"The Mars Global Surveyor"

Figure 1

"Mars Global Surveyor"

The Mars Global Surveyor, built by Lockheed Martin and launched by NASA, orbits our nearest planetary neighbor on a mission to map the surface of Mars and catalogue scientific data . The Surveyor spacecraft left Cape Canaveral, Florida aboard a Delta-7925 rocket, and then spent 300 days traveling approximately 750 million kilometers to reach Mars in September of 1997. After the Mars Global Surveyor reached Mars, it used its main rocket engine to lower itself into an elliptical orbit around the planet. The spacecraft then spent the next one and a half years reducing its orbit by using the friction 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 a propulsion system that consists of a main engine and 8 "attitude-control" thrusters. How do these propulsion devices work together to safely control the movement of the Surveyor spacecraft? In the initial phases of this spacecraft's design, engineers probably asked themselves the following questions to better understand this problem:

In this course, we will develop ways to answer these questions. In the beginning, we will take a look at linear dynamical systems and determine how to describe their dynamics with a concept known as state. In order to examine these dynamics and see how they form relationships between the inputs and outputs of a system, differential equations and their frequency-domain counterparts will be studied. After setting this foundation, the course material will then focus on concepts found in linear algebra. As many systems have multiple inputs and outputs, it makes sense to use matrices and 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 mentioned in the example above; specifically, we will examine system stability, controllability, observability, and feedback. With stability, we can see whether the output of a system will remain bounded or whether it will "blow up". This is obviously very useful when thinking about the spacecraft above. As the name implies, controllability of a system tells us whether or not we can control the output of the system without access to the dynamics of the system (i.e. when we can only modify the inputs to the system). The third idea, observability, gives us a method of monitoring the output of a system to determine its state. At the end of the course, we'll see how feedback can use this information about a system'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 http://mars.jpl.nasa.gov/mgs/overvu/slides/00.html. The above image of the MGS was found at http://mars.jpl.nasa.gov/mgs/images/highres.html