Question

1. Create a State-Space Representation of following coupled second order differential equation? Define state vector as X =[x,x',a,a']^T. Control input as u= V. And output as y = [x,a]

-0.85306x ''+ 0.08391a ''- 21.149x '- 0.444a' = V

0.399483x'' – 0.10241a'' - 21.149x'' – 0.444a' + 3.91892a= V

Answer 1

The state vector is given as

So the first differential equation becomes

'

'

Similarly second differential equation becomes

So the state equations are

Writing in state space form

Output Equation

OR