A Design Analysis Approach for Improving the Stability of Dynamic Systems with Application to the Design of Car-Trailer Systems

Abstract

A design analysis approach is developed for improving the stability of dynamic systems subject to non-conservative forces. It combines genetic algorithms, sequential quadratic programming (SQP), and dynamic mode tracking (DMT). The proposed approach automatically optimizes the stability criterion and is applicable to rotor dynamics, wind turbine dynamics, aeronautics, and ground vehicle dynamics. The Routh-Hurwitz criterion has traditionally been used for determining the stability characteristics of these dynamic systems. In the conventional trial and error approaches, designers iteratively change the values of the design variables and reanalyze until an acceptable stability characteristic is achieved. This is both time-consuming and tedious. The proposed approach automates the design/analysis cycle by using the DMT technique to identify the modes; then, the SQP algorithm determines the stability criterion; and finally a genetic algorithm is applied to optimize design variables. The proposed integrated approach has been tested and evaluated numerically using a linearized car-trailer model with three degrees of freedom and the results demonstrate its feasibility and efficacy. The performed parametric sensitivity analysis revealed that the geometric parameters have a much greater influence on the lateral stability of the vehicle systems, compared with inertia parameters and torsional spring stiffness coefficients.