arXiv subjects

Michael Ruderman

Publications and source records attributed to Michael Ruderman.

At least 37 records · Page 2Linked to original sources

arXiv2024

Power based adaptive compensator of output oscillations

Power-based output feedback compensator for oscillatory systems is proposed. The average input-output power of an oscillatory signal serves as an equivalent control effort, while the unknown amplitude and frequency of oscillations are detected at each half-period. This makes the compensator adaptive and discrete, while the measured oscillatory output is the single available signal in use. The resulting discrete control scheme enables a drastic reduction of communication efforts in the control loop. The compensator is designed for 2nd order systems, while an extension to higher-order dynamics, like e.g. in case of two-inertia systems, is also provided. Illustrative experimental case study of the 5th order oscillatory system is provided.

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arXiv2024

Adaptive time delay based control of non-collocated oscillatory systems

Time delay based control, recently proposed for non-collocated fourth-order systems, has several advantages over an observer-based state-feedback compensation of the low-damped oscillations in output. In this paper, we discuss a practical infeasibility of such observer-based approach and bring forward application of the time delay based controller, which is simple in both the structure and design. Moreover, robust estimation of the output oscillation frequency is used and extended by a bias canceling. The latter is required for positioning the oscillatory passive loads. This way, an adaptive version of time delay-based control is realized that does not require prior knowledge of the mass and stiffness parameters. The results are demonstrated on the oscillatory experimental setup with constraints in the operation range and control value.

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arXiv2023

Super-twisting based sliding mode control of hydraulic actuator without velocity state

This paper provides a novel surface design and experimental evaluation of a super-twisting algorithm (STA) based control for hydraulic cylinder actuators. The proposed integral sliding surface allows to track a sufficiently smooth reference without using the velocity state which is hardly accessible in the noisy hydraulic systems. A design methodology based on LMI's is given, and the STA gains are designed to be adjusted by only one free parameter. The feasibility and effectiveness of the proposed control method are shown on a standard hydraulic test bench with one linear degree of freedom and passive load, where a typical motion profile is tracked with a bounded average error below 1 % from the total drive effective output.

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arXiv2023

Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction

The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics e.g. of micro- and nano-positioning instruments and devices and their controlled operation. The associated energy dissipation and consequent convergence of the state trajectories occur due to the structural hysteresis damping of contact surface asperities during reversals, and it is neither exponential (i.e. viscous type) nor finite-time (i.e. Coulomb type). In this paper, we discuss the energy dissipation and convergence during the pre-sliding cycles and show how a piecewise smooth force-displacement hysteresis map enters into the energy balance of an unforced system of the second order. An existing friction modeling approach with a low number of the free parameters, the Dahl model, is then exemplified alongside the developed analysis.

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arXiv2023

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

We consider a robust stabilization of the fourth-order oscillatory systems with non-collocated output sensing. Worth recalling is that the fourth-order systems are relatively common in mechatronics as soon as there are two-mass or more generally two-inertia dynamics with significant elasticities in the link. 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 that leads to 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 the implementation of transfer functions with a numerator degree greater than zero are required to deploy the controller. This comes in favor of practical 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.

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arXiv2023

Robust asymptotic observer of motion states with nonlinear friction

This paper revisits the previously proposed linear asymptotic observer of the motion state variables with nonlinear friction and provides a robust design suitable for both, transient presliding and steady-state sliding phases of the relative motion. The class of motion systems with the only measurable output displacement is considered. The reduced-order Luenberger type observer is designed based on the obtained simplified state-space representation with a time-varying system matrix. The resulted observation error dynamics proves to be robust and appropriate for all variations of the system matrix, which are due to the nonlinear spatially varying friction. A specially designed tribological setup to accurately monitor the relative motion between two contacting friction surfaces is used to collect the experimental data of the deceleration trajectories when excited by a series of impulses. The performance of the state estimation using the proposed observer is shown based on the collected experimental data.

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arXiv2023

Energy-saving sub-optimal sliding mode control with bounded actuation

The second-order sub-optimal sliding mode control (SMC), known in the literature for the last two decades, is extended by a control-off mode which allows for saving energy during the finite time convergence. The systems with relative degree two between the sliding variable and switching control with bounded actuation are considered, while the matched upper-bounded perturbations are not necessarily continuous. Detailed analysis of the proposed energy-saving sub optimal SMC is performed with regard to the parametric conditions, reaching and convergence time, and residual steady oscillations if the parasitic actuator dynamics is added. Constraints for both switching threshold parameters are formulated with respect to the control authority and perturbations upper bound. Based on the estimated finite convergence time, the parameterization of the switching thresholds is solved as constrained minimization of the derived energy cost function. The total energy consuming control-on time is guaranteed to be lower than the upper-bounded convergence time of the conventional sub-optimal SMC. Numerical evaluations expose the properties of the proposed energy-saving sub-optimal SMC and compare it with conventional sub-optimal SMC in terms of the fuel consumption during the convergence.

