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.

On Switching between Motion and Force Control

In motion control technologies, an automatic switching between trajectory following and set reference force, upon the impact, is a frequently encountered requirement. Despite both, motion and force controls, are something of well-understood and elaborated in the control theory and engineering practice, a reliable switching between them is not always self-evident. It can lead to undesired deadlocks, limit cycles, chattering around switching point and, as consequence, to wearing or damages in the controlled plant and its environment. This paper contributes to analysis and understanding of the autonomous switching from the motion to force control and vice versa. Simple output and state feedbac…

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 a…

Modeling of an active torsion bar automotive suspension for ride comfort and energy analysis in standard road profiles

Abstract Chassis technology is evolving towards active suspension, in which actuators can provide forces to each wheel individually. This overcomes the traditional trade-off between comfort and handling, at the expense of increased complexity and electric consumption. To reduce power demand, regenerative solutions capable of harvesting a certain amount of energy otherwise dissipated in vehicle suspensions and to enhance vehicle dynamics for improving ride comfort and road safety at the same time have been researched. In this paper, an active suspension based on a torsion bar is modeled and analyzed under the excitation from standardized road profiles according to the ISO 8608 norm. A skyhoo…

Guest Editorial Special Section on Recent Trends and Developments in Industry 4.0 Motivated Robotic Solutions

The twelve papers in this special section focus on the development of robotic solutions for smart factories in industry - the concept of the fourth industrial revolution (industry 4.0). The inclusion of robotics is expected to deeply change the future manufacturing and production processes, and lead to smart factories that will benefit from the main design principles of Industry 4.0: interoperability, virtualization, decentralization, real-time capability, service orientation, and modularity. Robotics will have a key role in this development since innovative technologies and solutions, traditionally associated with the service robotics sector, are going to migrate to industrial smarter robo…

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.

Experimental framework of traveling trolley with swinging load for hybrid motion control

A novel experimental framework of the traveling trolley with swinging load is proposed. The system is designed as a controlled moving cart with pendulum for investigation of the hybrid motion control methods, involving the discrete sensors and impulsive event-based state observations and control actions. A mechatronic approach of principal system design, modeling, and identification are provided together with a motion control of the cart and simple event-based control of a-priori unknown final position. The coupled motion dynamics is analyzed and evaluated by using the discrete sensors, along with the control results.

Use of second-order sliding mode observer for low-accuracy sensing in hydraulic machines

Low-accuracy sensing is very common for the large hydraulic machines and does not allow for directly measuring the relative velocity which can be, otherwise, required for the control and monitoring purposes. This paper provides a case study of designing the second-order sliding mode observer based on the super-twisting robust exact differentiator. The nominal part of the system dynamics is derived from the simple available system measurements and incorporated into the observer structure. Parasitic by-effects, arising from the sensor sampling, quantization, and non-modeled distortions due to mechanical sensor interface, are shown as the main causes of hampering the final (steady-state) conve…

Dissipation in suspension system augmented by piezoelectric stack: port-Hamiltonian approach

Analysis of damping in semi-active and active suspension systems is prerequisite for an advanced control and, eventually, energy harvesting functions. This paper addresses the damping in suspension system augmented by the piezoelectric (PE) stack. The Hamiltonian system approach with port-power modeling of single subsystems is used for describing and studying the dissipative properties of piezoelectric stack element, integrated in series with a standard quarter-car suspension. The slightly improved, compared to the underlying passive suspension system, frequency response of the sprung mass acceleration is demonstrated. Moreover, the overall power flow in the system, caused by the disturbing…

Design and analysis of non-linear circuit with tunnel diode for hybrid control systems

Electric circuits with tunnel diode's represent a classical example of dynamic systems with nonlinearities, which feature piecewise negative damping and multiple equilibria and, as consequence, nontrivial trajectories in the state-space. In this paper, we describe the experimental design and analysis of an electrical circuit, including a tunnel diode, allowing for a storage behavior with bistable output voltage states - low and high. The system is modeled for simulation and an experimental setup is designed and implemented in order to run a formal verification on different tools, applying a variety of hybrid control methods. The nonlinear diode's characteristic curve is experimentally deter…

