‫Welcome back.
‫So we have our simplified states based equations now and now what?
‫Well, we could see if we can put them in this form.
‫Now note that I am not claiming that this is an LTI system in which your mattresses are constant.
‫I'm not even claiming that this is an LTV system, linear time, varying system in which you're A,
‫B, C and D matrices depend directly on time.
‫So A is A function of time, B as a function of time.
‫C as a function of time, and D as a function of time.
‫So that would be an LTV system.
‫I am not claiming that these matrices can also have states in them that in turn depend on time like
‫this.
‫A is a function of phi that theta dot and beside that and then all those three variables, they are
‫also as a function of time.
‫The same thing with be.
‫S..
‫And in this case, the system would, of course, be non-linear, but still as a first step, we want
‫to put it in this form if possible, and then we'll see how to proceed.
‫And so let it be your exercise.
‫Try putting your space equations.
‫These ones here, the simplified ones, try putting them in this form.
‫However, there is something extra.
‫The NPC receives the reference values, PHI are, Theta are and PSI are.
‫If you remember from the previous course, then in the NPC you had error variables.
‫So your error or just you can abbreviated like E equals reference value minus system output.
‫So in our case it would be like this you would have E Phi equals Phi R minus Phi then E Theta would
‫be theta are minus theta.
‫And then finally ipsi would be C R minus psi.
‫That means that when you put your equations in this state's base format, then you also have to have
‫an output vector.
‫And this output vector needs to equal Phi Theta and PSI, which is a column vector, and the units of
‫course, would be irradiance.
‫So how would you put these equations in this form in such a way that your output vector ends up being
‫Fifita Theta and Passi Radians tried out and I'll see you in the next video.