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
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
[A]=010001354;[B]=001
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
[A]=0100018106;[B]=001
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
[A]=01000161018;[B]=111
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B [A]=⎡⎢⎣010001−3−5−4⎤⎥⎦;[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=−3x1−5x2−4x3+u ...(iv) Using equation (ii), (iii) and (iv) we can write in state variable form as below, ⎡⎢⎣˙x1˙x2˙x3⎤⎥⎦=⎡⎢⎣010001−3−5−4⎤⎥⎦⎡⎢⎣x1x2x3⎤⎥⎦+⎡⎢⎣001⎤⎥⎦u So [A]=⎡⎢⎣010001−3−5−4⎤⎥⎦ and [B]=⎡⎢⎣001⎤⎥⎦ Hence option (b) is correct.

Suggest Corrections
0
Related Videos
Solution of States-2
CONTROL SYSTEMS
Watch in App
Explore more