Comparison of Fractional-Order and Integer-Order H-infinity 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∞ 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 line arized 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-forw…

On energy harvesting using piezoelectric transducer with two-port model under force excitation

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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 varyin…

Design, Control, and Analysis of Nonlinear Circuits with Tunnel Diode with Piecewise Affine Dynamics

Analysis of Linear Feedback Position Control in Presence of Presliding Friction

Identification and control design for path tracking of hydraulic loader crane

The controlled operation of hydraulic machines with multiple degrees of freedom is challenging due to complex nonlinear dynamics of cylinder actuators, in addition to multibody dynamics like in the case of hydraulic manipulators. This paper addresses the system identification and control design for path tracking of a standard hydraulic loader crane. The kinematics of the crane is solved for operation in the vertical plane and generation of trajectories for the tool tip to be followed. A frequency response measurements and analysis have been done for dynamics modeling of both hydraulic cylinders actuating main boom and jib. The static dead-zone type input non-linearity has been identified an…

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.

Linearized Piecewise Affine in Control and States Hydraulic System: Modeling and Identification

In this paper, the modeling and identification of a nonlinear actuated hydraulic system is addressed. The full-order model is first reduced in relation to the load pressure and flow dynamics and, based thereupon, linearized over the entire operational state-space. The dynamics of the proportional control valve is identified, analyzed, and intentionally excluded from the reduced model, due to a unity gain behavior in the frequency range of interest. The input saturation and dead-zone nonlinearities are considered while the latter is identified to be close to 10% of the valve opening. The mechanical part includes the Stribeck friction detected and estimated from the experiments. The lineariza…

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, a…

On Stability of Virtual Torsion Sensor for Control of Flexible Robotic Joints with Hysteresis

Author's accepted manuscript (postprint). This article has been published in a revised form in Robotica, http://doi.org/10.1017/S0263574719001358. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © 2019 Cambridge University Press. Available from 25/03/2020. Aim of the virtual torsion sensor (VTS) is in observing the nonlinear deflection in the flexible joints of robotic manipulators and, by its use, improving positioning control of the joint load. This model-based approach utilizes the motor-side sensing only and, therefore, replaces the load-side encoders at nearly zero hardware costs. For being applied in the closed control …

Hybrid State Feedback Position-Force Control of Hydraulic Cylinder

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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.

Frequency-domain experimental setup for mechatronic and suspension system components

This paper presents a frequency-domain experimental setup for modal analysis of mechatronic and suspension system components. Design, instrumentation and dynamic behavior of the one degree-of-freedom (DOF) system, capable of providing both, periodic and application-specific, excitation forces is described. The excitation is realized by an electromagnetic modal shaker with additional assembly and interface components designed and instrumented for frequency -domain analysis of vertical dynamics. Frequency response functions (FRFs) of the implemented system are experimentally measured and the associated basic model parameters are calculated, correspondingly identified. Accurate fit between the…

Discrete-Time Adaptive Hysteresis Filter for Parallel Computing and Recursive Identification of Preisach Model

High-precision motion control systems, for instance deployed for micro- and nano-positioning, often use the smart-material based actuators such as piezoelectric and magnetostrictive stages. Those exhibit inherent hysteresis nonlinearities which are challenging to compensate without precise hysteresis modeling. Even if a suitable hysteresis modeling approach is available, its parameter identification, correspondingly adaptation, at normal operating conditions constitute an essential task for the overall control design. This paper uses the direct recursive identification method for the Preisach hysteresis model and describes the fast parallel-computing discrete-time algorithm for an adaptive …

A Fractional-Order Control Approach to Ramp Tracking with Memory-Efficient Implementation

