Derivation of State Space Representation

Equation of motion for the cart

                      (Our characteristic equation of motion for the cart and motor system derived earlier.)
 
(Solve for )



Equation of motion for the Inverted Pendulum
                      (Our characteristic equation of motion for the inverted pendulum derived earlier. Now solve for )
 
 
 


State Space Representations

                     
(Equation of motion for the cart derived above)
(Equation of motion for the inverted pendulum derived above)

This can be represented in matrix form as:




This has the general form of:

          


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