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arXiv2023

Inversion-free feedforward hysteresis control using Preisach operator

We introduce a new inversion-free feedforward hysteresis control using the Preisach model. The feedforward scheme has a high-gain integral loop structure with Preisach hysteresis operator in negative feedback. This allows obtaining a dynamic quantity which corresponds to the inverse hysteresis output, as the loop error tends towards zero for a sufficiently high feedback gain. By analyzing the loop sensitivity function with hysteresis that acts as a state-varying phase lag, we demonstrate the achievable bandwidth and accuracy of the proposed control method. Remarkable fact is that the control bandwidth is theoretically infinite, provided the Preisach operator in feedback can be implemented in a way to ensure the $\mathcal{C}^0$ continuous hysteresis output. Numerical control examples with the Preisach hysteresis model in differential form are presented.

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arXiv2023

Robust two-degrees-of-freedom control of hydraulic drive with remote wireless operation

In this paper, a controller design targeting the remotely operated hydraulic drive system is presented. A two-degrees-of-freedom PID position controller is used, which is designed so that to maximize the integral action under robust constraint. A linearized model of the system plant, affected by the parameters uncertainties such as variable communication time-delay and overall system gain, is formulated and serves for the control design and analysis. The performed control synthesis and evaluation are targeting the remote operation where the wireless communication channel cannot secure a deterministic real-time of the control loop. The provided analysis of uncertainties makes it possible to ensure system stability under proper conditions. The theoretically expected results are confirmed through laboratory experiments on the standard industrial hydraulic components.

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arXiv2022

Dynamics of inertial pair coupled via frictional interface

Understanding the dynamics of two inertial bodies coupled via a friction interface is essential for a wide range of systems and motion control applications. Coupling terms within the dynamics of an inertial pair connected via a passive frictional contact are non-trivial and have long remained understudied in system communities. This problem is particularly challenging from a point of view of modeling the interaction forces and motion state variables. This paper deals with a generalized motion problem in systems with a free (of additional constraints) friction interface, assuming the classical Coulomb friction with discontinuity at the velocity zero crossing. We formulate the dynamics of motion as the closed-form ordinary differential equations containing the sign operator for mapping both, the Coulomb friction and the switching conditions, and discuss the validity of the model in the generalized force and motion coordinates. The system has one active degree of freedom (the driving body) and one passive degree of freedom (the driven body). We demonstrate the global convergence of trajectories for a free system with no external excitation forces. Then, an illustrative case study is presented for a harmonic oscillator with a frictionally coupled second mass that is not grounded or connected to a fixed frame. This simplified example illustrates a realization and main features of the proposed (general) modeling framework. Some future development and related challenges are discussed at the end of the paper.

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arXiv2022

Motion control with optimal nonlinear damping: from theory to experiment

Optimal nonlinear damping control was recently introduced for the second-order SISO systems, showing some advantages over a classical PD feedback controller. This paper summarizes the main theoretical developments and properties of the optimal nonlinear damping controller and demonstrates, for the first time, its practical experimental evaluation. An extended analysis and application to more realistic (than solely the double-integrator) motion systems are also given in the theoretical part of the paper. As comparative linear feedback controller, a PD one is taken, with the single tunable gain and direct compensation of the plant time constant. The second, namely experimental, part of the paper includes the voice-coil drive system with relatively high level of the process and measurement noise, for which the standard linear model is first identified in frequency domain. The linear approximation by two-parameters model forms the basis for designing the PD reference controller, which fixed feedback gain is the same as for the optimal nonlinear damping control. A robust sliding-mode based differentiator is used in both controllers for a reliable velocity estimation required for the feedback. The reference PD and the proposed optimal nonlinear damping controller, both with the same single design parameter, are compared experimentally with respect to trajectory tracking and disturbance rejection.

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arXiv2022

Analysis of relay-based feedback compensation of Coulomb friction

Standard problem of one-degree-of-freedom mechanical systems with Coulomb friction is revised for a relay-based feedback stabilization. It is recalled that such a system with Coulomb friction is asymptotically stabilizable via a relay-based output feedback, as formerly shown in [1]. Assuming an upper bounded Coulomb friction disturbance, a time-optimal gain of the relay-based feedback control is found by minimizing the derivative of the Lyapunov function proposed in [2] for the twisting algorithm. Furthermore, changing from the discontinuous Coulomb friction to a more physical discontinuity-free one, which implies a transient presliding phase at motion reversals, we analyze the residual steady-state oscillations. This is in the sense of stable limit cycles, in addition to chattering caused by the actuator dynamics. The numerical examples and an experimental case study accompany the provided analysis.

