In order to self-balance a bicycle, its open-loop transfer function is found to be (Lam, 2011): where
Question:
In order to self-balance a bicycle, its open-loop transfer function is found to be (Lam, 2011):
where θ(s) is the angle of the bicycle with respect to the vertical, and U(s) is the voltage applied to the motor that drives a flywheel used to stabilize the bicycle. Note that the bicycle is open-loop unstable with one open-loop pole in the right half-plane.
a. Draw the Nyquist diagram of the system.
b. Find the system’s gain and phase margins.
c. Assuming a unit feedback system, find the range of K for closed-loop stability if the forward path transfer function is KG(s).
d. Assuming a second-order approximation, what is the expected %OS if K = 0.141?
e. Use a computer program to simulate your system for a unit-step response using the value of K in Part d.
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