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‫Welcome back.

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‫So we have our simplified states based equations now and now what?

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‫Well, we could see if we can put them in this form.

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‫Now note that I am not claiming that this is an LTI system in which your mattresses are constant.

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‫I'm not even claiming that this is an LTV system, linear time, varying system in which you're A,

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‫B, C and D matrices depend directly on time.

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‫So A is A function of time, B as a function of time.

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‫C as a function of time, and D as a function of time.

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‫So that would be an LTV system.

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‫I am not claiming that these matrices can also have states in them that in turn depend on time like

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‫this.

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‫A is a function of phi that theta dot and beside that and then all those three variables, they are

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‫also as a function of time.

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‫The same thing with be.

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‫S..

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‫And in this case, the system would, of course, be non-linear, but still as a first step, we want

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‫to put it in this form if possible, and then we'll see how to proceed.

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‫And so let it be your exercise.

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‫Try putting your space equations.

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‫These ones here, the simplified ones, try putting them in this form.

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‫However, there is something extra.

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‫The NPC receives the reference values, PHI are, Theta are and PSI are.

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‫If you remember from the previous course, then in the NPC you had error variables.

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‫So your error or just you can abbreviated like E equals reference value minus system output.

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‫So in our case it would be like this you would have E Phi equals Phi R minus Phi then E Theta would

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‫be theta are minus theta.

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‫And then finally ipsi would be C R minus psi.

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‫That means that when you put your equations in this state's base format, then you also have to have

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‫an output vector.

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‫And this output vector needs to equal Phi Theta and PSI, which is a column vector, and the units of

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‫course, would be irradiance.

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‫So how would you put these equations in this form in such a way that your output vector ends up being

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‫Fifita Theta and Passi Radians tried out and I'll see you in the next video.