We investigate the fractional-order (FO) control of arbitrary order LTI systems. We show that, for ramp tracking or input disturbance rejection, it is advantageous to include an FO integrator to the open-loop if we have to increase the order of integration further than one. With the lower phase-loss of the FO integrator it is easier to guarantee a desired phase margin. Furthermore the flat phase response around the crossover-frequency (iso-damping property) can be achieved for a wider frequency range such that the closed-loop is more robust wrt. amplitude and phase margins. The drawback of the FO approach is the increased implementation effort and the algebraic decay, which slows down the t…

Integral Control Action in Precise Positioning Systems with Friction

Abstract For high precision positioning systems a fast and accurate settling to the reference state is most significant and, at the same time, challenging from the control point of view. Traditional use of an integral coaction in feedback can attain a desired reference tracking at steady-state motion, but can fail in case of precise positioning. Most crucial is that this is independent on how accurate the integral control part is tuned. This paper addresses the feedback control action in precise positioning systems with friction. Analyzing the closed-loop control dynamics with nonlinear friction in feedback it is shown why the integral action cannot efficiently cope with Coulomb friction wh…

Convergence of direct recursive algorithm for identification of Preisach hysteresis model with stochastic input

We consider a recursive iterative algorithm for identification of parameters of the Preisach model, one of the most commonly used models of hysteretic input-output relationships. The classical identification algorithm due to Mayergoyz defines explicitly a series of test inputs that allow one to find parameters of the Preisach model with any desired precision provided that (a) such input time series can be implemented and applied; and, (b) the corresponding output data can be accurately measured and recorded. Recursive iterative identification schemes suitable for a number of engineering applications have been recently proposed as an alternative to the classical algorithm. These recursive sc…

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 incipien…

Motion-control techniques of today and tomorrow: a review and discussion of the challenges of controlled motion

Motion-control technologies are at the core of multiple mechatronic products and applications. Wherever actuated motion takes place in machines and components, either position or force setting (or trajectory tracking), or even a combination of both, are demanded from the control system. In high-performance mechatronic systems, including micro- and/or nanoscale motion (such as data-storage devices, machine tools, manufacturing tools for electronics components, and industrial robots), the required specifications in motion performance, such as response/settling time and trajectory/settling accuracy, should be sufficiently achieved [1].

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 appli…

Modeling and field-experiments identification of vertical dynamics of vehicle with active anti-roll bar

This paper deals with modeling and identification of vertical dynamics of the ground vehicle equipped with two active anti-roll torsion bars. A series of field tests of a full-scale drive have been performed, from which multiple displacement and acceleration data of the unsprung and sprung masses have been collected for each vehicle corner. The standard full vertical vehicle model is extended by the developed model of an active anti-roll torsion bar and valve-controlled semi-active shock absorbing damper. Along with the three-dimensional damping map, the nonlinear progressive stiffness of the elastomer-based decoupling unit are identified from the available data. The multi-channel and multi…

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 on…

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 mo…

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 pa…

Creep Modeling with Time-Dependent Damping Parameters in Piezoelectric Actuators

This paper develops a creep model based on the Kelvin-Voigt model with time varying damping parameters. In the piezoelectric actuators, the creep phenomenon is an important issue in precise positioning applications as well as the hysteresis property. It is well-known that the creep effect can be represented by a series connection of a number of Kelvin-Voigt elements as a viscoelastic model. In the motion for the continuous stepwise positioning, however, the creep shape is different for each response. Since the phenomenon can be captured as temporal creep relaxation, time-dependent damping parameters are introduced to improve the reproducibility of the creep for the various motion. On the ot…

Stability Analysis of a Linear Parameter Varying Adaptive Output Feedback Control System

