arXiv subjects

Michael Ruderman

Publications and source records attributed to Michael Ruderman.

At least 19 recordsLinked to original sources

arXiv2026

Adaptive differentiating filter: case study of PID feedback control

This paper presents an adaptive causal discrete-time filter for derivative estimation, exemplified by its use in estimating relative velocity in a mechatronic application. The filter is based on a constrained least squares estimator with window adaptation. It demonstrates low sensitivity to low-amplitude measurement noise, while preserving a wide bandwidth for large-amplitude changes in the process signal. Favorable performance properties of the filter are discussed and demonstrated in a practical case study of PID feedback controller and compared experimentally to a standard linear low-pass filter-based differentiator and a robust sliding-mode based homogeneous differentiator.

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arXiv2026

On Cauchy problem and stability of inversion-free feedforward control of piecewise monotonic Krasnoselskii-Pokrovskii hysteresis

We consider the non-homogeneous first-order differential equation with hysteresis described by the Krasnoselskii-Pokrovskii rate-independent hysteresis operator. Existence and uniqueness of solutions as well as the boundedness of solution in response to a bounded input are proved. The global stability of the equation is also investigated. Periodic solutions and their stability are studied in addition. The differential equation under analysis constitutes the so-called inversion-free feedforward control, which was proposed for mitigating arbitrary rate-independent hysteresis effects in the actuated systems. The experimentally identified non-smooth and non-strictly monotonic hysteresis of a magnetic shape memory alloy (MSMA) actuator serves as the case study. The performed analysis is settled in a series of theorems which are illustrated by numerical examples.

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arXiv2025

Modified global finite-time quasi-continuous second-order robust feedback control

A non-overshooting quasi-continuous sliding mode control with sub-optimal damping was recently introduced in Ruderman and Efimov (2025) for perturbed second-order systems. The present work proposes an essential modification of the nonlinear control law which (i) allows for a parameterizable control amplitude limitation in a large subset of the initial values, (ii) admits an entire state-space R2 (that was not given in Ruderman and Efimov (2025)) for the finite-time control, and finally (iii) enables for the found analytic solution of the state trajectories in the unperturbed case. The latter allows also for an exact estimation of the finite convergence time, and open an avenue for other potentially interesting analysis of the control properties in the future. For a perturbed case, the solution-based and Lyapunov function-based approaches are developed to show the uniform global asymptotic stability. The proposed robustness and convergence analysis are accompanied by several illustrative numerical examples.

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arXiv2025

Model-free practical PI-Lead control design by ultimate sensitivity principle

Practical design and tuning of feedback controllers has often to get by without a model of the dynamic process at hand. Only some general assumptions about the system dynamics, in this work type-one stable, can be available for engineers, for instance in motion control applications and many others. This paper proposes a practical and simple in realization procedure for designing a robust PI-Lead control without modeling. The developed method derives from the ultimate sensitivity principles, known in empirical Ziegler-Nichols tuning of PID controllers, and makes use of some general characteristics of the loop shaping. A three-steps procedure is proposed to determine the integration time constant, control gain, and Lead-element in a way to guarantee a sufficient phase margin, while all steps are served by only experimental monitoring of the output value. Proposed method is demonstrated and discussed with experiments accomplished on a noise-perturbed electro-mechanical actuator system.

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arXiv2025

Comparison of linear observation techniques for robust load torque estimation in actuators

The paper addresses the problem of estimating robustly the external load torque in rotary actuator systems, when only the generated motor drive torque and angular displacement are the available input and output. We compare, theoretically and experimentally, two sufficiently established linear observation techniques (i) reduced-order Luenberger observer and (ii) disturbance observer, both using the same identified model of a permanent magnet synchronous motor (PMSM)-based actuator. Our goal is to highlight several aspects related to the implementation, relative degree of the input-torque to estimated-load-torque transfer characteristics, observer open-loop transfer function, and the associated sensitivity (respectively stability margins) with respect to inherently uncertain system plants. Apart from the developed analysis, a detailed experimental case study is demonstrated where the load torque sensor provides reference measurements and allows for evaluation of both observers.

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arXiv2025

Robust Synchronous Reference Frame Phase-Looked Loop (PLL) with Feed-Forward Frequency Estimation

Synchronous reference frame phase-locked loop (SRF-PLL) techniques are widely used for interfacing and control applications in the power systems and energy conversion at large. Since a PLL system synchronizes its output with an exogenous harmonic signal, often 3-phases voltage or current, the locking of the frequency and phase angle depends on the performance of the feedback loop with at least two integrator terms, and on the distortions of the measured input quantities. For the conventional SRF-PLL with a proportional-integral (PI) control in feedback, we are providing a robust design which maximizes the phase margin and uses the normalization scheme for yielding the loop insensitive to the input amplitude variations. The main improvement in the transient behavior and also in tracking of frequency ramps is achieved by using the robust feed-forward frequency estimator, which is model-free and suitable for the noisy and time-varying harmonic signals. The proposed feed-forward-feedback SRF-PLL scheme is experimentally evaluated on the 3-phases harmonic currents from a standard PMSM drive with the varying angular speeds and loads. Both, the tracked angular frequency and locked phase angle are assessed as performance indicators of the proposed SRF-PLL with feedforwarding.

