multi-DOF System Research Articles

Dynamic analysis of multi-DOF acoustic resonant system involving highly viscous fluids based on fluid-structure interaction

This paper investigates the dynamic characteristics of a multi-degree-of-freedom (multi-DOF) acoustic resonant system involving highly viscous fluids. First, a fluid-structure interaction (FSI) model is established to describe the interaction between the multi-DOF acoustic resonant system and the two-phase fluids, and then the effects of various excitation parameters on the dynamic response of the coupled system are studied. Under the influence of vertical acoustic vibration, the fluid in the container undergoes violent and irregular motions, which leads to a decrease and fluctuation in the equivalent mass of the fluid. The reduction in fluid equivalent mass causes the excitation frequency to deviate from the natural frequency of the multi-DOF acoustic resonant system, thus significantly reducing the dynamic response of the coupled system. Furthermore, the fluctuation of the fluid equivalent mass induces a quasi-periodic motion pattern of the acoustic resonant system. Although increasing the excitation amplitude can effectively increase the dynamic response of the coupled system, it can also increase the fluctuation level of the dynamic response to a certain extent. By appropriately increasing the excitation frequency, the coupled system can operate at a new resonant frequency, thereby reducing the influence of fluid motion on the dynamic response of the system.

High-Precision Positioning Stage Control Based on a Modified Disturbance Observer.

High-precision positioning systems play a crucial role in various industrial applications. This study focuses on improving the performance of a high-precision multi-degrees-of-freedom (DOF) stage. In terms of the controller design, the following two key challenges must be addressed: the cross-decoupling of different DOFs and the impact of external disturbances. To address these problems, a self-tuning approach is proposed for simultaneous decoupling and disturbance suppression. Initially, the stage undergoes static decoupling using a data-based approach, facilitating feedback control for each DOF through single-input, single-output controllers. Addressing dynamic coupling and external disturbance challenges, we introduced a comprehensive evaluation index and a self-tuning multi-input, multi-output disturbance observer. This approach enabled the evaluation and optimization of the disturbance compensation for all DOFs, ensuring optimal positioning accuracy. Finally, we tested the proposed method using a high-precision multi-DOF stage with a real-time control platform. The results demonstrated a significant reduction in the standard deviations of positioning errors in the rx, ry, and z directions by 46%, 58%, and 6%, respectively. The approach used in this study opens avenues for advancements in the design and control of complex multi-DOF systems.

Control co-design and uncertainty analysis of the LUPA’s PTO using WecOptTool

Control co-design has been shown to significantly improve the performance of wave energy converters (WEC). By considering the control and WEC design concurrently, the space searched by the optimization routine is greatly expanded which results in better performing devices. Recently, an open-source WEC co-design code, WecOptTool, was released to perform control co-design research and facilitate its adoption in the community. In this study, we use WecOptTool to perform control co-optimization and uncertainty analysis of the LUPA device. The Laboratory Upgrade Point Absorber (LUPA) is a new open-source laboratory-scale WEC that provides a platform for testing new concepts, innovating control schemes, and validating numerical models. The LUPA can be adjusted to different configurations, including changing the number of bodies, the degrees of freedom (DOF), the float and spar geometry, and the diameter of the drive sprocket pulley in the power take off (PTO) system, as well as providing different control algorithms and input waves. The drive sprocket diameter influences the torque vs speed of the generator, which allows for more flexibility in operating under different wave conditions or with different control schemes. In this study we optimize the drive sprocket diameter, while considering the optimal control algorithm for each potential design, to identify the optimal diameter for electric power production at the PacWave South WEC test site. This case study demonstrates several new capabilities of WecOptTool including a multi-body multi-DOF system and multi-directional irregular waves. The PTO dynamics are modeled using first principle methods for a parametrized model of the mechanical subcomponents in combination with generator model obtained using a power-invariant Park transform. The case-study will be made available to serve as a design tool along the LUPA hardware. Users can readily use this model to perform their own design optimization prior to testing with the physical LUPA device. Finally, we use the automatic differentiation capability of WecOptTool to perform a sensitivity and uncertainty analysis of the LUPA device.

