input.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
See similar textbooks
icon
Related questions
Question
3. Consider the system shown below. The outputs of the system are the angular displacement of the upper gear (positive about the x-axis) and the Contact force between the upper and lower gear. Assume that the initial conditions for all state variables are zero and that the gears are massless. There are two inputs Ti(t) acting on the top gear and T₂(t) acting on the rightmost disk. If you let • 9₁ denote the state variable for the spring 92 denote the state variable for the rightmost disk. u₁ denote T₁. u₂ denote T₂. You should expect to get the following state space representation and 9= KR + 0₁ 0 LIR -1. 7/2 Ti(t) Jun 0:0⁰ 40² T₂(t) 03 Figure 3: System for problem 3 21 (a) Derive the state-space model (state equation and output equation) in vector form. (b) For the system parameters I = 8 kg m², k = 1 N m,b=2 N s m/rad, R₁ = 1 m, and R₂ = 3 m: i. Use MATLAB to determine the transfer function matrix [G(s)]. ii. What is the ristic equation AS the system? iii. What are the values of the system poles? iv. What do the values of the system poles imply about the number and types of terms (exponential, sinusoidal, constant, etc.) that should be expected in the system output? v. Use MATLAB to plot the system output for a unit step function input. vi. Use MATLAB to plot the system output for a unit impulse input. (c) For the system parameters I = 8 kg m², k = 1 N m,b=2 N s m/rad, R₁ = 1 m, and R₂ = 2 m: i. Use MATLAB to determine the transfer function matrix [G(s)]. ii. What is the characteristic equation AS of the system? iii. What are the values of the system poles? iv. What do the values of the system poles imply about the number and types of terms (exponential, sinusoidal, constant, etc.) that should be expected in the system output? v. Use MATLAB to plot the system output for a unit step function input. vi. Use MATLAB to plot the system output for a unit impulse input.
Transcribed Image Text:3. Consider the system shown below. The outputs of the system are the angular displacement of the upper gear (positive about the x-axis) and the Contact force between the upper and lower gear. Assume that the initial conditions for all state variables are zero and that the gears are massless. There are two inputs Ti(t) acting on the top gear and T₂(t) acting on the rightmost disk. If you let • 9₁ denote the state variable for the spring 92 denote the state variable for the rightmost disk. u₁ denote T₁. u₂ denote T₂. You should expect to get the following state space representation and 9= KR + 0₁ 0 LIR -1. 7/2 Ti(t) Jun 0:0⁰ 40² T₂(t) 03 Figure 3: System for problem 3 21 (a) Derive the state-space model (state equation and output equation) in vector form. (b) For the system parameters I = 8 kg m², k = 1 N m,b=2 N s m/rad, R₁ = 1 m, and R₂ = 3 m: i. Use MATLAB to determine the transfer function matrix [G(s)]. ii. What is the ristic equation AS the system? iii. What are the values of the system poles? iv. What do the values of the system poles imply about the number and types of terms (exponential, sinusoidal, constant, etc.) that should be expected in the system output? v. Use MATLAB to plot the system output for a unit step function input. vi. Use MATLAB to plot the system output for a unit impulse input. (c) For the system parameters I = 8 kg m², k = 1 N m,b=2 N s m/rad, R₁ = 1 m, and R₂ = 2 m: i. Use MATLAB to determine the transfer function matrix [G(s)]. ii. What is the characteristic equation AS of the system? iii. What are the values of the system poles? iv. What do the values of the system poles imply about the number and types of terms (exponential, sinusoidal, constant, etc.) that should be expected in the system output? v. Use MATLAB to plot the system output for a unit step function input. vi. Use MATLAB to plot the system output for a unit impulse input.
Expert Solution
steps

Step by step

Solved in 5 steps with 7 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Forced Undamped Vibrations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY
SEE MORE TEXTBOOKS