Analysis and Control of the Vehicle Roll Dynamics Using Sum of Squares Polynomial Approach

The safety of vehicle travel relies on good stability performance,making vehicle motion control a vital technology in vehicles.This paper focuses on investigating the impact of roll control on vehicle performance,particularly in terms of avoiding rollover and ensuring lateral stability.By introducing a feedback roll moment,the roll motion can be effectively controlled.The paper considers two roll reference generators:A static one aimed at zero roll,and a dynamic one based on the vehicle's lateral acceleration.The static roll reference generator enhances stability by employing a fixed reference,particularly beneficial during routine driving conditions.In contrast,the dynamic roll reference generator continually adapts the roll angle reference in response to real-time vehicle dynamics and driving conditions.These proposed reference generators can be paired with varying suspension systems—Static reference could be achieved using semi-active suspensions,while the dynamic one is integrated into advanced active suspension systems,offering heightened adaptability and performance.To address the roll control objectives,this paper proposes a novel sum of squares(SOS)integral polynomial tracking control.The proposed controller satisfies control bounds and considers control constraints during the design phase.The effectiveness and robustness of the proposed control scheme are evaluated through numerical simulations using a full vehicle nonlinear model in Matlab/Simulink.The results of these simulations are compared to super-twisting sliding mode and Lyapunov-based controllers.