Abstract Output feedback control systems often require an adaptive filter for properly shaping the loop transfer function, as certain system plant parameters may be uncertain or varying. This renders the overall closed loop to a linear parameter varying (LPV) system, for which the stability analysis is challenging due to non-trivial dynamics of the adaptation law. This paper develops a stability analysis technique of a feedback controlled oscillatory system. A polytopic overapproximation of the parameter set together with the feasibility of certain LMIs guarantees asymptotic stability of the closed loop. The varying filter parameter is only required to be lower and upper bounded, where the …

Pressure-flow dynamics with semi-stable limit cycles in hydraulic cylinder circuits

In hydraulic circuits of the standard fluid-power actuators and mechanisms, like the linear-stroke cylinders, some hydrodynamic effects are often neglected. It happens mainly due to their complexity and secondariness in comparison with the principal transient and steady-state behavior of the hydromechanical process variables, such as the differential pressure and relative displacement and its rate, in other words the piston stroke and velocity. However, a constrained motion of the cylinder piston can give rise to the back coupled excitation of the pressure-flow dynamics, especially upon mechanical impact at the cylinder limits. Following to that, semi-stable limit cycles can arise while the…

Virtual sensing of load forces in hydraulic actuators using second- and higher-order sliding modes

Abstract External load forces are challenging for sensing or estimating in the hydraulic actuators. Once it is due to inconvenient instrumentation of the force sensors, especially on an open-end mechanical interface. The other way, the complex nonlinear system behavior aggravates reconstructing the system states in a robust and real-time suitable manner. This paper proposes a sensorless estimation of external load forces in standard hydraulic actuators by using a well-established equivalent output injection of the second-order sliding mode and also higher-order sliding mode differentiator. Only the basic inertial and frictional parameters are assumed to be known from an initial identificati…

Minimal-model for robust control design of large-scale hydraulic machines

Hydraulic machines are in use where the large forces, at relatively low velocities, are required by varying loads and often hazardous and hard-to-reach environments, like e.g. offshore, mining, forestry, cargo logistics, and others industries. Cranes and excavators equipped with multiple hydraulic cylinders are typical examples for that. For design of the robust feedback controls of hydraulic cylinders, already installed into large-scale machines, there is a general lack of reliable dynamic models. Also the suitable and feasible identification techniques, especially in frequency domain, yield limited. This paper pro­poses a minimal-modeling approach for determining the most relevant open-lo…

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…

Fractional-Order System Identification of Viscoelastic Behavior: A Frequency Domain Based Experimental Study

In this work, the fractional-order modeling of viscoelastic behavior is investigated based on measurement data in the frequency domain. For the results of two different test setups we apply existing parameter estimation algorithms designed for fractional-order transfer functions. These algorithms require a priori knowledge of the system structure including the commensurate order of differentiation. An iterative procedure is used to evaluate the influence of the unknown structure. The measured polymer samples show a viscoelastic stress response. We can show that integer-order models are not capable of capturing this behavior. For a set of predefined structures, the best obtained fractional-o…

On stability and robustness of Virtual Torsion Sensor (VTS) for flexible joint robots

The so called ‘Virtual Torsion Sensor’ (VTS) has been introduced in pervious works for flexible joint robots without sensing of the joint output states, i.e. link position and velocity. Since VTS is incorporated into the feedback control loop, so as to improve the links' positioning accuracy, the related stability is crucial for the overall control design and robust operation of VTS. In this paper, we analyze the stability of including VTS into the feedback loop while assuming the predicted joint torsion is gained by the proportional term of the underlying motor position feedback control. We start our consideration by an ideal case of the linear joint stiffness, first assuming the measured …

Asymptotic observer of the link states of flexible joint robots with motor-side sensing

This paper proposes an approach for observing the link states, i.e. angular position and velocity, of the robotic joints with elasticities, when only the motor-side sensing is available. By separating the state-dependent nonlinearities of the rigid manipulator dynamics a linear sub-model of the elastic joint robot is obtained in an observable state-space form. The standard asymptotic Luenberger state observer is then designed for the given motor position signal which is measured by encoder and rectified from the nonlinear contribution. The configurable poles of observer allow shaping the estimated states dynamics to be fast enough in relation to the actual resonant joint behavior. Therefore…

