In our previous post we discussed the need of the Attitude Determination and Control System (ADCS), shed some light on the different co-ordinate frames and skimmed through their applications. With this we can dive further down into our study and understand ADCS in a better way.
As discussed earlier, ADCS is responsible for pointing the satellite in the desired direction in the space at any given time. However, it might not be possible for the satellite to attain hundred percent pointing accuracy, and it may happen that the satellite shakes a bit while trying to point towards a particular direction. This shaky nature of the satellite can be quantified in terms of angular velocity, also known as the “body rates”. With this, the whole objective of ADCS boils down to pointing the satellite in a given direction with least possible body rates. Different satellites, depending on their payload requirements are tolerant to different body rates, and this tolerance determines the complexity of the ADCS on a satellite.
After reading all these, you must be wondering, how do we determine where the satellite has to point at any given time in space? How to calculate the pointing accuracy and how to measure the body rates of the satellite? The parameters, pointing accuracy and body rates can be measured with respect to some ideal values, so the next question which pops up is, how do we obtain those ideal values?
These why’s, what‘s and how’s will be answered in this and the upcoming posts.
So, let’s start with our first question, how do we determine where the satellite has to point at any given time in space? Different satellites need to point at different things while they are orbiting the earth. Some need to point at the earth all the time, while a few need to look at different heavenly bodies at different times, and a few of the satellites have to orient themselves along other satellites in space. The different axes of the Satellite Body Frame has to keep rotating in such a way that the satellite is able to point where it has to point. Hence, if we consider a hypothetical satellite whose body axis or the Satellite Body Frame keep on rotating with time in such a way, that the satellite is able to attain its desired orientation at any given time with hundered percent accuracy, then we will get something which we can call as the “reference satellite”. The Satellite Body Frame of this reference satellite is called the reference frame.
The reference frames for different satellites are different. In a few cases where the satellite’s Z axis has to point continuously towards the earth (imagine a satellite which has to perform terrestrial imaging and has its camera coinciding with the Z axis) in such a way that the Y axis points towards the orbital angular momentum (Cross product of position vector and velocity vector of the satellite in ECI frame), then the reference frame of this satellite will be called the Orbit reference frame.
At any given time, the Satellite Reference Frame and Satellite Body Frame will be at the same location, i.e., the origin of the Satellite Body Frame will always coincide with that of the Satellite Reference Frame, however, the Satellite Reference Frame may not be aligned with Satellite Body Frame. The ADCS of a satellite works to align the Satellite Body Frame with the Satellite Reference Frame. To simplify our test cases and to understand ADCS in an easy way, we will be considering a satellite whose reference frame is the Orbit Reference Frame
With this, our first step in providing stability to a satellite is to trace the orientation and position of the reference satellite at any point in space. Initially the position and velocity of the satellite can be acquired using an on-board GPS receiver or telemetry data containing the TLEs (Something we will be discussing later on, for now you can read about this at https://en.wikipedia.org/wiki/Two-line_element_set), which can be sent to the satellite from the ground. Because of the power constraints on a satellite, it is not feasible to acquire position and velocity 24X7 using a GPS receiver or though telemetry data. This calls for the need of an on-board orbit propagator, which can predict the position and velocity of the satellite at any time instant, based on the initial data provided by the on-board GPS receiver or through the TLE containing telemetry data. Next, we find out the orientation of the reference frame at the satellite’s position. Considering a satellite whose Satellite Reference Frame is the Orbit Reference Frame, we have a rotation matrix which gives us the orientation of the Orbit Reference Frame with respect to the ECI frame, something which we will be discussing in our next post.