CONTROL SYSTEMS ENGINEERING
7th Edition
ISBN: 9781119185666
Author: NISE
Publisher: WILEY
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Chapter 1, Problem 12RQ
Describe a typical control system analy sis task.
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Problem 2 (40 Points)
A particle of mass m is embedded at a distance a from the center of a massless circular disk of
radius r. The disk rolls without slipping down a plane inclined at an angle a with the horizontal.
A horizontal force of Ễ = −Fxî + Fyĵ resists motion of the disk down the plane by pushing on
the disk at the axle that runs through the center of the disk.
a) Find the kinetic energy T. (10 points)
b) Find the potential energy V. (10 points)
c) Write a position vector to the axle at the center of the wheel in terms of x and y. (10
points)
d) Using virtual work, find the applied force Q₁ that would go in Lagrange's Equations. DO
NOT WRITE OUT OR SOLVE LAGRANGES'S EQUATIONS. (10 points)
x
r
m
e
10
g
F
α
HINTS
1) Consider using the STATIONARY red xy frame a reference frame from which to draw
vectors
2) The red xy system DOES NOT move. It is stationary.
3) Consider that the disk rolls a distance of re down the ramp
Draw a counter balance circuit of a vertical cylinder.
using counter balance valve and external load.
please sketch a stress-strain diagram for a typical structural steel in tension and display all of the important features.
Chapter 1 Solutions
CONTROL SYSTEMS ENGINEERING
Ch. 1 - Prob. 1RQCh. 1 - Prob. 2RQCh. 1 - Prob. 3RQCh. 1 - Prob. 4RQCh. 1 - State one condition under which the error signal...Ch. 1 - Prob. 6RQCh. 1 - Name two advantages of having a computer in the...Ch. 1 - Name the three major design criteria for control...Ch. 1 - Prob. 9RQCh. 1 - Physically, what happens to a system that is...
Ch. 1 - Instability is attributable to what pan of the...Ch. 1 - Describe a typical control system analy sis task.Ch. 1 - Describe a typical control system design task.Ch. 1 - Prob. 14RQCh. 1 - Name three approaches to the mathematical modeling...Ch. 1 - Briefly describe each of your answers to Question...Ch. 1 - Prob. 1PCh. 1 - Prob. 2PCh. 1 - An aircraft's attitude varies in roll, pitch, and...Ch. 1 - We can build a control system that will...Ch. 1 - Prob. 5PCh. 1 - During a medical operation an anesthesiologist...Ch. 1 - Prob. 7PCh. 1 - Prob. 8PCh. 1 - The human eye has a biological control system that...Ch. 1 - A Segway ®5 Personal Transporter (PT) (Figure Pl...Ch. 1 - In humans, hormone levels, alertness, and core...Ch. 1 - Tactile feedback is an important component in the...Ch. 1 - Prob. 13PCh. 1 - Moored floating platforms are subject to external...Ch. 1 - In the Case Study of Section 1.4. an antenna...Ch. 1 - Figure Pl.5 shows the topology of a photo-voltaic...Ch. 1 - Prob. 17PCh. 1 - Prob. 18PCh. 1 - Prob. 19PCh. 1 - Prob. 20PCh. 1 - Prob. 21PCh. 1 - Contol of HIV/AIDS. As of 2012. the number of...Ch. 1 - Prob. 23PCh. 1 - Parabolic trough collector. A set of parabolic...
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- Problem 1 (30 Points) Consider the following 2 scenarios. In scenario 1, a mass m slides on a cylindrical surface of radius R. In scenario 2, a mass m hangs at the end of a thin massless rod of length R. In both scenarios, there is no friction either on the surface (scenario 1), or at the pivot point of the pendulum (scenario 2). Also in both scenarios, there is one generalized coordinate, . R Scenario 1 R m R g Scenario 2 m HINT: In both scenarios, it is much easier to choose your datum for potential energy as the center of the bowl (scenario 1), or the pivot point of the pendulum (scenario 2). Part I a) Determine the Lagrangian for each system. DO NOT FIND THE EQUATIONS OF MOTION (5 points) b) What can you say about the systems based on the Lagrangian? (2 points) c) Solve for the equations of motion for both systems. (8 points) Part II Now, for scenario 1, introduce an additional coordinate and treat it as a nonholonomic system to determine the normal force acting on the mass. a)…arrow_forwardConsider 0.65 kg of N2 at 300 K, 1 bar contained in a rigid tank connected by a valve to another rigid tank holding 0.3 kg of CO2 at 300 K, 1 bar. The valve is opened and gases are allowed to mix, achieving an equilibrium state at 290 K. Determine: (a) the volume of each tank, in m³. (b) the final pressure, in bar. (c) the magnitude of the heat transfer to or from the gases during the process, in kJ. (d) the entropy change of each gas and of the overall system, in kJ/K.arrow_forward(Read Image) (Answer: ω = 1.10 rad/sec CW)arrow_forward
- What is the configuration of the control loop if steam must be shut down in case of a problem? (I found this question on the internet and was wondering what the answer is) A.Valve is fail open, PIC is direct-acting, TIC is reverse acting, and controller algorithm is feed-forwarding.B. Valve is fail open, PIC is reverse-acting, TIC is direct acting, and controller algorithm is cascade.C. Valve is fail closed, PIC is direct-acting, TIC is reverse acting, and controller algorithm is feed-forward.D. Valve is fail closed, PIC is reverse-acting, TIC is reverse acting, and controller algorithm is cascade.arrow_forwardWhat is the procedure to replace the input bellows?(I found this question on the internet and was wondering what the correct answer is out of interest) Remove tubing, old bellows and flapper assembly, install new bellows, connect tubing, install flapper assembly, then calibrate the positioner.Remove tubing, old bellows and cam, install new bellows, connect tubing, install cam, then calibrate the positioner.C. Remove tubing and old bellows, align the quadrant beam, install new bellows and connect tubing, then calibrate the positioner.D. Remove tubing and old bellows, install new bellows and connect tubing, align the quadrant beam, then calibrate the positioner.arrow_forwardGiven the following information: (I found this question on the internet and was wondering what the correct answer is) Firing rate demand = 20% Fuel air ratio = 2:1 Fuel flow = 20% Minimum air flow setting = 5% What is the set point for the air flow controller? 5%B. 10%C. 25%D. 40%arrow_forward
- . Where is a dew point analyzer installed to measure instrument air?(I found this question on the internet and am wondering what the correct answer is) A. AB. BC. CD. Darrow_forwardThe piston at the bottom of the stroke is 0% open. Which adjustment will change the zero setting to 5% open? ( I found this sample question on the internet and was wondering what the correct answer is out of interest) A.Slide component 2 towards the pivotB. Slide component 2 away from the pivot.C. Increase spring tension using adjustment 1.D. Decrease spring tension using adjustment 1.arrow_forward(read image) (Answer: vA = 4.57 ft/sec)arrow_forward
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