Model-Free Sliding-Mode-Based Detection and Estimation of Backlash in Drives With Single Encoder

Backlash is a frequently encountered problem for various drives, especially those equipped with a single encoder onside of the controlled actuator. This brief proposes a sliding-mode differentiator-based estimation of unknown backlash size while measuring the actuator displacement only. Neither actuator nor load dynamics are explicitly known, while a principal second-order actuator behavior is assumed. We make use of the different perturbation dynamics distinctive for different backlash modes and an unbounded impulse-type perturbation at impact. The latter leads to transient loss of the sliding-mode and allows for detecting an isolated time instant of the backlash occurrence. The proposed m…

Use of Prandtl-Ishlinskii hysteresis operators for Coulomb friction modeling with presliding

Prandtl-Ishlinskii stop-type hysteresis operators allow for modeling elasto-plasticity in the relative stress-strain coordinates including the saturation level of the residual constant-tension flow. This lies in direct equivalence to the force-displacement characteristics of nonlinear Coulomb friction, whose constant average value at unidirectional motion depends on the motion sign only, after the transient presliding phase at each motion reversal. In this work, we analyze and demonstrate the use of Prandtl-Ishlinskii operators for modeling the Coulomb friction with presliding phase. No viscous i.e. velocity-dependent component is considered at this stage, and the constant damping rate of t…

Impulse-based Discrete Feedback Control of Motion with Damping Uncertainties

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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 mot…

Interdisciplinary design methodology for systems of mechatronic systems focus on highly dynamic environmental applications

This paper discusses a series of research challenges in the design of systems of mechatronic systems. A focus is given to environmental mechatronic applications within the chain “Renewable energy production — Smart grids — Electric vehicles”. For the considered mechatronic systems, the main design targets are formulated, the relations to state and parameter estimation, disturbance observation and rejection as well as control algorithms are highlighted. Finally, the study introduces an interdisciplinary design approach based on the intersectoral transfer of knowledge and collaborative experimental activities.

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 identif…

On damping characteristics of frictional hysteresis in pre-sliding range

Frictional hysteresis at relative motion in the pre-sliding range is considered. This effect is characterized by an elasto-plastic interaction, and that on the micro-scale, between two rubbing surfaces in contact that gives rise to nonlinear friction force. The pre-sliding friction force yields hysteresis in displacement. In this study, the damping characteristics of frictional hysteresis are analyzed. It is worth noting that we exclude the viscous damping mechanisms and focus on the pure hysteresis damping to be accounted in the friction modeling. The general properties of pre-sliding friction hysteresis are demonstrated and then compared with the limit case of discontinuous Coulomb fricti…

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 ste…

Relay feedback systems - established approaches and new perspectives for application

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Energy harvesting using piezoelectric transducers for suspension systems

Abstract Energy harvesting by using functional materials in suspension systems bear potential to win-back certain (even if low) amounts of vibrational energy, otherwise dissipated via the conventional (passive) dampers. Piezoelectric (PE) ceramics are functional materials that can be used for transforming mechanical energy into electrical and vice versa. In this paper, we study the capabilities and efficiency of energy harvesting (EH) with PE transducers under two different kinds of external excitation: i) Periodic and ii) stochastic. An appropriate nonlinear lumped parameter electromechanical model (LPEM) is brought into the two-port network notation. Laboratory experiments were conducted …

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. Experiment…

Piecewise Affine (PWA) Modeling and Switched Damping Control of Two-Inertia Systems with Backlash

Backlash degrades positioning accuracy and can induce mechanical wear and breakage by collisions. Therefore, a lot of studies have been conducted on backlash compensation. The simplest control method for the impact attenuation is torsional damping addition by feedback of torsional velocity. This paper reveals the advantages and disadvantages of the torsional damping addition. Based on the analyses, a novel switched damping control is proposed to realize the responses with smaller overshoot while attenuating the impact. The mechanical system and the proposed controller are described as piecewise affine systems for analyses. The performance of the proposed method is compared with a linear dam…

