Stability and gain analysis of a robust steering control system for a corner module with hybrid time delay

In distributed vehicles with corner modules, independent wheel steering improves chassis motion freedom but weakens mechanical constraints and increases reliance on the X-by-wire feedback chain. This makes wheel-end steering more sensitive to kingpin disturbances and time delays. Existing studies on disturbance rejection for steering systems often ignore feedback delays or simplify them as a single continuous delay, which may distort stability prediction and gain selection. To address this issue, a composite closed-loop model for a disturbance-observer-based corner-module steering system is proposed by introducing the disturbance estimation error into the state vector. Continuous actuator delay and sampling-induced discrete delay are formulated as a hybrid feedback delay. Based on the resulting hybrid-delay model, the semi-discretization method is used to construct the characteristic matrix, and the stability region in the ( K _P , K _D ) plane is obtained from Floquet multipliers. The results show that the proposed method extracts the stability boundary of the hybrid-delay system and divides the stable region into low frequency, high frequency, and zero phase angle regions according to the dominant multiplier phase. An optimal gain point with fast convergence and weak oscillation is identified using the dominant multiplier modulus and the normalized convergence index based on the step size. Compared with an equivalent continuous-delay model, the hybrid-delay model gives different optimal gains and a higher convergence index as the sampling-delay ratio increases.