Date of Award
Doctor of Philosophy
Engineering Science and Mechanics
The lateral stability of the driver/vehicle system is considered. It is first shown that, if the classical problem of the lateral stability of an automobile is considered in an absolute reference frame, the automobile is unstable. A driver responding proportionally to yaw angle and lateral displacement is added to the bicycle model of the automobile and the stability of the driver/vehicle system is considered. The Routh-Hurwitz criterion is applied to the characteristic equation of the system and the critical speed of the driver/vehicle system is obtained. It is shown that the critical speed of the driver/vehicle system may be less than the critical speed from the classical result;Lyapunov's second method is then considered for the classical problem and a Lyapunov function is found which gives the same conditions for stability as the Routh-Hurwitz criterion. An attempt is then made to find a Lyapunov function for a driver/vehicle system where the driver responds only to the yaw angle. The Lyapunov matrix equation is written and solved for the resulting third order system. Next, the Lyapunov matrix equation for the case of a driver responding to both yaw angle and lateral displacement is written. The solution of the equation requires solving ten equations for ten unknowns analytically, which is extremely difficult. However, if these equations were solved it is suspected that general expressions for any n x n system could then be written by generalizing the results observed for the 2 x 2, 3 x 3 and 4 x 4 cases.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Charles Wayne Johnson
Johnson, Charles Wayne, "Lateral stability of the driver/vehicle system: analytical results " (1983). Retrospective Theses and Dissertations. 8485.