Derivation of State Space Representation

Equation of motion for the cart

           p11c6            (Our characteristic equation of motion for the cart and motor system derived earlier.)
 
p20a2 (Solve for xdot2p)



Equation of motion for the Inverted Pendulum
           p2_9            (Our characteristic equation of motion for the inverted pendulum derived earlier. Now solve for thetad2 )
 
p20b2
 
p20b3
 
p20b4


State Space Representations

           p20c1           
p20a2 (Equation of motion for the cart derived above)
p20c3
p20b4 (Equation of motion for the inverted pendulum derived above)

This can be represented in matrix form as:

p20c5


This has the general form of:

          p20d1


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