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Get Full Access to Control Systems Engineering - 7 Edition - Chapter 8 - Problem 49
Get Full Access to Control Systems Engineering - 7 Edition - Chapter 8 - Problem 49

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# A technique to control the steering of a vehicle that

ISBN: 9781118170519 162

## Solution for problem 49 Chapter 8

Control Systems Engineering | 7th Edition

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Problem 49

A technique to control the steering of a vehicle that follows a line located in the middle of a lane is to define a look-ahead point and measure vehicle deviations with respect to the point. A linearized model for such a vehicle is V_ r_ _ Y_ g 2 6 6 6 6 6 4 3 7 7 7 7 7 5 a11 a12 b1K b1K d a21 a22 b2K b2K d 01 0 0 1 0 U 0 2 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 5 V r Yg 2 6 6 6 6 4 3 7 7 7 7 5 where V vehicles lateral velocity,r vehicles yaw velocity, vehicles yaw position, and Yg the y-axis coordinate of the vehicles center of gravity. K is a parameter to be varied depending upon trajectory changes. In a specific vehicle traveling at a speed of U 10 m/sec, the parameters are a11 11:6842; a12 6:7632; b1 61:5789; a21 3:5143; a22 24:0257, and b2 66:8571: d 5 m is the look-ahead distance (nyelioglu , 1997). Assuming the vehicle will be controlled in closed loop: a. Find the systems characteristic equation as a function of K. b. Find the systems root locus as K is varied. c. Using the root locus found in Part b, show that the system will be unstable for all values K

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Think Java How to Think Like a Computer Scientist Allen B. Downey 5.1.2 Copyright ' 2012 Allen Downey. Permission is granted to copy, distribute, transmit and adapt this work under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License: http://creativecommons.org/licenses/by-nc-sa/3.0/ If you are interested in distributing a commercial version of this work, please contact Allen B. Downey. The original form of this book is LT X source code. Compiling this LT X E E source has the e▯ect of generating a device-independent representation of the book, which can be converted to other formats and printed.

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##### ISBN: 9781118170519

This textbook survival guide was created for the textbook: Control Systems Engineering, edition: 7. Since the solution to 49 from 8 chapter was answered, more than 256 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 49 from chapter: 8 was answered by , our top Engineering and Tech solution expert on 11/23/17, 05:05AM. The answer to “A technique to control the steering of a vehicle that follows a line located in the middle of a lane is to define a look-ahead point and measure vehicle deviations with respect to the point. A linearized model for such a vehicle is V_ r_ _ Y_ g 2 6 6 6 6 6 4 3 7 7 7 7 7 5 a11 a12 b1K b1K d a21 a22 b2K b2K d 01 0 0 1 0 U 0 2 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 5 V r Yg 2 6 6 6 6 4 3 7 7 7 7 5 where V vehicles lateral velocity,r vehicles yaw velocity, vehicles yaw position, and Yg the y-axis coordinate of the vehicles center of gravity. K is a parameter to be varied depending upon trajectory changes. In a specific vehicle traveling at a speed of U 10 m/sec, the parameters are a11 11:6842; a12 6:7632; b1 61:5789; a21 3:5143; a22 24:0257, and b2 66:8571: d 5 m is the look-ahead distance (nyelioglu , 1997). Assuming the vehicle will be controlled in closed loop: a. Find the systems characteristic equation as a function of K. b. Find the systems root locus as K is varied. c. Using the root locus found in Part b, show that the system will be unstable for all values K” is broken down into a number of easy to follow steps, and 233 words. Control Systems Engineering was written by and is associated to the ISBN: 9781118170519. This full solution covers the following key subjects: vehicle, vehicles, Systems, velocity, varied. This expansive textbook survival guide covers 13 chapters, and 734 solutions.

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