Improving the monodromy matrix computation in pathfollowing schemes for nonsmooth dynamics

An enhanced pathfollowing strategy was recently proposed employing a modified Newton–Raphson solver accelerated by a low-cost routine via a Krylov subspace iterator. One of the key points of the numerical strategy is the computation of the Jacobian of the Poincaré map (i.e., the monodromy matrix), which, by serving as iteration matrix, governs both the accuracy and robustness of the whole strategy. In the context of nonsmooth nonlinear dynamic systems, this matrix can only be computed via numerical differentiation, which leads to subtractive cancellation errors.A new technique is here proposed by performing a central finite difference of the vector field associated with the ODE problems within the time-step integration to assemble the monodromy matrix. This technique allows us to bound the errors induced by the standard numerical differentiation.By means of a wide numerical campaign for meaningful multi-dof dynamical systems, the enhanced pathfollowing scheme is shown to yield a higher level of accuracy than the standard one, as well as higher robustness, with improved convergence properties for the whole numerical strategy.The C++ code implementing the proposed methodology is freely available at https://zenodo.org/record/7245478, and includes code for both the classic method as well as the new approaches for the computation of the Jacobian matrix.

Theory for computing vehicle-rail contact responses from a multi-DOF test vehicle and detecting track modulus and rail damages

The vibration data recorded for the test vehicle cannot be directly used to detect the rail and bridge frequencies due to the overshadowing effect of vehicle's frequencies. To overcome this problem, the vehicle-rail contact response may be used instead. However, current techniques on this are available only for simple test vehicles with single or two degrees of freedom (DOFs). Normally, a train car contains a car body and two bogies (each of two wheelsets), and should be modeled by a multi-DOF system. The objective of this paper is first to solve the four wheelset-rail contact responses from the six measured vehicle responses. Then the contact responses are employed to retrieve the track modulus, while detecting the rail damages, for their salient feature of being free of the vehicle's frequencies. The railway track is modeled by a dual-beam system, with the upper (rail) and lower (bridge) beams connected by a spring-dashpot layer. The track modulus is retrieved through identification of the first “plus” frequency of the dual-beam, and the rail damage is detected from the instantaneous amplitude squared (IAS) generated from the driving component of the contact response. Through comparison with results by the finite element method (FEM), it is confirmed that: (1) the proposed procedure for computing the multi contact responses from the multi-DOF vehicle responses is reliable; (2) track irregularity presents a limited influence even for high disturbance; (3) to trade-off between efficiency and accuracy, a medium vehicle speed is suggested for the field measurement; (4) for the dual-beam with sufficient length, the use of simply supported condition is acceptable for rails; and (5) the effect of track damping is small and can be ignored.

Basic Study on Mechanical Vibration Suppression System Using 2-Degree-of-Freedom Vibration Analysis

Mechanical vibrations adversely affect mechanical components, and in the worst case, lead to serious accidents by breaking themselves. To suppress vibrations, various studies have been conducted on vibration isolation, suppression, and resistance. In addition, technologies to actively suppress vibration have been rapidly developed in recent years, and it has been reported that vibrations can be suppressed with higher performance. However, these studies have been conducted mostly for low-order systems, and few studies have employed control models that consider the complex vibration characteristics of multi-degree-of-freedom (DOF) systems. This study is a basic study that establishes a control model for complex control systems, and the vibration characteristics of a 2-DOF system are calculated using the vibration analysis of a multi-DOF system. Furthermore, the vibration suppression performance of the 2-DOF system is investigated by performing vibration experiments.

Hierarchical strategy for sEMG classification of the hand/wrist gestures and forces of transradial amputees.

The myoelectric control strategy, based on surface electromyographic signals, has long been used for controlling a prosthetic system with multiple degrees of freedom. Several methods classify gestures and force levels but the simultaneous real-time control of hand/wrist gestures and force levels did not yet reach a satisfactory level of effectiveness. In this work, the hierarchical classification approach, already validated on 31 healthy subjects, was adapted for the real-time control of a multi-DoFs prosthetic system on 15 trans-radial amputees. The effectiveness of the hierarchical classification approach was assessed by evaluating both offline and real-time performance using three algorithms: Logistic Regression (LR), Non-linear Logistic Regression (NLR), and Linear Discriminant Analysis (LDA). The results of this study showed the offline performance of amputees was promising and comparable to healthy subjects, with mean F1 scores of over 90% for the "Hand/wrist gestures classifier" and 95% for the force classifiers, implemented with the three algorithms with features extraction (FE). Another significant finding of this study was the feasibility of using the hierarchical classification strategy for real-time applications, due to its ability to provide a response time of 100 ms while maintaining an average online accuracy of above 90%. A possible solution for real-time control of both hand/wrist gestures and force levels is the combined use of the LR algorithm with FE for the "Hand/wrist gestures classifier", and the NLR with FE for the Spherical and Tip force classifiers.