On Energy Harvesting Using Piezoelectric Transducer with Two-Port Model Under Force Excitation

Piezoelectric (PE) materials are functional materials that can be used for transforming mechanical stress into electrical energy, that can then be stored and used for powering other devices. In this paper, we provide experimental investigation of PE transducers used for energy harvesting under external force-controlled excitation. The lumped parameter electromechanical model (LPEM) has been assumed and brought into a generalized two-port network notation. Laboratory experiments using a universal test machine (UTM) were performed and used for the parameter identification of the model. The two-port model formulation is validated by comparing results of numerical simulations and experimental d…

Integral Control Action in Precise Positioning Systems with Friction

- For high precision positioning systems a fast and accurate settling to the reference state is most significant and, at the same time, challenging from the control point of view. Traditional use of an integral coaction in feedback can attain a desired reference tracking at steady-state motion, but can fail in case of precise positioning. Most crucial is that this is independent on how accurate the integral control part is tuned. This paper addresses the feedback control action in precise positioning systems with friction. Analyzing the closed-loop control dynamics with nonlinear friction in feedback it is shown why the integral action cannot efficiently cope with Coulomb friction which bec…

Guest Editorial: Advanced Motion Control for Mechatronic Applications With Precision and Force Requirements

The articles in this special section focus on advanced motion control for mechatronic applications with precision and force requirements. Motion control is concerned with all the issues arising in the control of the movement of a physical device. This means that MC is not limited to the use of proper devices for sensing and actuation, in addition to suitable control algorithms, but it also deals with all the possible interactions of the controlled devices with the environment. This is the most remarkable aspect of MC, nowadays deployed in numerous mechatronic systems, especially those which are dynamically acting in heterogenous, time-varying, active, and human-accessible environments. With…

Linearized Piecewise Affine in Control and States Hydraulic System: Modeling and Identification

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Robust output feedback control of non-collocated low-damped oscillating load

For systems with order of dynamics higher than two and oscillating loads with low damping, a non-collocation of the sensing and control can deteriorate robustness of the feedback and, in worst case, even bring it to instability. Furthermore, for a contactless sensing of the oscillating mechanical load, like in the system under investigation, the control structure is often restricted to the single proportional feedback only. This paper proposes a novel robust feedback control scheme for a low-damped fourth-order system using solely the measured load displacement. For reference tracking, the loop shaping design relies on a band reject filter, while the plant uncertainties are used as robustne…

Hybrid State Feedback Position-Force Control of Hydraulic Cylinder

A hybrid position-force control is proposed using a unified state feedback controller in combination with feedforward dead-zone compensation. Dead-zone compensator was constructed as inverse of the identified static map while the state feedback gains were obtained using a numerical optimization routine. An accurate state-space model affine in states and control, derived in a previous work, was used for closed-loop simulations and control tuning. A trigger event for automatic switching between position and force control was defined and integrated into overall control architecture alongside with a feedforward low-pass filter reducing high frequency components in the control signal. Experiment…

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.

Estimating Sway Angle of Pendulum System Using Hybrid State Observer Incorporating Continuous and Discrete Sensing Signals

Estimation of Sway-angle Based on Hybrid State Observer Using Continuous and Discrete Sensing

A hybrid state observer design is presented herein to estimate sway-angle and angular velocity in trolley systems with pendulum. In general, anti-sway control for trolley systems with pendulum such as overhead cranes are designed based on sway-angle signals detected by angular sensors. Opposed to that, a state observer without those sensors is proposed to estimate the sway-angle of the pendulum. A standard linear continuous feedback observer causes estimation error owing to the system nonlinearity and modeling error. This paper proposes a hybrid state observer incorporating discrete sensor signals. In the hybrid state observer, the estimation performance is improved by correcting the state …