Impulse-Based Hybrid Motion Control

The impulse-based discrete feedback control has been proposed in previous work for the second-order motion systems with damping uncertainties. The sate-dependent discrete impulse action takes place at zero crossing of one of both states, either relative position or velocity. In this paper, the proposed control method is extended to a general hybrid motion control form. We are using the paradigm of hybrid system modeling while explicitly specifying the state trajectories each time the continuous system state hits the guards that triggers impulsive control actions. The conditions for a stable convergence to zero equilibrium are derived in relation to the control parameters, while requiring only the upper bound of damping uncertainties to be known. Numerical examples are shown for an underdamped closed-loop dynamics with oscillating transients, an upper bounded time-varying positive system damping, and system with an additional Coulomb friction damping.Comment: 6 pages, 4 figures, IEEE conferenc

Full- and Reduced-order Model of Hydraulic Cylinder for Motion Control

This paper describes the full- and reduced-order models of an actuated hydraulic cylinder suitable for system dynamics analysis and motion control design. The full-order model incorporates the valve spool dynamics with combined dead-zone and saturation nonlinearities - inherent for the orifice flow. It includes the continuity equations of hydraulic circuits coupled with the dynamics of mechanical part of cylinder drive. The resulted model is the fifth-order and nonlinear in states. The reduced model neglects the fast valve spool dynamics, simplifies both the orifice and continuity equations through an aggregation, and considers the cylinder rod velocity as output of interest. The reduced model is second-order that facilitates studying the system behavior and allows for direct phase plane analysis. Dynamics properties are addressed in details, for both models, with focus on the frequency response, system damping, and state trajectories related to the load pressure and relative velocity.Comment: 6 pages, 6 figures, IEEE conferenc

Time-delay based output feedback control of fourth-order oscillatory systems

We consider robust stabilization of the fourth-order oscillatory systems with non-collocated output sensing. A novel yet simple control method is introduced based on the time-delayed output feedback. The delayed output feedback requires only the oscillation frequency to be known and allows for a robust control design with cancelation of the resonance peak. We use the stability margins to justify the transfer characteristics and robustness of the time-delay control in frequency domain. The main advantage of the proposed method, over the other possible lead-based loop shaping strategies, is that neither time derivatives of the noisy output nor implementation of any transfer functions are required for deploying the controller, that comes in favor of applications. An otherwise inherently instable proportional-integral (PI) feedback of the non-collocated output is shown to be stabilized by the proposed method. The control developed and associated analysis are also confirmed by the experimental results shown for the low damped two-mass oscillator system with uncertainties.Comment: 6 pages, 8 figure

On stability of linear dynamic systems with hysteresis feedback

Abstract. The stability of linear dynamic systems with hysteresis in feedback is considered. While the absolute stability for memoryless nonlinearities (known as Lure’s problem) can be proved by the well-known circle criterion, the multivalued rate-independent hysteresis poses significant challenges for feedback systems, especially for proof of convergence to an equilibrium state correspondingly set. The dissipative behavior of clockwise input-output hysteresis is considered with two boundary cases of energy losses at reversal cycles. For upper boundary cases of maximal (parallelogram shape) hysteresis loop, an equivalent transformation of the closed-loop system is provided. This allows for the application of the circle criterion of absolute stability. Invariant sets as a consequence of hysteresis are discussed. Several numerical examples are demonstrated, including a feedback-controlled double-mass harmonic oscillator with hysteresis and one stable and one unstable poles configuration.acceptedVersio

On stiffness and damping of vibro-impact dynamics of backlash

We consider the instantaneous stiffness and damping of the vibro-impact in a backlash pair. Opposed to the existing and mostly used models of the backlash, we address the problem of contact and separation, and the associated force propagation within a mechanical pair, from a viewpoint of the vibro-impact dynamics. We discuss the impact forces with the coefficient of restitution as a principal factor which shapes the transient backlash response.We show that a common approach to modeling the backlash by means of a dead-zone in a restoring force is unsuitable for correctly capturing the mechanical impact. We exemplary demonstrate a qualitative accord between an experimental backlash response and the postulated modeling approach. Backlash related energy losses by damping of vibro-impact system are also addressed in brief.acceptedVersio