The control input is thruster acceleration, u Next, let us consider an orbit transfer problem with Keplerian orbital elements. Define x = [glow M]", where M is the mean anomaly of the orbit and low = [a, e, i, 2, w], representing the slow variables. R³, whose components are aligned with the radial, transverse, and orbit angular momentum. Denote the relative state between the current and target orbits by slow =Talow-target. Table 3 lists slow at t = 0 and target- Table 3: Keplerian orbital elements of the spacecraft at epoch (t = 0) and the target (ECI frame) Orbital element semi-major axis Spacecraft a=10,000 Target Unit eccentricity inclination e = 0.3 i = 10 target = 60,000 etarget = 0.7 km itarget = 130 degree right ascension of ascending node =0 argument of periapsis Starget = 180 degree w=0 Wtarget = 270 degree slow Consider a candidate Lyapunov function V = xow Kбlow, where K >0. Discuss the positive definiteness of V, and derive the Lyapunov rate of this system. Derive a stabilizing controller for the system, and discuss the stability property of the controlled system (Lyapunov/asymptotic? local/global?), where assume that Balow, i.e., a matrix form of Gauss planetary equations for the slow variables, is full rank. Under no control magnitude constraint, perform the numerical integrations of the controlled system with K = 15, and discuss the results with relevant plots. Be sure to scale the length and time units appropriately and propagate the dynamics for at least 10 days.
The control input is thruster acceleration, u Next, let us consider an orbit transfer problem with Keplerian orbital elements. Define x = [glow M]", where M is the mean anomaly of the orbit and low = [a, e, i, 2, w], representing the slow variables. R³, whose components are aligned with the radial, transverse, and orbit angular momentum. Denote the relative state between the current and target orbits by slow =Talow-target. Table 3 lists slow at t = 0 and target- Table 3: Keplerian orbital elements of the spacecraft at epoch (t = 0) and the target (ECI frame) Orbital element semi-major axis Spacecraft a=10,000 Target Unit eccentricity inclination e = 0.3 i = 10 target = 60,000 etarget = 0.7 km itarget = 130 degree right ascension of ascending node =0 argument of periapsis Starget = 180 degree w=0 Wtarget = 270 degree slow Consider a candidate Lyapunov function V = xow Kбlow, where K >0. Discuss the positive definiteness of V, and derive the Lyapunov rate of this system. Derive a stabilizing controller for the system, and discuss the stability property of the controlled system (Lyapunov/asymptotic? local/global?), where assume that Balow, i.e., a matrix form of Gauss planetary equations for the slow variables, is full rank. Under no control magnitude constraint, perform the numerical integrations of the controlled system with K = 15, and discuss the results with relevant plots. Be sure to scale the length and time units appropriately and propagate the dynamics for at least 10 days.
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
Related questions
Question
Can you help with a code in MATLAB?
![The control input is thruster acceleration, u
Next, let us consider an orbit transfer problem with Keplerian orbital elements. Define x = [glow M]",
where M is the mean anomaly of the orbit and low = [a, e, i, 2, w], representing the slow variables.
R³, whose components are aligned with the radial,
transverse, and orbit angular momentum. Denote the relative state between the current and target
orbits by slow =Talow-target. Table 3 lists slow at t = 0 and target-
Table 3: Keplerian orbital elements of the spacecraft at epoch (t = 0) and the target (ECI frame)
Orbital element
semi-major axis
Spacecraft
a=10,000
Target
Unit
eccentricity
inclination
e = 0.3
i = 10
target = 60,000
etarget = 0.7
km
itarget = 130
degree
right ascension of ascending node =0
argument of periapsis
Starget
= 180
degree
w=0
Wtarget = 270
degree
slow
Consider a candidate Lyapunov function V = xow Kбlow, where K >0. Discuss the
positive definiteness of V, and derive the Lyapunov rate of this system.
Derive a stabilizing controller for the system, and discuss the stability property of the controlled
system (Lyapunov/asymptotic? local/global?), where assume that Balow, i.e., a matrix form of
Gauss planetary equations for the slow variables, is full rank.
Under no control magnitude constraint, perform the numerical integrations of the controlled
system with K = 15, and discuss the results with relevant plots. Be sure to scale the length and
time units appropriately
and propagate the dynamics for at least 10 days.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad0d55fe-d83b-4711-86a1-cee8ecea510f%2F39e3d8f6-d8ae-4f39-87f5-b5e87a1d6c41%2Fh5s8oj7_processed.png&w=3840&q=75)
Transcribed Image Text:The control input is thruster acceleration, u
Next, let us consider an orbit transfer problem with Keplerian orbital elements. Define x = [glow M]",
where M is the mean anomaly of the orbit and low = [a, e, i, 2, w], representing the slow variables.
R³, whose components are aligned with the radial,
transverse, and orbit angular momentum. Denote the relative state between the current and target
orbits by slow =Talow-target. Table 3 lists slow at t = 0 and target-
Table 3: Keplerian orbital elements of the spacecraft at epoch (t = 0) and the target (ECI frame)
Orbital element
semi-major axis
Spacecraft
a=10,000
Target
Unit
eccentricity
inclination
e = 0.3
i = 10
target = 60,000
etarget = 0.7
km
itarget = 130
degree
right ascension of ascending node =0
argument of periapsis
Starget
= 180
degree
w=0
Wtarget = 270
degree
slow
Consider a candidate Lyapunov function V = xow Kбlow, where K >0. Discuss the
positive definiteness of V, and derive the Lyapunov rate of this system.
Derive a stabilizing controller for the system, and discuss the stability property of the controlled
system (Lyapunov/asymptotic? local/global?), where assume that Balow, i.e., a matrix form of
Gauss planetary equations for the slow variables, is full rank.
Under no control magnitude constraint, perform the numerical integrations of the controlled
system with K = 15, and discuss the results with relevant plots. Be sure to scale the length and
time units appropriately
and propagate the dynamics for at least 10 days.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY