For cruise control, the longitudinal motion of a vehicle on a flat road can he m

Question

For cruise control, the longitudinal motion of a vehicle on a flat road can he modeled, with the use of Newton's second law, by the first-order differential equation mvdot = u - Kc sgn(v) - Kfv - Kav2 where m is the vehicle's mass, v is its speed, u is the tractive force generated by the engine, Kc sgn(v) is the coulomb friction force, Kfv is the viscous friction force, and Kav2 is the aerodynamic drag. The coefficients Kc, Kf and Ka are nonnegative. When a PI controller is used, u = K I, sigma + KP (vd - v), where vd is the desired speed, sigma is the state of the integrator sigma = vd - v, and Kf, and Kp are positive constants. We are only interested in the region v 0. Let vd be a positive constant. Find all equilibrium points and determine the type of each point.

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