Partial Lagrangian for Efficient Extension and Reconstruction of Multi-DoF Systems and Efficient Analysis Using Automatic Differentiation

In the fields of control engineering and robotics, either the Lagrange or Newton–Euler method is generally used to analyze and design systems using equations of motion. Although the Lagrange method can obtain analytical solutions, it is difficult to handle in multi-degree-of-freedom systems because the computational complexity increases explosively as the number of degrees of freedom increases. Conversely, the Newton–Euler method requires less computation even for multi-degree-of-freedom systems, but it cannot obtain an analytical solution. Therefore, we propose a partial Lagrange method that can handle the Lagrange equation efficiently even for multi-degree-of-freedom systems by using a divide-and-conquer approach. The proposed method can easily handle system extensions and system reconstructions, such as changes to intermediate links, for multi-degree-of-freedom serial link manipulators. In addition, the proposed method facilitates the derivation of the equations of motion-by-hand calculations, and when combined with an analysis algorithm using automatic differentiation, it can easily realize motion analysis and control the simulation of multi-degree-of-freedom models. Using multiple pendulums as examples, we confirm the effectiveness of system expansion and system reconstruction with the partial Lagrangians. The derivation of their equations of motion and the results of motion analysis by simulation and motion control experiments are presented. The system extensions and reconstructions proposed herein can be used simultaneously with conventional analytical methods, allowing manual derivations of equations of motion and numerical computer simulations to be performed more efficiently.

A Feasibility Study on Use of an Accelerometer to Measure the Dynamic Forces in Turning

Metal cutting is a highly dynamic process that generates continuously varying forces. Measurement of these forces is essential to characterizing a cutting process and to fully utilize the machine tool. A force dynamometer is often used to measure these varying forces; however, it is limited by the natural frequency of the sensor and can sometimes be hard to set up on a machine. Therefore, this study aims to estimate the dynamic component of the cutting force using an accelerometer placed directly below the cutting edge. The placement of the sensor helps achieving better signal to noise ratio (S/N). The cutting tool is modelled as a single degree of freedom (SDOF) system relative to the workpiece and dynamic loads are experimentally simulated on it. The measured acceleration is numerically integrated to obtain velocity and deflection, which along with the natural frequency (ωn) and damping ratio (ζ), is used to predict the dynamic load using the system equation. The dynamic forces tested over a wide range of frequencies, show good agreement with the data from simultaneous dynamometer measurement and the force estimated using the proposed method. The study shows the feasibility of this method in a real cutting scenario and the capability to apply it to a multi DOF system. One major limitation is the inability to capture the static or quasi-static component of the cutting force.

Probabilistic Identification of Multi-DOF Structures Subjected to Ground Motion Using Manifold-Constrained Gaussian Processes

Bayesian uncertainty quantification has a pivotal role in structural identification, yet the posterior distribution estimation of unknown parameters and system responses is still a challenging task. This study explores a novel method, named manifold-constrained Gaussian processes (GPs), for the probabilistic identification of multi-DOF structural dynamical systems, taking shear-type frames subjected to ground motion as a demonstrative paradigm. The key idea of the method is to restrict the GPs (priorly defined over system responses) on a manifold that satisfies the equation of motion of the structural system. In contrast to widely used Bayesian probabilistic model updating methods, the manifold-constrained GPs avoid the numerical integration when formulating the joint probability density function of unknown parameters and system responses, hence achieving an accurate and computationally efficient inference for the posterior distributions. An eight-storey shear-type frame is analyzed as a case study to demonstrate the effectiveness of the manifold-constrained GPs. The results indicate the posterior distributions of system responses, and unknown parameters can be successfully identified, and reliable probabilistic model updating can be achieved.

A Krylov accelerated Newton–Raphson scheme for efficient pseudo-arclength pathfollowing

The computational efficiency of an enhanced version of a pseudo-arclength pathfollowing scheme tailored for general multi-degree-of-freedom (multi-dof) nonlinear dynamical systems is discussed. The pathfollowing approach is based on the numerical computation of the Poincaré map and its Jacobian in order to tackle nonautonomous systems with discontinuous vector fields. The scheme is applied to obtain frequency response curves of multi-dof hysteretic systems with a state vector size up to 120, as well as various reduced-order models of single and multiple cantilever beams on a shuttle mass. The proposed approach is shown to drastically increase the speed of convergence in the modified Newton–Raphson scheme thanks to a Krylov sub-space iteration which makes use of the LU decomposition of a frozen Jacobian matrix, which, upon convergence, becomes the monodromy matrix. Several numerical tests performed on mechanical systems with material or geometric nonlinearities corroborate the efficiency of the numerical strategy.The C++ code implementing the proposed methodology is freely available at https://doi.org/10.5281/zenodo.6616482.

