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[2] Consider an ni-th order system described by SystemI:x,(t)=Ax(t)+Bu(t)y(t)=Cx(t) and an n2-th order system described by SystemII:x(t=Ax(t)+Bu(t),y(t=Cx(t) Assume that System I and system II are both controllable and observable. a. State condition(s) so that the series combination of System I and II in Figl (a) is controllable and observable. The input and output of the combined system is u, and y,, respectively. b. State condition(s) so that the parallel combination of System I and II in Figl (b) is controllable and observable. The input and output of the combined system is u = u, = u, andy = yy + Y2 . Note:In both combinations, the order of the combined system ni and n2 

          [2] Consider an ni-th order system described by SystemI:x,(t)=Ax(t)+Bu(t)y(t)=Cx(t) and an n2-th order system described by SystemII:x(t=Ax(t)+Bu(t),y(t=Cx(t)
Assume that System I and system II are both controllable and observable.
a. State condition(s) so that the series combination of System I and II in Figl (a) is controllable and observable. The input and output of the combined system is u, and y,, respectively.
b. State condition(s) so that the parallel combination of System I and II in Figl (b) is controllable and observable. The input and output of the combined system is u = u, = u, andy = yy + Y2 .
Note:In both combinations, the order of the combined system ni and n2
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2 consider an ni th order system described by systemixtaxtbutytcxt and an n2 th order system described by systemiixtaxtbutytcxt assume that system i and system ii are both controllable and o 16684

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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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[2] Consider an ni-th order system described by SystemI:x,(t)=Ax(t)+Bu(t)y(t)=Cx(t) and an n2-th order system described by SystemII:x(t=Ax(t)+Bu(t),y(t=Cx(t) Assume that System I and system II are both controllable and observable. a. State condition(s) so that the series combination of System I and II in Figl (a) is controllable and observable. The input and output of the combined system is u, and y,, respectively. b. State condition(s) so that the parallel combination of System I and II in Figl (b) is controllable and observable. The input and output of the combined system is u = u, = u, andy = yy + Y2 . Note:In both combinations, the order of the combined system ni and n2
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Transcript

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00:01 In this question, we're going to be focusing on a reaction or a set of reactions where we've got a, forming b, and then we've got b forming c and b also forming d through parallel reactions.
00:15 So here we've got k1 and we've got k2 and k3 as the respective rate constants.
00:22 So what we can do here to simplify this here, looking at the differential equations that we've been given.
00:27 Here we've got a minus x.
00:30 Here we've got our variable as being y and here we've got our variable z and here we've got u so looking at this if we are looking at the reaction where we've got a forming b making reference to the previous question what we have here is d a minus x d t being equal to negative k1 a minus x so what we do here is to separate the variables where we've got 1, a minus x, d a minus x being equal to negative k1 d t.
01:10 So solving this, what we have is a minus x being equal to a the exponent of negative k1...
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