Stability analysis of lateral dynamics of a vehicle model utilizing state feedback with integral control and bifurcation method

In this work, a novel control strategy is proposed to obtain the stability boundary in addition to reduce the transients around the equilibrium points. To encounter the described problem, a new approach of combining the bifurcation analysis with the state feedback controller is proposed. A bifurcation analysis at different equilibrium points is performed to obtain the stable region of operation. In addition to this, the transients behavior of the system is also obtained simultaneously in the form of eigenvalues plots. The objective of the proposed controller is to generate a control law and state variables to reduce the transients keeping the system within the stability boundary by tuning the reference input matrix. From the obtained simulation results, it is seen that, by combining the bifurcation analysis with state feedback controller, the transients and the steady state error are reduced by selecting the purely negative real eigenvalues and reference input matrix respectively. The obtained closed loop control law and the state variables utilizing Ackerman's Formula are found within the stability limit. A sensitivity index obtained from local sensitivity analysis verifies the relationship between the stability boundary at different longitudinal velocity on a low-friction road obtained from bifurcation analysis.