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In this article we consider the γ‐stabilization of nth‐order linear time‐invariant dynamical systems using multiplicity‐induced‐dominancy‐based controller design in the presence of delays in the input or the output channels. A sufficient condition is given for the dominancy of a real root with multiplicity at least n+1 and at least n using an integral factorization of the corresponding characteristic function. A necessary condition for γ‐stabilizability is analyzed utilizing the property that the derivative of a γ‐stable quasipolynomial is also γ‐stable under certain conditions. Sufficient and necessary conditions are given for systems with real‐rooted open‐loop characteristic function: the delay intervals are determined where the conditions for dominancy and γ‐stabilizability are satisfied. The efficiency of the proposed controller design is shown in the case of a multilink inverted pendulum. [ABSTRACT FROM AUTHOR]

This paper deals with damping oscillations of a payload suspended to a fixed position base (e.g., a standing crane trolley). The damping is done by utilizing the Coriolis force generated by synchronizing translational and rotational motion of the payload. After revising existing approaches mainly based on approximating the payload motion by the motion of a mathematical pendulum, several nonlinear time-delay algorithms are proposed to handle the given task efficiently. The key benefit of the proposed methods is the feedback character of the algorithms guaranteeing the required synchronization of the cable length adjustment with the payload swing motion under the varying oscillation period and even under the effect of external disturbances. Note that the preceding algorithms were of open-loop character where such a synchronization was not guaranteed. The theoretical design is validated by simulations. The implementation aspects are discussed by relaxing the simplifying assumptions. Finally, the proposed time-delay feedback method is experimentally verified on a laboratory setup. The achieved results demonstrate viability of the proposed method for payload oscillation damping, e.g., in crane applications. [ABSTRACT FROM PUBLISHER]

This article addresses three stability problems related to networked-control systems (NCSs) with periodic scheduling, where control systems may have multiple samplings in a hyperperiod (a hyperperiod is a periodically repeated scheduling sequence for all tasks in an NCS). As expected, the analysis of a system with multiple samplings is much richer than the case with single sampling. For example, a system with two samplings may be stable (unstable) even if it is unstable (stable) when sampled by either sampling. In this context, it is important to understand how network-induced delays and multiple samplings affect the system's stability. In this article, three particular stability problems involving constant and/or time-varying parameters are investigated, and the corresponding stability regions are derived. Numerical examples and various discussions complete the presentation. [ABSTRACT FROM AUTHOR]

This paper addresses a new control strategy for synchronizing two or more distributed and interconnected dynamic systems having communication time delays. The proposed strategy that uses the Smith predictor principle and delay information not only achieves synchronization but also preserves the natural local dynamics of each subsystem without being affected by the feedback nature of control. The proposed synchronization scheme is generalized to cases that deal with an arbitrary number of heterogeneous interconnected systems through dynamic scaling of input under a ring-type network configuration. In addition, possibility of applying the proposed scheme to nonlinear systems is discussed. Simulation and experimental tests are conducted to validate theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a synchronization scheme to achieve a high level of consistency in peer-to-peer-based shared virtual environments (SVEs), as well as to display natural and realistic motions of virtual objects, in collaborative haptic tasks. The synchronization scheme utilizes an advanced feedback controller to compensate for the state error between geographically separated sites with a significant amount of time delay. It is designed using the mathematical model of a two-user SVE manipulating a freely moving object represented as a mass with damping resistance, with a haptic interface. Thanks to feedback control theory of time delay systems, the controller is shown to result in closed-loop stability and is be robust to perturbations in the time delay. Together with the synchronization control, a recovery filter is also designed and integrated so as to preserve the natural behavior of the synchronized object, which is, otherwise, affected by the feedback control action. In addition to verifying the theoretical results, two experiments using real Internet and local area network communications are carried out. These tests clearly support the validity of the analyses and demonstrate the applicability of the synchronization scheme. [ABSTRACT FROM AUTHOR]

