Michael Ruderman

Michael Ruderman, Elia Brescia, Paolo Roberto Massenio et al.

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.

Michael Ruderman

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.

Michael Ruderman, Shota Yamada, Hiroshi Fujimoto

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.

Michael Ruderman

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.

Alexey Pavlov, Michael Ruderman

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.

Michael Ruderman

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.

Michael Ruderman

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.

Michael Ruderman

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.

Michael Ruderman

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.

Michael Ruderman

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.