Active Suspension Design Based on Geometric Parameters of a Formula SAE Car for Roll Minimization

This paper describes a methodology through which is possible to design an active suspension control beginning on the geometric characteristics of a double-wishbone suspension. The used data is based on the 2011 Formula SAE car developed by the Formula UFSC Team. A front half-car model with two degrees-of-freedom was used, taking into account the parameters of the suspension and considering each tire a rigid body. The behavior of the geometric model is analyzed and equations are generated to determine the spring deformation due to each degree-of-freedom. Following, Lagrange's equations are used to obtain the movement equations of the model, which will be converted to a simplified model with the same dynamic behavior used in the control development. Furthermore, the methodology provides the tools for efficient suspension design, allowing a quick conversion between the simplified model, commonly used for calculating the initial parameters of a new suspension, and a more close-to-reality dynamic model, from which a behavior preview can be obtained. This paper also proposes a control structure based on a Linear Quadratic Regulator (LQR) to be used on this equivalent model. It increases the performance optimizing the magnitude of the vertical and lateral displacement in the closed-loop system. The process of determining the weighting matrices of the variables priorities using the method of the energy of the state variables and control effort is presented. Finally, the results achieved by simulation tests are compared with the behavior of the system without control to prove its efficacy.