Abstract: For the general linear scalar time-delay systems of arbitrary order with two delays, this article provides a detailed study on the stability crossing curves consisting of all the delays such that the characteristic quasipolynomial has at least one imaginary zero. The crossing set, consisting of all the frequencies corresponding to all the points in the stability crossing curves, are expressed in terms of simple inequality constraints and can be easily identified from the gain response curves of the coefficient transfer functions of the delay terms. This crossing set forms a finite number of intervals of finite length. The corresponding stability crossing curves form a series of smooth curves except at the points corresponding to multiple zeros and a number of other degenerate cases. These curves may be closed curves, open ended curves, and spiral-like curves oriented horizontally, vertically, or diagonally. The category of curves are determined by which constraints are violated at the two ends of the corresponding intervals of the crossing set. The directions in which the zeros cross the imaginary axis are explicitly expressed. An algorithm may be devised to calculate the maximum delay deviation without changing the number of right half plane zeros of the characteristic quasipolynomial (and preservation of stability as a special case). [Copyright &y& Elsevier]

The paper presents a controller design for systems suffering from multi-harmonic periodic disturbance and substantial input time-delay. It forms an alternative approach to Repetitive Control where the goal is to stabilize a close-loop that encapsulates an explicit time-delay model of the periodic signal. The proposed controller design is based on the Internal Model Control (IMC) framework, and it consists of the inverse system model and a tuneable distributed delay with an overall length related to the period of the disturbance. The properness of the controller can be ensured by utilizing a low-pass filter, however, such a component is shown to be unnecessary when the relative order of the system model is one. This fact makes the alternative approach especially suitable for systems approximated by a first-order model with input time-delay, leading to a straightforward controller design thanks to its simple structure and attainable conditions. Stability of the configuration is guaranteed by an ideal IMC framework. For further performance and robustness requirements for the non-ideal case the tuning of the controller is posed as a weighted- H ∞ optimization problem where frequency-, spectral- and time-domain requirements are formulated as constraints. The overall control design is experimentally verified on a laboratory setup that has high-order dynamics approximated by a first-order model with input delay. [ABSTRACT FROM AUTHOR]

This paper studies the migration of double imaginary roots of the systems’ characteristic equation when two parameters are subjected to small deviations. The proposed approach covers a wide range of models. Under the least degeneracy assumptions, we found that the local stability crossing curve has a cusp at the point that corresponds to the double root, and it divides the neighborhood of this point into an S-sector and a G-sector. When the parameters move into the G-sector, one of the roots moves to the right half-plane, and the other moves to the left half-plane. When the parameters move into the S-sector, both roots move either to the left half-plane or the right half-plane depending on the sign of a quantity that depends on the characteristic function and its derivatives up to the third order. [ABSTRACT FROM AUTHOR]

• Payload swing damping by the pivot vertical motion is feasible by nonlinear control. • The problem is not controllable in the linear system sense. • Exponential decay can be achieved by a controller derived by Lyapunov's second. • Time delay controller proofed practical as it allows phase shift compensation. The solution of a case study problem of suspended payload sway damping by moving a pivot base in vertical direction is presented. Unlike for the classical problem of anti-sway control for moving the base in the horizontal direction, implemented e.g. in cranes, a direct solution by using control feedback theory for linear systems is not possible. Once the model is linearized, it becomes uncontrollable. Thus, a derivation of a nonlinear controller is needed to solve the task. In this context, two solutions are proposed. The first solution is based on imposing harmonic motion of the base with double frequency of the payload natural frequency. Synchronization of the base and the payload deflection angle is done either by proportional time-delay controller or by proportional-derivative delay free controller. Secondly, the Lyapunov's second method is directly applied to derive a nonlinear controller. For both cases, balancing the dissipated energy, rules for determining equivalent damping are explicitly derived. After discussing and solving the corresponding implementation aspects, both simulation and experimental validations are performed. The experimental validation is performed on a simplified problem, where only horizontal motion is possible. The simulation based validation is performed on a nonlinear two dimensional model of a quadcopter carrying a suspended payload. [ABSTRACT FROM AUTHOR]