Elec 302: state space systems overview

"the 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)