Stabilization Control of Underactuated Spring-Coupled Three-Link Horizontal Manipulator Based on Energy Absorption Idea

A spring-coupled three-link horizontal manipulator (STHM) is an underactuated mechanical system that possesses two control inputs and three degrees of freedom (DOF). This paper discusses the stabilization control problem for this multi-DOF underactuated system. By using an energy-absorbing idea, we design two types of virtual friction controllers: PsD controller and PD controller. Additionally, the stability of the control system is analyzed based on Lyapunov theory and LaSalle’s invariance principle. The design of the stabilizing controller in this paper makes good use of the physical characteristics of the STHM system. The design process of the whole control system is simple. Numerical examples demonstrate the validity and superiority of our developed control strategy.

Stress Dispersion Design in Continuum Compliant Structure toward Multi-DOF Endoluminal Forceps

Gastrointestinal cancer, when detected early, is treated by accessing the lesion through the natural orifice using flexible endoscopes. However, the limited degree-of-freedom (DOF) of conventional treatment devices and the narrow surgical view through the endoscope demand advanced techniques. In contrast, multi-DOF forceps systems are an excellent alternative; however, these systems often involve high fabrication costs because they require a large number of micro-parts. To solve this problem, we designed compact multi-DOF endoluminal forceps with a monolithic structure comprising compliant hinges. To allow an efficient stress dispersion at the base end when the hinge bends, we proposed a novel design method to obtain the hinge parameters using the beam of uniform strength theory. This method does not involve a high computational cost. The results show that the improved design with a variable hinge thickness can reduce the maximum bending stress, dispersing the stress in a larger area than that of the previous design considering a constant thickness of the hinge. Moreover, the experiments conducted in a prototype confirm that the radius of the curvature was significantly improved. The proposed method could aid in designing other continuum robots relying on compliant hinges.

Applications of Magnetorheological Fluid Actuator to Multi-DOF Systems: State-of-the-Art from 2015 to 2021

This review article presents various multi-DOF application systems that utilize smart magnetorheological (MR) fluid. It is well known that MR fluid has been actively studied and applied in many practical systems such as vehicle suspension dampers. The design requirements for the effective applications of MR fluid include geometry optimization, working principles, and control schemes. The geometry optimization is mostly related to the size minimization with high damping force, while the working principles are classified into the shear mode, the flow mode, and the squeeze mode depending on the dominant dynamic motion of the application system. The control schemes are crucial to achieve final targets such as robust vibration control against disturbances. It should be addressed that advanced output performances of MR application systems heavily depends on these three requirements. This review article presents numerous application systems such as sandwich structures, dampers, mounts, brakes, and clutches, which have been developed considering the three design requirements. In addition, in this article some merits and demerits of each application system are discussed to enable potential researchers to develop more effective and practical MR application systems featuring the multi-DOF dynamic motions.

Multi-DoF wireless power transfer systems based on magnetic dipole coils with multiple receivers

Multi-DoF wireless power transfer systems based on magnetic dipole coils with multiple receivers

On the principle of impedance-matching for underactuated wave energy harvesting systems

In recent years, the fundamental principle of impedance-matching (IM) has inspired a number of sophisticated, yet simple, control solutions for wave energy converters (WEC). Such controllers have the capability of maximising energy absorption from incoming waves with mild computational requirements, being often intuitive in their design, hence especially appealing for real-time industrial applications. Nonetheless, these control solutions are, to date, almost exclusively developed for single degree-of-freedom (DoF) (and hence fully actuated) WEC systems, hindering their application to realistic underactuated multi-DoF devices, i.e. harvesting systems where energy is extracted from only a handful of its total set of modes of motion. Motivated by this, we present, in this paper, a comprehensive derivation and discussion of the IM conditions for maximum energy absorption in underactuated multi-DoF WEC systems. In particular, we show that the IM principle for single-DoF devices can be effectively extended to underactuated multi-DoF systems, and that a set of optimality conditions can be explicitly derived. In addition, we discuss both the impact and use of this set of optimal conditions for control design and synthesis, hence effectively taking a fundamental step towards the general extension of current IM-based techniques to the case of underactuated multi-DoF devices.

