CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A second order system starts with an initial condition of [23] without any external input. The state transition matrix for the system is given by [e2t00et]. The state of the system at the end of 1 second is given by

A
[0.2711.100]
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
[0.1350.368]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
[0.2710.736]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
[0.1351.100]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A [0.2711.100]

State transition matrix,
ϕ(t)=[e2t00et]
Initial conditions,
x(0)=[23]
Zero input response is given by
x(t)=ϕ(t)x(0)
=[e2t00et][23]=[2e3t3e1]
State of the system at t=1s
x(t)|t=1[2e23e1]=[0.2711.100]

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
State Vector and Matrix
CONTROL SYSTEMS
Watch in App
Join BYJU'S Learning Program
CrossIcon