Abstract
In this paper, the inherent stability problem for multibody systems with variable-stiffness springs (VSSs) is studied. Since multibody systems with VSSs may consume energy during the variation of stiffness, the inherent stability is not always ensured. The motivation of this paper is to present sufficient conditions that ensure the inherent stability of multibody systems with VSSs. The absolute stability theory is adopted, and N-degree-of-freedom (DOF) systems with VSSs are formulated as a Lur’e form. Furthermore, based on the circle criterion, sufficient conditions for the inherent stability of the systems are obtained. In order to verify these conditions, both frequency-domain and time-domain numerical simulations are conducted for several typical low-DOF systems.
Highlights
Vibration control can generally be classified into passive control, active control, and semiactive control
Since semiactive control devices are obtained based on their passive counterparts, it is expected to inherit the stability of passive control, which means that even though failures and improper control actions of the parameter adjustments may occur, the semiactive control system can remain stable
The inherent stability studied in this paper implies the stability for a group of control laws within certain sectors, instead of a special control law in the aforementioned papers. erefore, in this paper, the inherent stability problem for the multibody systems with Variable-stiffness spring (VSS) is studied via the absolute stability theory, and the general multibody system with VSSs is transformed into a Lur’e-type system described as a linear passive system with feedback-connected nonlinearities. e most celebrated methods to analyze the absolute stability of a Lur’e-type systems are circle criterion (CC) and Popov criterion (PC)
Summary
Vibration control can generally be classified into passive control, active control, and semiactive control. E VSS-based systems are typical nonlinear control systems, where the nonlinearities are induced by the variable stiffness within a sector reflecting the bounds of VSSs. For nonlinear mechanical systems, several control strategies have been proposed to ensure stability and performance, such as sliding mode backstepping [15], adaptive finite-time control [16, 17], etc. Erefore, in this paper, the inherent stability problem for the multibody systems with VSSs is studied via the absolute stability theory, and the general multibody system with VSSs is transformed into a Lur’e-type system described as a linear passive system with feedback-connected nonlinearities.
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