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arXiv2025

Regularization of non-overshooting quasi-continuous sliding mode control for chattering suppression at equilibrium

Robust finite-time feedback controller introduced for the second-order systems in [1] can be seen as a non-overshooting quasi-continuous sliding mode control. The paper proposes a regularization scheme to suppress inherent chattering due to discontinuity of the control [1] in the origin, in favor of practical applications. A detailed analysis with ISS and iISS proofs are provided along with supporting numerical results.

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arXiv2025

Design and Application of Energy-saving Sub-Optimal Sliding Mode Control

The recently introduced energy-saving extension of the sub-optimal sliding mode control (SOSMC), which is known in the literature for the last two and half decades, incorporates a control-off mode that allows for saving energy during the finite-time convergence process. This novel energy-saving algorithm (denoted by ES-SOSMC) assumes the systems with relative degree two between the sliding variable and the switching control with a bounded magnitude, while the matched upper-bounded perturbations are not necessarily continuous. The design and practical application of the ES-SOSMC are the subject of this chapter. A method for parameterizing the ES-SOSMC through a constrained minimization of the energy cost function is recalled which guarantees the total energy consumption is lower than that of the conventional SOSMC. Also the residual steady-state oscillations (chattering), occurring when additional (actuator) dynamics are taken into account, are addressed. An application example for scanning and machining a rough surface, both of which require a stiff position control in contact with a moving surface, demonstrates practical suitability of the control. Here, ES-SOSMC is compared with SOSMC by showing an equivalent tracking and stabilization performance and evaluating the energy-saving operation with respect to a fuel consumption norm.

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arXiv2025

Reduced-order asymptotic observer of nonlinear friction for precise motion control

Nonlinear friction has long been, and continues to be, one of the major challenges for precision motion control systems. A linear asymptotic observer of the motion state variables with nonlinear friction uses a dedicated state-space representation of the dynamic friction force (including pre-sliding) [25], which is robust to the noisy input signals. The observer implements the reduced-order Luenberger observation law, while assuming the output displacement is the only available measurement. The latter is relevant for multiple motion control applications with use of encoder-type sensors. The uniform asymptotic stability and convergence analysis of the proposed observer are elaborated in the present work by using the Lyapunov function-based stability criterion by Ignatyev and imposing parametric constraints on the time-dependent eigenvalues of the system matrix to be always negative real. A design procedure for assigning a dominant, and thus slowest, real pole of the observer is proposed. Explanative numerical examples accompany the developed analysis. In addition, a thorough experimental evaluation is given for the proposed observer-based friction compensation which is performed for positioning and tracking tasks. The observer-based compensation, which can serve as a plug-in to a standard feedback controller, extends a PID feedback control that is optimally tuned for disturbance suppression. The experimental results are compared with and without the plugged-in observer-based compensator.

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arXiv2025

Power-based control of output oscillations with online estimation of biased harmonics

The recently introduced discrete power-based control (Ruderman (2024b)) reduces largely the communication efforts in the control loop when compensating for the marginally damped or even slowly diverging output oscillations. The control commutates twice per oscillations period (at the amplitude peaks) and uses the measured harmonic output only. The power-based control scheme requires the knowledge of the instantaneous frequency, amplitude, and bias parameters of the harmonic signal. This paper extends the power-based control by the finite-time estimation of the biased harmonics (Ahmed et al. (2022)). Also an improved analytic calculation of the impulse weighting factor is provided. The power-based oscillations control with online estimation of the harmonic parameters is evaluated experimentally on the fifth-order actuator system with a free hanging load under gravity and measurement noise.

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arXiv2025

Inversion-free feed-forward and feedback control of MSM based actuator with large non-smooth input hysteresis

Dynamic systems with a large and non-smooth hysteresis in the feedforward channel challenge the design of feedback control since the instantaneous input gain is varying during the operation, in the worst case between zero and infinity. Magnetic shape memory (MSM) actuators with multi-stable transitions represent such untypical system plant with only the output displacement being measured. This paper provides a case study of designing the feedforward and feedback control system for an MSM-based actuator setup with a fairly high level of the output sensing noise. First, the recently introduced inversion-free feedforward hysteresis compensator is adapted for the Krasnoselskii-Pokrovskii operator model. Then, a robust feedback proportional-integral (PI) loop shaping is performed, while taking into account the lagging behavior of the low-pass filtering and system uncertainties. Experimental results show that the parallel action of feedforward and feedback parts improves the overall performance of position control.

