Closed-form solution exploration study for general second-order vehicle control system modeling

This paper first studies the math model for heavy duty vehicle (HDV) control systems with focus on the general 2^nd order system model that can be represented by a 2^nd order differential equation. For general 2^nd order differential equations, the paper discusses them in two categories, one is the homogeneous and the other is non-homogeneous, and illustrates the general closed-form solutions for each category. Then the paper moves on to the practical 2^nd order mechanical vibration system considering Coulomb friction since most HDV system models can be simplified to such a system model. The paper illustrates closed-form solutions for both steering forced and force-free scenarios assuming certain forms of steering force. Overall, the paper demonstrates a set of solutions on what closed-form solutions are available for general HDV control system and how to use them to get the exact closed-form solutions under various simplification assumptions or conditions.