Consider the following system of equations of a single link robotic manipulator with a flexible joint I6, (t) + mgl sin O1 (t) + k(01 (t) – 02 (t)) = 0 JÖ, (t) – k(0, (t) – 02 (t)) = u(t) where 01 (t), 02 (t) are the angular positions, I, J are moments of inertia, m, l, k are link mass, length and spring constant respectively. Introduce the change of variables as r1(t) = 01 (t), x2(t) = 01(t), x3(t) = 02 (t), x4(t) = 02(t) Find the linearised state space model of the system with equilibrium conditions [x; a; x;; x;]". Take the values of k = 0.5 N/m; g = 9.8m/s²; m = 0.5 kg; l = 0.5 m; I = 1 kg. m²; J = 0.5 kg. m² . 12) Assume that the system output is equal to the link's angular position (y(t) = x1(t)), then output matrix C is given by C = [1 0 0 0] = [0 1 0 0] = [0 0 1 0] ' = [0 0 0 1]
Consider the following system of equations of a single link robotic manipulator with a flexible joint I6, (t) + mgl sin O1 (t) + k(01 (t) – 02 (t)) = 0 JÖ, (t) – k(0, (t) – 02 (t)) = u(t) where 01 (t), 02 (t) are the angular positions, I, J are moments of inertia, m, l, k are link mass, length and spring constant respectively. Introduce the change of variables as r1(t) = 01 (t), x2(t) = 01(t), x3(t) = 02 (t), x4(t) = 02(t) Find the linearised state space model of the system with equilibrium conditions [x; a; x;; x;]". Take the values of k = 0.5 N/m; g = 9.8m/s²; m = 0.5 kg; l = 0.5 m; I = 1 kg. m²; J = 0.5 kg. m² . 12) Assume that the system output is equal to the link's angular position (y(t) = x1(t)), then output matrix C is given by C = [1 0 0 0] = [0 1 0 0] = [0 0 1 0] ' = [0 0 0 1]
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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![Consider the following system of equations of a single link robotic manipulator with a flexible joint
I6, (t) + mgl sin O1 (t) + k(01 (t) – 02 (t)) = 0
JÖ, (t) – k(0, (t) – 02 (t)) = u(t)
where 01 (t), 02 (t) are the angular positions, I, J are moments of inertia, m, l, k are link mass, length and spring constant respectively. Introduce the change
of variables as r1(t) = 01 (t), x2(t) = 01(t), x3(t) = 02 (t), x4(t) = 02(t) Find the linearised state space model of the system with equilibrium conditions
[x; a; x;; x;]". Take the values of k = 0.5 N/m; g = 9.8m/s²; m = 0.5 kg; l = 0.5 m; I = 1 kg. m²; J = 0.5 kg. m² .
12) Assume that the system output is equal to the link's angular position (y(t) = x1(t)), then output matrix C is given by
C = [1
0 0 0]
= [0 1 0 0]
= [0 0 1 0]
' = [0 0 0 1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf754e95-f233-48b0-b3f3-cfafbec7e21f%2Ff4ff7032-03ae-4d6b-a1fd-11e20aa16142%2F91yqhyb_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following system of equations of a single link robotic manipulator with a flexible joint
I6, (t) + mgl sin O1 (t) + k(01 (t) – 02 (t)) = 0
JÖ, (t) – k(0, (t) – 02 (t)) = u(t)
where 01 (t), 02 (t) are the angular positions, I, J are moments of inertia, m, l, k are link mass, length and spring constant respectively. Introduce the change
of variables as r1(t) = 01 (t), x2(t) = 01(t), x3(t) = 02 (t), x4(t) = 02(t) Find the linearised state space model of the system with equilibrium conditions
[x; a; x;; x;]". Take the values of k = 0.5 N/m; g = 9.8m/s²; m = 0.5 kg; l = 0.5 m; I = 1 kg. m²; J = 0.5 kg. m² .
12) Assume that the system output is equal to the link's angular position (y(t) = x1(t)), then output matrix C is given by
C = [1
0 0 0]
= [0 1 0 0]
= [0 0 1 0]
' = [0 0 0 1]
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