Decoupling Control of Multi-DOF Supporting System of MLDSB

Magnetic liquid double suspension bearing (MLDSB) is composed of an electromagnetic system and hydrostatic system and its bearing capacity and stiffness can be greatly improved. It is very suitable for occasions of medium speed, heavy load, and starting frequently. Due to the gyroscopic effect and interference between the supporting system, the space state of the rotor can be affected and the operation stability of the MLDSB can be reduced greatly. Therefore, the coupling features of the multi-degree of freedom (multi-DOF) system are analyzed and a decoupling controller is designed and verified in the paper. Firstly, the paper introduces the structural characteristics, stress forms, and control regulation mechanism. Then, the mathematical transfer function of the multi-DOF supporting system is established and the coupling principle is revealed. The state feedback decoupling controller is designed by means of a state feedback decoupling, and its decoupling effect is analyzed by the Simulink module. Finally, the single-DOF decoupling system is independently controlled by the use of the root locus method. The coupling characteristics between channel x and channel y are tested experimentally, and the decoupling controller is added and its effect tested. The results show that the state feedback decoupling controller can effectively reduce the coupling degree in the multi-DOF system and convert the multi-DOF coupling problem into a single-DOF independent control problem. The coupling effect of channel x and channel y is reduced by using the decoupling controller, with the subsequent displacement characteristic of the rotor increased, and then the operation stability of the MLDSB is improved greatly. This paper can enrich the support system of the MLDSB and provide a theoretical reference for stability control.

Observer-based fast nonlinear MPC for multi-DOF maglev positioning system: Theory and experiment

This paper presents an observer-based fast nonlinear model predictive control (NMPC) scheme for translation control of magnetically levitated (maglev) positioning system subject to input saturation. The motivation lies in the improvement of transient characteristics and control performance for positioning systems. The nonlinear dynamical translation model of the maglev positioning system is derived that does not affect the rotation dynamics with special current conditions. The disturbance estimation, obtained by nonlinear disturbance observer, is introduced in the state receding prediction to compensate the errors caused by disturbances and uncertainties. To reduce the computational burden, the stability of the proposed NMPC is established without using any stability-related terminal costs or constraints, and only the short prediction horizon is required for real-time feasibility. The online optimization algorithm underlying the NMPC scheme takes the process constraints into account, and solves the optimal control problem using a parallel structure at each iteration. Comparative experiments are carried out on the positioner to validate the proposed controller has the outperformance in transient/steady-state trajectory tracking, frequency characteristics and robustness against disturbances. The proposed scheme also provides a guidance for the application of NMPC in industrial mechatronic system with fast dynamics.

Model identification and parametric adaptive control of hydraulic manipulator with neighborhood field optimization

The model identification and uncertain parameters estimation are common control problems in multi-DOF manipulator system, since both model parametric uncertainties and unknown external disturbance often degrade the output performance and the close-loop system stability. In this study, by using the joint angle and the torque information, a neighborhood field optimization is adopted to identify the Lagrange model parameters of two-DOF hydraulic manipulator. The fitness function of the neighborhood field optimization is designed to optimize the minimal squared error of the torque estimation and to obtain the lumped estimated parameters with high accuracy. Then based on the identification model, a parametric adaptive controller is designed to address uncertain electro-hydraulic parameters and external disturbances. Furthermore, a new stable control variable is redesigned to avoid the redundant input saturation of electro-hydraulic actuator. The effectiveness of the proposed controller is verified by the comparative experimental results with the general backstepping controller.

Stochastic Response and Bifurcation of a Two-Degree-of-Freedom Energy Harvesting System with Stoppers

It was shown previously that the synergy of the multi-degree-of-freedom (multi-DOF) and the mechanical stopper techniques is an effective way to further broaden the operation bandwidth of vibration energy harvesters. Considering the stochastic factor at the same time, this paper is devoted to developing a theoretical method for analyzing the dynamical characteristics of an impact-engaged 2DOF energy harvesting system under stochastic excitation, in which the impact is modeled as a nonlinear piecewise function. The existence of the impact and multi-DOF brings complexity in analyses, and the main theoretical method utilized in this paper is the stochastic averaging method which is suitable for multi-DOF quasi-nonintegrable systems. After that, the joint and marginal probability density functions of the system are derived, and numerical examples are shown to verify the effectiveness of the theoretical method. It is noteworthy that the theoretical method has the potential to be extended to more complex multi-DOF systems with stoppers. Subsequently, the stochastic response, bifurcations in the stochastic and corresponding deterministic systems, and the relationship between the D-bifurcation and the mean square voltage are discussed. Effects of crucial system coefficients, the impact stiffness and distance on the system are investigated as well.