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arXiv2025

Study of Frictional and Impact Transients in Active-Passive Mechanical Pair

We consider an active-passive mechanical pair in which the relative motion of the latter is constrained by the mechanical impact. The system dynamics is described by the previously introduced modeling frameworks of force transition and dissipation through the nonlinear Coulomb friction and structural damping, the later in accord with Hertzian contact theory. The focus of the recent study is on combining both interaction mechanisms, and the detailed experimental evaluation which discloses validity of the modeling assumptions. Such mechanical pair interactions can be found in various mechatronic systems and mechanisms, like for example clutches, backlash elements, sliding items on the shaking and inclining surfaces, conveyor belts and others. This practical study demonstrates and discusses the transients of a vibro-impact dynamics and shows theoretical developments in line with experimental evaluation.

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arXiv2024

Loop Shaping of Hybrid Motion Control with Contact Transition

A standard motion control with feedback of the output displacement cannot handle unforeseen contact with environment without penetrating into the soft, i.e. viscoelastic, materials or even damaging the fragile materials. Robotics and mechatronics with tactile and haptic capabilities, and in particular medical robotics for example, place special demands on the advanced motion control systems that should enable the safe and harmless contact transitions. This paper shows how the basic principles of loop shaping can be easily used to handle sufficiently stiff motion control in such a way that it is extended by sensor-free dynamic reconfiguration upon contact with the environment. A thereupon based hybrid control scheme is proposed. A remarkable feature of the developed approach is that no measurement of the contact force is required and the input signal and the measured output displacement are the only quantities used for design and operation. Experiments on 1-DOF actuator are shown, where the moving tool comes into contact with grapes that are soft and simultaneously penetrable.

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arXiv2024

Experimental Benchmarking of Energy-saving Sub-Optimal Sliding Mode Control

The recently introduced energy-saving extension of the sub-optimal sliding mode control allows for control-off phases during the convergence to second-order equilibrium. This way, it enables for a lower energy consumption compared to the original sub-optimal sliding mode (SM) algorithm, both commutating a discontinuous control signal. In this paper, the energy-saving sub-optimal SM control is experimentally benchmarked against a standard second-order SM controller which also has a discontinuous control action. Here the so-called terminal second-order SM algorithm is used. The controlled plant is affected by the matched bounded disturbances which are unknown, and the output is additionally subject to the sensor noise. Moreover, a first-order actuator dynamics can lead to chattering, which is parasitic for SM applications. For a fair comparison, the same quadratic terminal surface is designed when benchmarking both SM controllers. Both experimentally compared SM algorithms have the same (bounded) control magnitude and states initial conditions.

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arXiv2024

Non-overshooting continuous in convergence sliding mode control of second-order systems

This paper proposes a novel nonlinear sliding mode state feedback controller for perturbed second-order systems. In analogy to a linear proportional-derivative (PD) feedback control, the proposed nonlinear scheme uses the output of interest and its time derivative. The control has only one free design parameter, and the closed-loop system is shown to possess uniform boundedness and finite-time convergence of trajectories in the presence of matched disturbances. We derive a strict Lyapunov function for the closed-loop control system with a bounded exogenous perturbation, and use it for both, the control parameter tuning and analysis of the finite-time convergence. The essential features of the proposed new control law is non-overshooting despite the unknown dynamic disturbances and the continuous control action during the convergence to zero equilibrium. Apart from the numerical results, a revealing experimental example is also shown in favor of the proposed control and in comparison with PD and sub-optimal nonlinear damping regulators.

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arXiv2024

Nonlinear integral extension of PID control with improved convergence of perturbed second-order dynamic systems

Nonlinear extension of the integral part of a standard proportional-integral-derivative (PID) feedback control is proposed for perturbed second-order systems. The approach is model-free and requires solely the Lipschitz boundedness of the unknown matched perturbations. For constant disturbances, the global asymptotic stability is shown based on the circle criterion. For Lipschitz perturbations, an ultimately bounded output error is provided based on the steady-state behavior in frequency domain. Also the transient response to the stepwise disturbances is analyzed for the control tuning. Based on the developed analysis, the design recommendations are formulated as a step by step procedure. It is also discussed how the proposed control is applicable to second-order systems extended by additional (parasitic) actuator dynamics with low-pass characteristics. The proposed nonlinear control is proven to outperform its linear PID counterpart during the settling phase, i.e. at convergence of the residual output error. An experimental case study of the second-order system with an additional actuator dynamics and considerable perturbations is demonstrated to confirm and benchmark the control performance.

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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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arXiv2023

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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