Adaptive Sliding Mode Control of Rack Position Tracking System for Steer-by-Wire Vehicles

Abstract

This paper describes adaptive sliding mode control of a steer-by-wire (SBW) system to guarantee rack position tracking performance in various driving situations. The proposed control algorithm was developed using only motor position sensors (MPS) without information on tire/road friction. A stiffness parameter adaptation law was designed to compensate for disturbances in the SBW rack system. It is demonstrated that the proposed adaptation algorithm provides good tracking performance without using an additional gain tuning approach under various road conditions. Moreover, in the proposed algorithm, a dynamic stiffness model has been developed to improve rack position tracking performance under a zero vehicle speed scenario. In a dynamic stiffness model, the stiffness center is not fixed but changes depending on the actual rack position. In the event than an SBW vehicle is parking, it is important to ensure rack position tracking performance at low and zero vehicle speeds. Computer simulations and vehicle tests were performed under various driving situations to test the performance of the proposed control algorithm. The results demonstrate that the proposed control algorithm ensures tracking performance on dry asphalt and wet road conditions, as well as at zero vehicle speed. INDEX TERMS steer-by-wire (SBW) system, adaptive sliding mode control, rack position tracking,

Robust adaptive control of steer‐by‐wire systems under unknown state‐dependent uncertainties

“…where K, 𝜇 are user defined scalars selected as K = 1, 𝜇 = 0.01 for the simulations. To avoid chattering, the signum function in (29) is replaced by the saturation function as in (7) with 𝜖 = 0.1.…”

“…1,[7][8][9][10] While the adaptive control solutions do not require a priori knowledge of the bound of uncertainties compared with a robust controller, a few observations worth mentioning: the state-of-the-art adaptive control methods either require structural knowledge of uncertainty, 8,10 or assume the uncertain dynamics to be bounded by a constant a priori. 1,7,9 However, the upper bound of uncertain dynamics of a SBW system has explicit dependency on states; 8 under such an uncertainty setting, presumption of constant upper bound on uncertainty is not only conservative, [11][12][13][14][15][16] it may even lead to instability. 17,18 In light of the above discussions, an adaptive control solution that can tackle unknown dynamics of SBW system is still missing.…”

“…Remark 4. Owing to the structures of the error variable r as in (2) and of saturation based robustness component in control input as in (7), the proposed design can also be considered as a kind of adaptive sliding mode control (ASMC). Nevertheless, compared with the state-of-the-art solutions, the proposed method (i) does not require any knowledge of system dynamics parameters (cf.…”

“…Theorem 1. Under Property 1 and Assumption 1-2, the closed-loop trajectories of (3 ) using the control laws (7 ) and (8 ) in conjunction with the adaptive law ( 9) are globally uniformly ultimately bounded. Furthermore, an ultimate bound 𝜔 on the tracking error variable 𝜉 is found to be…”

Robust Controller Design for Steer-by-Wire Systems in Vehicles

“…The auto industry has implemented many modern and advanced systems in an attempt to raise the quality of driving, especially in off-road, as well as increase the safety and comfort of users of these vehicles [11,13,17]. Parallel to these developments, we see a significant shift from classical to modern systems [9] and SbW is another very promising application in terms of practicality, safety, and functionality [4,14]. For that reason, several automobile manufacturers have introduced SbW systems in vehicles to improve operational efficiency and fuel economy [3,8,19,24,36].…”