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Question

If the transfer function of a control system is given below:
Y(s)U(s)=1s3+4s2+5s+3

The matrix [A] and [B] in state variable representation of the system will be


A
[A]=010001453;[B]=111
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B
[A]=010001354;[B]=001
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C
[A]=0100018106;[B]=001
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D
[A]=01000161018;[B]=111
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Solution

The correct option is B [A]=010001354;[B]=001
For the given system we can write,
Y(s)[s3+4s2+5s+3]=U(s)[1] ....(i)

Let, x1=y
So, x2=˙x1=˙y ...(ii)
x3=˙x2=¨y ....(iii)

The equation (i) can be written as

˙x3+4x3+5x2+3x1=u

i.e. ˙x3=3x15x24x3+u ...(iv)

Using equation (ii), (iii) and (iv) we can write in state variable form as below,

˙x1˙x2˙x3=010001354x1x2x3+001u

So [A]=010001354

and [B]=001

Hence option (b) is correct.

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