Predefined-time (PdT) synchronous navigation is essential for the cooperative operation of unmanned surface vessels (USVs), as it guarantees rapid formation recovery and precise coordination under stringent temporal constraints. In practice, however, this objective is severely challenged by the concurrent presence of unknown ocean disturbances, model uncertainties, and unavailable leader velocity–factors that jointly undermine disturbance-rejection accuracy and invalidate conventional synchronization schemes. To counteract these obstacles, we develop a PdT precise anti-disturbance synchronous navigation control framework comprising three core components: a PdT nonlinear disturbance observer (enhanced by an auxiliary dynamic system) for accurate estimation of lumped uncertainties; a PdT velocity estimator that recovers the leader’s velocity within a PdT without direct measurements; and a PdT synchronous navigation controller, synthesized via backstepping, that ensures global PdT stability. The effectiveness and practicality of the proposed strategy are substantiated through simulations on a representative USV model.
Self-excited vibration (SEV), often induced by spline misalignment and tooth friction in spline-connected driveshaft systems, poses a severe threat to rotor system operational safety. Consequently, a reliability assessment is imperative. This paper presents a reliability analysis framework for floating spline-connected driveshaft systems based on the nonlinear dynamic response of the rotor, using the Bayes formula in conjunction with the AK-MCS (B-AK-MCS) method. A finite element dynamic model of the floating spline-connected driveshaft system is established, incorporating analytical spline nonlinear stiffness and friction torque models, and validated against experimental results obtained from a spline-connected driveshaft test rig. Self-excited vibration is treated as the system failure mode, and limit state functions are formulated based on the vibration amplitude thresholds of the shaft. The failure probability function (FPF) is efficiently computed via B-AK-MCS in a single reliability assessment. Four uncertainty cases are systematically investigated, considering the spline friction coefficient, coupling angular stiffness, coupling lateral stiffness and support lateral stiffness as random inputs. It is revealed that the spline friction coefficient and coupling angular stiffness are the dominant sensitive parameters governing SEV onset. Bifurcation analysis demonstrates that these critical parameters exhibit distinct bifurcation points beyond which the system transitions abruptly from period-1 motion to quasi-periodic motion. The proposed framework provides theoretical guidance for the reliability-oriented design of floating spline-connected driveshaft systems.
The traditional nonlinear energy sink (NES) consists of an essentially nonlinear spring, which can be difficult to realize in practical implementations. In this study, three variant NESs without an essentially nonlinear spring are designed and compared with a target cubic NES: a mono-stable NES (MNES), a bi-stable NES (BNES), and a tri-stable NES (TNES). A finite-amplitude equivalent-stiffness design framework is proposed in which the restoring force of each variant NES is matched to that of the target NES at a prescribed reference displacement. The resulting representative designs are evaluated for transient vibration suppression and simultaneous vibration-suppression/energy-harvesting trade-offs using piezoelectric and electromagnetic energy harvesters. For the steady-state harmonically forced case, the electromagnetic-harvester-equipped systems are formulated using a normalized harmonic-balance approach implemented with NLvib. An auxiliary electrical coordinate is introduced to express the electromagnetic current equation in a second-order form suitable for continuation, and Hill-based stability analysis with Floquet-exponent filtering is used to classify the computed periodic branches. Direct time integration is used to validate the harmonic-balance frequency responses and to interpret modulated responses near unstable resonance-region branches. Multiobjective optimization is then performed over operating conditions, and additional sensitivity studies are added to examine the dependence of the reported rankings on the reference displacement and design-specific absorber parameters. The results show that no single NES configuration is universally preferred. For the selected equivalent-stiffness parameter sets, the BNES provides strong low-energy transient performance, while the preferred steady-state configuration depends on the excitation regime and on the relative priority assigned to vibration suppression and energy harvesting. The comparison between PEH and EMEH is likewise conditional on the adopted harvester parameters.
This paper is an investment to develop a robust fixed-time fault-tolerant control for a seven DoF full-car active suspension system subjected to unknown nonlinearity, parameter uncertainties, and actuator faults. Although unknown dynamic and fault problems are well-known to usually exist in the dynamic model of the active suspension system on vehicles, solving for both issues simultaneously significantly increases the complexity of the control design. Moreover, the maximum suspension deflection constraint is discussed. To address this problem, a fixed-time disturbance observer is employed to accurately compensate for unknown dynamics and actuator faults in real-time. A nonlinear low-pass filter is proposed to generate the desired reference for the displacement of the vehicle body, which manages the tradeoffs between handling stability and riding comfort. By using a fixed-time control scheme to guarantee the tracking error convergence within a fixed time, the maximum suspension deflection constraint is ensured while successfully achieving ride comfort. The stability of the closed-loop system is demonstrated by the Lyapunov theory. Numerical simulation results are presented to verify the effectiveness and robustness of the proposed method. The defective node–focus transition, equivalently a second-order exceptional point (EP) of the reduced Jacobian, changes stable relaxation; the later Hopf bifurcation creates breathing.
Mitigation of galloping in bluff body structures by passive and active means is a topic of increasing interest. Recently researchers have demonstrated galloping suppression using High Frequency Excitation (HFE). In this context we present a novel, unified computational method to predict galloping behavior under harmonic excitation including HFE, which complements existing analytical approaches and provides additional insights. The proposed method combines the Frequency Response Boundary (FRB) of the linear structure and the Two Sinusoid Input Describing Function (TSIDF) of the nonlinear aerodynamics. TSIDFs are derived for polynomial nonlinearities up to heptic order in this work. Results are provided for a representative structure with various bluff body characteristics. These include galloping responses without and with forcing, and excitation thresholds for galloping suppression, which also contribute to a better qualitative understanding of LCO suppression in general. It is noted that the new approach has broad applicability as it does not require the conventional assumption of a large frequency separation between the slow and fast dynamics.
