arXiv subjects

Michael Ruderman

Publications and source records attributed to Michael Ruderman.

50 records · Page 3Linked to original sources

arXiv2021

Extended fractional-order Jeffreys model of viscoelastic hydraulic cylinder

A novel modeling approach for viscoelastic hydraulic cylinders, with negligible inertial forces, is proposed, based on the extended fractional-order Jeffreys model. Analysis and physical reasoning for the parameter constraints and order of the fractional derivatives are provided. Comparison between the measured and computed frequency response functions and time domain transient response argues in favor of the proposed four-parameter fractional-order model.

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arXiv2020

Optimal nonlinear damping control of second-order systems

Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global stability, passivity property, and convergence time and accuracy are demonstrated. Also the control saturation case is explicitly analyzed. The suggested nonlinear damping is denoted as optimal since requiring no design additional parameters and ensuring a fast convergence, without transient overshoots for a non-saturated and one transient overshoot for a saturated control configuration.

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arXiv2020

Hybrid Position/Force Control for Hydraulic Actuators

In this paper a novel hybrid position/force control with autonomous switching between both control modes is introduced for hydraulic actuators. A hybrid position/force control structure with feed-forwarding, full-state feedback, including integral control error, pre-compensator of the deadzone, and low-pass filtering of the control value is designed. Controller gains are obtained via local linearization and pole placement accomplished separately for the position and force control. A hysteresis-based autonomous switching is integrated into the closed control loop, while multiple Lyapunov function based approach is applied for stability analysis of the entire hybrid control system. Experimental evaluation is shown on the developed test setup with the standard industrial hydraulic cylinders, and that for different motion and load profiles.

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arXiv2020

On stability of linear dynamic systems with hysteresis feedback

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.

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arXiv2019

Lead-Lag-Shaped Interactive Force Estimation by Equivalent Output Injection of Sliding-Mode

Estimation of interactive forces, which are mostly unavailable for direct measurement on the interface between a system and its environment, is an essential task in various motion control applications. This paper proposes an interactive force estimation method, based on the well-known equivalent output injection of the second-order sliding mode. The equivalent output injection is used to obtain a frequency-unshaped quantity that appears as a matched external disturbance and encompasses the interactive forces. Afterwards, a universal lead-lag shaper, depending on dynamics of the motion control system coupled with its environment, is used to extract an interactive force quantity. Once identified, the lead-lag shaper can be applied to the given system structure. An experimental case study, using a valvecontrolled hydraulic cylinder counteracted by the dynamic load, is demonstrated with an accurate estimation of the interactive force, that in comparison to the reference measurement.

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arXiv2019

Backlash Identification in Two-Mass Systems by Delayed Relay Feedback

Backlash, also known as mechanical play, is a piecewise differentiable nonlinearity which exists in several actuated systems, comprising, e.g., rack-and-pinion drives, shaft couplings, toothed gears, and other machine elements. Generally, the backlash is nested between the moving parts of a complex dynamic system, which handicaps its proper detection and identification. A classical example is the two-mass system which can approximate numerous mechanisms connected by a shaft (or link) with relatively high stiffness and backlash in series. Information about the presence and extent of the backlash is seldom exactly known and is rather conditional upon factors such as wear, fatigue and incipient failures in the components. This paper proposes a novel backlash identification method using one-side sensing of a two-mass system. The method is based on the delayed relay operator in feedback that allows stable and controllable limit cycles to be induced and operated within the (unknown) backlash gap. The system model, with structural transformations required for the one-side backlash measurements, is given, along with the analysis of the delayed relay in velocity feedback. Experimental evaluations are shown for a two-inertia motor bench that has coupling with backlash gap of about one degree.

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arXiv2017

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.

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arXiv2017

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.

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arXiv2016

On break-away forces in actuated motion systems with nonlinear friction

The phenomenon of so-called break-away forces, as maximal actuation forces at which a sticking system begins to slide and thus passes over to a steady (macro) motion, is well known from engineering practice but still less understood in its cause-effect relationship. This note analyzes the break-away behavior of systems with nonlinear friction, which is analytically well-described by combining the Coulomb friction law with rate-independent presliding transitions and, when necessary, Stribeck effect of the velocity-weakening steady-state curve. The break-away conditions are harmonized with analytic form of the system description and shown to be in accord with a relationship between the varying break-away force and actuation force rate -- well known from the experiments reported in several independently published works.

