‫OK, so that was for the vehicle.
‫How about the wave?
‫Remember that the reason why we wanted the LTI system was because we wanted to use the easiest NPC version
‫that was developed to handle linear time invariant systems.
‫They are easier to deal with than.
‫It is with robust and non-linear NPC control strategies, and so the question is, can we use this NPC
‫technique that we used in the previous course?
‫Can we use it for the UAE as well?
‫Well, you might think that we can if we can put the UVs states based equations in the LTI form and
‫so can we.
‫Let's see, these are the US states based equations in the body frame.
‫This is a screenshot from the previous section, seen this course.
‫Remember that the NPC only takes care of the Oves attitude, not its position, and therefore we only
‫need these three equations from here.
‫P dot equals something, Cuidad equals something, and ah, that equals something.
‫But of course, we also have to be able to move between the inertial frame and the body frame.
‫And for that we use the transfer matrix.
‫And that's how the transfer matrix looked like.
‫This transfer matrix was unique for our convention, which was our step Z, Y, X, that we first rotate
‫about the moving frame Z axis, then we rotate about the moving frame Y axis and then about the moving
‫frame x axis.
‫And that's why you have Z, Y, X.
‫And they are lower case letters because they indicate the body frame axes, not the initial frame axes.