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

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SUMMARY

The discussion focuses on converting a nonlinear equation of motion involving two configuration variables, q1 and q2, into a state-space model. The state variables are defined as x1 = q1_dot, x2 = q1_2dot, x3 = q2_dot, and x4 = q2_2dot. Participants highlight the challenge of decoupling the coupled equations of motion to formulate a state-space representation. Insights are sought on the roles of g1 and g2 in this context, emphasizing the need for practical examples of applying state-space techniques to nonlinear systems.

PREREQUISITES
  • Understanding of nonlinear dynamics and equations of motion
  • Familiarity with state-space representation and state variables
  • Knowledge of control theory principles
  • Experience with mathematical modeling techniques
NEXT STEPS
  • Research methods for decoupling nonlinear equations of motion
  • Study examples of state-space modeling for nonlinear systems
  • Learn about the role of input variables in state-space equations
  • Explore advanced control techniques applicable to nonlinear dynamics
USEFUL FOR

This discussion is beneficial for mechanical engineers, control system designers, and students studying nonlinear dynamics and state-space modeling techniques.

Sean L
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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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What are g1 and g2?
 
Sean L said:

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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