‫Welcome back.
‫So let's just recap what we have done here in the case of an autonomous vehicle, you first had your
‫equations of motion in the lateral direction, then you reformulated it to get your non-linear state
‫space equations.
‫Then, thanks to the small BPCI angle approximation in the autonomous vehicle, you got your system
‫in the LTI form, you had your constant A, B, C and D matrices, then you decided to do it and you
‫got your discrete A, B, C and D matrices.
‫And then you applied the NPC strategy to your descriptivist LTI system where you worked with your discrete
‫A, B, C and D matrices, and then you sent your control inputs into your plant and then the plant
‫would produce new states and then those new states would go back into the controller to compute the
‫new control inputs.
‫And so it would go in a loop.
‫However, your discrete A, B, C and D matrices, they would be constant throughout the entire maneuver.
‫And you have a similar case with your UA V at the beginning, you had your equations of motion, your
‫degree of freedom.
‫Newton oilor equations.
‫Then you transform them in the non-linear states space equations, then you make a small phi and theta
‫angle approximation, you would assume that they would equal to zero radians.
‫That made your transfer matrix equal to an identity matrix.
‫Then from your nonlinear state based equations, you took only those equations that were relevant to
‫your additive control, and then you got your nonlinear state based equations.
‫But with these variables, phi that theta that inside that, then you reformulated them and you put
‫them in the HPV form, then you democratised your Lopevi form.
‫You apply your discreetness form to your NPC controller.
‫Now, in the case of an autonomous vehicle, your MPAC controller gave you a steering wheel angled Deltans,
‫your control input.
‫But now you send you to U3 and EUFOR into your plans and then your plant will give you new states,
‫so out of those new states, you take your P, Q and R variables and you put them through a transfer
‫matrix and then you get your file that, that and BPCI that and then find out and setar that will go
‫back into your continuous LP form.
‫And this HPV update happens every inner circle, every zero point one second, and so note that we assumed
‫that our transfer matrix equals the identity matrix here, not here, but here.
‫We do this assumption one time and then we get a simplified, non-linear state based equation form with
‫final thought that implied that as its variables and in order to be complete.
‫I should also say that one of the variables in this nonlinear equation is Omega.
‫But Omega is not a state in our situation.
‫So this small angle approximation happened here.
‫However, when you now actually use this LP form, then here you do not have the small ÀNGEL approximation.
‫All right.
‫Here you still take your pick your states and then you use the real transfer matrix with all its angles
‫in order to get your updated find that theta that and decide that in order to get more correct values.
‫And then these values, specifically Phi Dot and Theta, that will enter the LP system along with your
‫omega variable, which is not a state, but still it gets updated every zero point one second.