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Converting a nonlinear eqn of motion to a state-space model

  • #1
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Homework Statement


upload_2019-2-7_0-3-21.png

equations above are descriptive of a system with two configuration variables, q1 and q2. inputs are tau1 and tau2. d and c values are given.
the question is about conversion of above equations to a state-space equation where the state-variables are x1 = q1_dot, x2 = q1_2dot, x3 = q2_dot, x4 = q2_2dot.

Homework Equations



The Attempt at a Solution


Since variables q1 and q2 are coupled in the equations of motion, so I haven't been able to come up with a way to decouple them and makes a state-state equation. Any insights on this would very much be appreciated.
 

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Answers and Replies

  • #2
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What are g1 and g2?
 
  • #3
rude man
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Homework Statement


View attachment 238367
equations above are descriptive of a system with two configuration variables, q1 and q2. inputs are tau1 and tau2. d and c values are given.
the question is about conversion of above equations to a state-space equation where the state-variables are x1 = q1_dot, x2 = q1_2dot, x3 = q2_dot, x4 = q2_2dot.

Homework Equations



The Attempt at a Solution


Since variables q1 and q2 are coupled in the equations of motion, so I haven't been able to come up with a way to decouple them and makes a state-state equation. Any insights on this would very much be appreciated.
I've taken an entire semester of state space techniques and have yet to find an example of applying the technique to a non-linear problem.
 

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