Abstract
A robust saturation control approach is developed for input-time delay Macpherson active suspensions, subject to dynamical uncertainties, exogenous disturbances, and road excitations. The proposed control method comprises of a linear combination of two smooth saturation functions of a filtered signal and a regulation error, hence the control law is smooth and bounded by a known and adjustable constant bound. An auxiliary signal involving a finite integral over the delayed time interval of past control values is exploited to convert the delayed system into a delay-free system, and Lyapunov–Krasovskii (LK) functionals are constructed to eliminate the residual delayed terms in a Lyapunov-based analysis. The vertical displacement and velocity of the sprung mass are proven to uniformly ultimately bounded regulating to improve the ride comfort, despite model uncertainties, additive disturbances and the input delay. Several simulations are performed to verify the improvement in the ride comfort under different road profiles, while the tire deflection and suspension deflection are within an admissible limitation in comparison with two other suspensions.
Highlights
Due to its important roles in vehicle performance, vehicle suspension control has been an interested subject in research literature
Nguyen: Saturated Feedback Control to Improve Ride Comfort control (SMC) methodologies; Chen et al introduced an improved SMC for nonlinear active suspensions to accomplish the nominal optimal performance and better robustness in [13]; Taghavifar et al presented an adaptive SMC based indirect fuzzy neural network system for a nonlinear suspension subject to uncertain parameters and road excitations in [14], or Wang et al developed an Active Disturbance Rejection Control combining with a fuzzy SMC to improve the ride comfort of full car suspension systems, whereas unmodeled dynamics and external disturbances are estimated by an extended state observer in [15]
STABILITY ANALYSIS Theorem 1: Given the input- delayed nonlinear Macpherson active suspension system in (1), the saturated controller given in (10) guarantees semi-globally uniformly bounded regulation of the vertical displacement of the chassis zs, provided the adjustable control gains α, γ, k are selected according to the following sufficient conditions ε ψ2 ε k1
Summary
Due to its important roles in vehicle performance, vehicle suspension control has been an interested subject in research literature. Nguyen: Saturated Feedback Control to Improve Ride Comfort control (SMC) methodologies; Chen et al introduced an improved SMC for nonlinear active suspensions to accomplish the nominal optimal performance and better robustness in [13]; Taghavifar et al presented an adaptive SMC based indirect fuzzy neural network system for a nonlinear suspension subject to uncertain parameters and road excitations in [14], or Wang et al developed an Active Disturbance Rejection Control combining with a fuzzy SMC to improve the ride comfort of full car suspension systems, whereas unmodeled dynamics and external disturbances are estimated by an extended state observer in [15] These approaches are discontinuous feedback methods with infinite control bandwidth and chattering limitations. The performance of the proposed control method is examined by numerical simulations in comparison with two other suspensions in the improvement of the ride comfort while the suspension deflection and tire deflection within acceptable level
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