Should only take a few hours to complete, for more details see attached file.
The required tasks for this simulation exercise are
1. Design a simulink model for the system described by dynamic equations above assuming that Also assume that the track on which the cart runs is 4 metres long.
2. Derive a continuous time linear state space model for this system about the point
3. Determine the eigenvalues of this linear state space model and comment on the system stability
4. Determine the controllability of the system
5. Determine a control strategy for the system which will stabilise the system around . Your control strategy should bring the system from an initial small deviation from to the upright position in minimum time
6. Investigate what happens if you try to use your control strategy with an initial angle of
7. Determine the range in initial angles over which your control will work.
8. Comment on why your control only works over a limited range of angles.
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