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arXiv2016

Damping of prominence longitudinal oscillations due to mass accretion

We study the damping of longitudinal oscillations of a prominence thread caused by the mass accretion. In this model we considered a thin curved magnetic tube filled with the plasma. The parts of the tube at the two sides of the thread are filled with hot rarefied plasma. We assume that there are flows of rarefied plasma toward the thread caused by the plasma evaporation at the magnetic tube footpoints. Our main assumption is that the hot plasma is instantaneously accommodated by the thread when it arrives at the thread, and its temperature and density become equal to those of the thread. Then we derive the system of ordinary differential equations describing the thread dynamics. We consider linear and nonlinear oscillation. The nonlinearity reduces the damping time, however this reduction is small. The damping time is inversely proportional to the accretion rate. We also obtain that the oscillation periods decrease with time. However even for the largest initial oscillation amplitude considered in our article the period reduction does not exceed 20%. We conclude that the mass accretion can damp the motion of the threads rapidly. Thus, this mechanism can explain the observed strong damping of large-amplitude longitudinal oscillations. In addition, the damping time can be used to determine the mass accretion rate and indirectly the coronal heating.

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arXiv2015

Compensation of Nonlinear Torsion in Flexible Joint Robots: Comparison of Two Approaches

Flexible joint robots, in particularly those which are equipped with harmonic-drive gears, can feature elasticities with hysteresis. Under heavy loads and large joint torques the hysteresis lost motion can lead to significant errors of tracking and positioning of the robotic links. In this paper, two approaches for compensating the nonlinear joint torsion with hysteresis are described and compared with each other. Both methods assume the measured signals available only on the motor side of joint transmissions. The first approach assumes a rigid-link manipulator model and transforms the desired link trajectory into that of the motor drives by using the inverse dynamics and inverse hysteresis map. The second approach relies on the modeling of motor drives and inverse hysteresis and uses the generalized momenta when predicting the joint torsion. Both methods are discussed in details along with a numerical example of two-link planar manipulator under gravity.

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arXiv2015

Computationally efficient formulation of relay operator for Preisach hysteresis modeling

An algebraic expression for the Preisach hysteron, which is a non-ideal (delayed) relay operator, is formulated for a computationally efficient real-time implementation. This allows representing the classical scalar Preisach hysteresis model as a summation of a large number of weighted hysterons which computation can be accomplished in parallel. The latter makes possible an efficient FPGA or ASIC realization of the scalar Preisach hysteresis model that can be useful for multiple applications. The signal flow which specifies the model implementation is provided in form of the block diagram. The proposed computation of Preisach hysterons, aggregated to the entire Preisach hysteresis model, is evaluated numerically and on a real-time hardware platform.

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arXiv2015

State-space formulation of scalar Preisach hysteresis model for rapid computation in time domain

A state-space formulation of classical scalar Preisach model (CSPM) of hysteresis is proposed. The introduced state dynamics and memory interface allow to use the state equation, which is rapid in calculation, instead of the original Preisach equation. The main benefit of the proposed modeling approach is the reduced computational effort which requires only a single integration over the instantaneous line segment in the Preisach plane. Numerical evaluations of the computation time and model accuracy are provided in comparison to the CSPM which is taken as a reference model.

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arXiv2010

Nonlinear effects in resonant layers in solar and space plasmas

The present paper reviews recent advances in the theory of nonlinear driven magnetohydrodynamic (MHD) waves in slow and Alfven resonant layers. Simple estimations show that in the vicinity of resonant positions the amplitude of variables can grow over the threshold where linear descriptions are valid. Using the method of matched asymptotic expansions, governing equations of dynamics inside the dissipative layer and jump conditions across the dissipative layers are derived. These relations are essential when studying the efficiency of resonant absorption. Nonlinearity in dissipative layers can generate new effects, such as mean flows, which can have serious implications on the stability and efficiency of the resonance.

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