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arXiv2022

Comparison of Fractional-Order and Integer-Order H-infinty Control of a Non-Collocated Two-Mass Oscillator

We consider the robust control of a two-mass oscillator with a dominant input delay. Our aim is to compare a fractional-order tuning approach including the partial compensation of non-minimum phase zeros with a classical H-infinity loop-shaping design, since both these designs lead to a relatively high controller order. First of all a detailed physical model is derived and validated using measurement data. Based on the linearized model both controllers are designed to be comparable, i.e. they show a similar crossover frequency in the open loop and the final controller order is reduced to the same range for both designs. The major differences between both are the different methods how the feed-forward action is included. The loop-shaping approach with fractional-order elements relies on the plant inverse using a flat output, whereas the H-infinty design incorporates a two-degree of freedom control, i.e. the reference signal is included into the known inputs of the generalized plant. Each controller is tested in simulation and experiment. As both open-loops are nearly identical in the frequency range of interest, the results from an input disturbance experiment show no major difference. The different design approaches of the feed-forward path are clearly visible in the tracking experiment.

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arXiv2022

Fractional-Order Partial Cancellation of Integer-Order Poles and Zeros

The key idea of this contribution is the partial compensation of non-minimum phase zeros or unstable poles. Therefore the integer-order zero/pole is split into a product of fractional-order pseudo zeros/poles. The amplitude and phase response of these fractional-order terms is derived to include these compensators into the loop-shaping design. Such compensators can be generalized to conjugate complex zeros/poles, and also implicit fractional-order terms can be applied. In the case of the non-minimum phase zero, its compensation leads to a higher phase margin and a steeper open-loop amplitude response around the crossover frequency resulting in a reduced undershooting in the step-response, as illustrated in the numerical example.

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arXiv2021

One-parameter robust global frequency estimator for slowly varying amplitude and noisy oscillations

Robust online estimation of oscillation frequency belongs to classical problems of system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as in the case of damped vibrations. A novel robust frequency-estimation algorithm is proposed here, motivated by the existing globally convergent frequency estimator. The advantage of the proposed estimator is in requiring one design parameter only and being robust against measurement noise and initial conditions. The proven global convergence also allows for slowly varying amplitudes, which is useful for applications with damped oscillations or additionally shaped harmonic signals. The proposed analysis is simple and relies on an averaging theory of the periodic signals. Our results show an exponential convergence rate, which depends, analytically, on the sought frequency, adaptation gain and oscillation amplitude. Numerical and experimental examples demonstrate the robustness and efficiency of the proposed estimator for signals with slowly varying amplitude and noise.

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arXiv2021

Stick-slip and convergence of feedback-controlled systems with Coulomb friction

An analysis of stick-slip behavior and convergence of trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an invariant equilibrium set, is proved to be always reachable and globally attractive. It is shown that only asymptotic convergence can be achieved, with at least one but mostly an infinite number of consecutive stick-slip cycles, independent of the initial conditions. Theoretical developments are supported by a number of numerical results with dedicated convergence examples.

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arXiv2021

Convergent dynamics of optimal nonlinear damping control

Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking of $\mathcal{C}^1$-trajectories, it is shown that all solutions of the control system are globally uniformly asymptotically stable. The existence of the unique limit solution in the origin of the control error and its time derivative coordinates are shown in the sense of Demidovich's convergent dynamics. Explanative numerical examples are also provided along with analysis.

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arXiv2021

Optimal terminal sliding-mode control for second-order motion systems

Terminal sliding mode (TSM) control algorithm and its non-singular refinement have been elaborated for two decades and belong, since then, to a broader class of the finite-time controllers, which are known to be robust against the matched perturbations. While TSM manifold allows for different forms of the sliding variable, which are satisfying the $q/p$ power ratio of the measurable output state, we demonstrate that $q/p=0.5$ is the optimal one for the second-order Newton's motion dynamics with a bounded control action. The paper analyzes the time-optimal sliding surface and, based thereupon, claims the optimal TSM control for the second-order motion systems. It is stressed that the optimal TSM control is fully inline with the Fuller's problem of optimal switching which minimizes the settling time, i.e. with time-optimal control of an unperturbed double-integrator. Is is also shown that for the given plant characteristics, i.e. the overall inertia and control bound, there is no need for additional control parameters. The single surface design parameter might (but not necessarily need to) be used for driving system on the boundary layer of the twisting mode, or for forcing it to the robust terminal sliding mode. Additional insight is given into the finite-time convergence of TSM and robustness against the bounded perturbations. Numerical examples with different upper-bounded perturbations are demonstrated.

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