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Consider the double integrator system given by p(t) = u(t), p(0) = 0, p(0) = 0, where p(t) R denotes the position (in meters), and u(t) = R is the force input (in Newtons). Here, the system needs to visit p(10) = 15, p(20) = 5, p(30) = 25, p(40) = 15, p(50) = 5, and p(60) = 10. Note that the system has to stop in each location with zero velocity and zero acceleration. 2 (a) Generate the path c(t) using constrained function construction method. (b) Pick an appropriate inner loop control algorithm and theoretically design it to achieve the control objective. (c) Simulate the closed-loop system and present: A plot of p(t) versus time illustrating the system's position tra- jectory (include the generated path c(t) to the same plot using a dotted line). A plot of u(t) versus time showing the applied control input. Comment on your numerical results.

Consider the double integrator system given by p(t) = u(t), p(0) = 0, p(0) = 0, where p(t) R denotes the position (in meters), and u(t) = R is the force input (in Newtons). Here, the system needs to visit p(10) = 15, p(20) = 5, p(30) = 25, p(40) = 15, p(50) = 5, and p(60) = 10. Note that the system has to stop in each location with zero velocity and zero acceleration. 2 (a) Generate the path c(t) using constrained function construction method. (b) Pick an appropriate inner loop control algorithm and theoretically design it to achieve the control objective. (c) Simulate the closed-loop system and present: A plot of p(t) versus time illustrating the system's position tra- jectory (include the generated path c(t) to the same plot using a dotted line). A plot of u(t) versus time showing the applied control input. Comment on your numerical results.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Consider the double integrator system given by p(t) = u(t), p(0) = 0, p(0) = 0, where p(t) R denotes the position (in meters), and u(t) = R is the force input (in Newtons). Here, the system needs to visit p(10) = 15, p(20) = 5, p(30) = 25, p(40) = 15, p(50) = 5, and p(60) = 10. Note that the system has to stop in each location with zero velocity and zero acceleration. 2 (a) Generate the path c(t) using constrained function construction method. (b) Pick an appropriate inner loop control algorithm and theoretically design it to achieve the control objective. (c) Simulate the closed-loop system and present: A plot of p(t) versus time illustrating the system's position tra- jectory (include the generated path c(t) to the same plot using a dotted line). A plot of u(t) versus time showing the applied control input. Comment on your numerical results.
Transcribed Image Text:Consider the double integrator system given by p(t) = u(t), p(0) = 0, p(0) = 0, where p(t) R denotes the position (in meters), and u(t) = R is the force input (in Newtons). Here, the system needs to visit p(10) = 15, p(20) = 5, p(30) = 25, p(40) = 15, p(50) = 5, and p(60) = 10. Note that the system has to stop in each location with zero velocity and zero acceleration. 2 (a) Generate the path c(t) using constrained function construction method. (b) Pick an appropriate inner loop control algorithm and theoretically design it to achieve the control objective. (c) Simulate the closed-loop system and present: A plot of p(t) versus time illustrating the system's position tra- jectory (include the generated path c(t) to the same plot using a dotted line). A plot of u(t) versus time showing the applied control input. Comment on your numerical results.
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