A simple modified and linearized model for the transfer function of a certain bicycle from steer angle () to roll angle () is given by

A simple modified and linearized model for the transfer function of a certain bicycle from steer angle (δ) to roll angle (φ) is given by (Åstrom, 2005)

Assume the rider can be represented by a gain K, and that the closed-loop system is shown in Figure 10.20 with G(s)= KP(s) and H = 1. 

Use MATLAB and the Nyquist stability criterion to find the range of K for closed-loop stability.

 

P(s)_ 12(s + 20) P(s) = 8(s) s2 + 25