Spacecraft Attitude Determination & Control covers the entire range of techniques for determining the orientation of a spacecraft and then controlling it so that the spacecraft points in some desired direction. The majority of today's spacecraft have pointing requirements or pointing modes, which are necessitated by the mission for which they are deployed. Some examples include earth pointing spacecraft such as communications, broadcast and weather satellites. There are inertial pointing craft like the Hubble Space Telescope, and then we have sun pointing satellites such as the solar and heliospheric observatory. As we look at images of these satellites, the simplicity of their outer structure often belies the complexity of the systems beneath. And well-researched control systems must be seamlessly integrated into the rest of the spacecraft. There are actually many types of spacecraft, each with their own goals and priorities for system operation. So how do control system designers employ strategies for tackling these priorities? Well, let's start by taking a look at some of the challenges involved. One major obstacle to developing effective controllers is the non-linear and time-vary nature of the dynamics which these systems are designed to address. For example, for spacecraft in low-earth orbit, the magnetic field strength will vary along the satellite's path. This would, by definition, make the problem time varying. In this instance, designers may elect to use a static gain controller which can exploit the onboard measurements of the magnetic field vector. However, in order to linearize the system, they must develop a reliable linear, time-invariant, or LTI, mathematical model from the real-world non-linear time periodic behavior of the system. To this end, some designers may employ an acceptable but less accurate, average, geomagnetic field model to avoid time-varying input. Another way to address non-linear time-varying behavior is to utilize the gain scheduling approach for controlling a system with changing dynamics and operating conditions. If we examine a non-linear dynamics function represented here by the green line, we can imagine it would be highly difficult to design a controller which could handle all the varying inputs and demands. But what if we decompose the non-linear problem into much simpler linear sub-problems? Then we could design a family of linear controllers, each of which provides control which remains highly effective near its own operating point in the system. Thus, as the satellite progresses in its mission, gain scheduling allows the controller to rewrite the control law to suit a specific part of the space mission. Here, you can see circles at the operating points where the dynamics have been linearized. Each controller gain at x1, x2, x3, and so on will activate for its specific role in the control problem. Observable variables or scheduling variables are used to determine what operating region the system is currently in and enable the appropriate linear controller to operate for the portion of the problem for which it was designed. Linearization imposes limits. In this illustration of spacecraft rendezvous, the control system only works when the distance from the target craft to the center of the earth, which is its inertial frame, is much greater than the distance between the two spacecraft. Another challenge is designing a controller to handle uncertainties in the system including thrust misalignment, disturbance inputs, parametric uncertainties, and unknown inertial and motion information. Greater ability to handle uncertainty means a controller is more robust. Robust methods generally assume uncertainties are unknown, but bounded. H infinity control can be a good choice to handle uncertainty since it is applicable to multivariate systems with cross coupling between channels as the problem of low-earth orbit attitude control presents. In magnetic control of the coupled roll-yaw attitude dynamics, it is based on a single magnetic torque or aligned with the pitch axis. Also, the H infinity approach minimizes the sensitivity of the system over its frequency spectrum, so disturbances and their associated uncertainty have minimal effect. Further, we have the International Geomegnetic Reference Field Model, which is sufficiently accurate as H infinity shaping requires. This animation shows a satellite responding to a notation dampened control algorithm, simultaneous with stabilization about its control axis along the most efficient path, and therefore with a minimum of energy expended. Control designers must identify their objectives, be it to work with an actuator or sensor saturation constraints, minimize the cost function, or decrease settling time. Those objectives help set the design strategy that we ultimately pursue.