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State Space Systems Overview

"the mars global surveyor"

"mars global surveyor"

The Mars Global Surveyor, built by Lockheed Martin and launched by NASA, orbits our nearest planetary neighbor on amission to map the surface of Mars and catalogue scientific data . The Surveyor spacecraft left Cape Canaveral, Floridaaboard a Delta-7925 rocket, and then spent 300 days traveling approximately 750 million kilometers to reach Mars inSeptember of 1997. After the Mars Global Surveyor reached Mars, it used its main rocket engine to lower itself into anelliptical orbit around the planet. The spacecraft then spent the next one and a half years reducing its orbit by using thefriction between itself and the atmosphere of Mars to slow down and thus lose 55,000 km of altitude. In March of 1999,the Surveyor spacecraft began its mapping of the Martian surface. The motion of this spacecraft is managed by apropulsion system that consists of a main engine and 8 "attitude-control" thrusters. How do these propulsion deviceswork together to safely control the movement of the Surveyor spacecraft? In the initial phases of this spacecraft'sdesign, engineers probably asked themselves the following questions to better understand this problem:

  • How do we guarantee that the satellite stays in its orbit and doesn't wonder off into space?
  • How do we characterize the relationship between the available thrust controls and the position of the spacecraft?
  • Can we use the knowledge of the satellite's thruster/position relationship to understand how to efficiently control its movement?
  • By observing the satellite's movement, can we better understand of how the dynamics (memory) of the system change with respect to the current and past thruster use?
  • Finally, after understanding the dynamics of the system, can we do something to modify them so that the response of the satellite has more desirable properties?

In this course, we will develop ways to answer these questions. In the beginning, we will take a look at lineardynamical systems and determine how to describe their dynamics with a concept known as state. In order to examine thesedynamics and see how they form relationships between the inputs and outputs of a system, differential equations andtheir frequency-domain counterparts will be studied. After setting this foundation, the course material will then focuson concepts found in linear algebra. As many systems have multiple inputs and outputs, it makes sense to use matricesand the tools of linear algebra to deal with the computations involved in describing them.

Once these tools are covered, we can use them along with our knowledge of dynamical systems to analyze the issues mentionedin the example above; specifically, we will examine system stability, controllability, observability, and feedback. Withstability, we can see whether the output of a system will remain bounded or whether it will "blow up". This isobviously very useful when thinking about the spacecraft above. As the name implies, controllability of a system tellsus whether or not we can control the output of the system without access to the dynamics of the system (i.e. when we canonly modify the inputs to the system). The third idea, observability, gives us a method of monitoring the output of asystem to determine its state. At the end of the course, we'll see how feedback can use this information about asystem's state to alter the system's dynamics in such a way as to improve its properties and response.

To learn more about the Mars Global Surveyor, visit (External Link) . The above image of the MGS was found at (External Link)

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, State space systems. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10143/1.3
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