2-DOF Model Research Articles

Modeling and Robust Control of a 5 DOF Model for Rowing Motion by Inverse Dynamics Method.

Competitive sailing requires efforts pertinent to physiological limitations and coordination between different parts of the body. Such coordination depends on the torques applied by muscles to the joints. This study aims to simulate the motion and provide a control law for the joint torques in order to track the desired motion paths. In this analytical study, an inverse dynamics based control is employed in order to simulate the motion by tracking the desired movement trajectories. First, the dynamics equations are obtained using Lagrange method for 5 degrees of freedom (5 DOF) model. In the following, a robust control scheme with inverse dynamics method based on the Proportional-Integral-Derivative (PID) approach is employed to track the desired joint angles obtained from the experiment. The simulation results demonstrate the performance of the proposed control method. Low settling times are achieved for the entire joint, which is appropriate in comparison with the time period of each cycle (3.75 s). Also, the maximum torques required to be applied to the joints are in physiological range. This study provided an appropriate model for the analysis of human movement in rowing sport. The model can also be cited in terms of basic biological theories in addition to practical computational uses in biomechanical engineering. Accordingly, the generated control signals can help to improve the interactive body movements during paddling and in designing robotic arms for automatic rowing.

Application of a Trajectory Tracking Algorithm for Underactuated Underwater Vehicles Using Quasi-Velocities

In this work, an application of the trajectory tracking algorithm proposed in the literature for underactuated marine vehicles is presented. The main difference relies on that here the dynamics of the vehicle are expressed in terms of some quasi-velocities (QV). This fact has a double meaning. First of all, it is shown that using the QV, it is possible to control a vehicle in the absence of one variable because the works related to marine vehicles have only concerned fully actuated systems. In addition, a controller using QV provides information that gives some insight into vehicle dynamics and that is not available in classical equations of motion. The simulations done on two 3-DOF models of different underwater vehicles and using two desired trajectories show performance of the considered control strategy. A discussion of the presented control scheme and selected control approaches from recent years was also conducted, and the benefits of the proposed approach were pointed out.

Experimental and numerical modeling of a piezoelectric floating system for wave energy harvesting

In this paper, a floating wave energy converter (WEC) employing a piezoelectric power take-off (PTO) for off-grid powering of electronic devices at sea is presented and its electro-mechanical behavior is investigated both experimentally and numerically. The prototype floating structure consists of two box-shaped bodies joined by flexible beam elements. Due to the wave excitation, the floaters experience relative pitch rotations and vertical displacements, which dynamically deform the piezoelectric linking element, producing a superficial charge distribution. A small-scale prototype, built in an innovative way with LEGO™ bricks, is tested under regular wave excitation in a small basin. The recorded relative motion between the floaters is used as input to calculate via multiphysics software the voltage and power output of a piezoelectric device having the same flexibility of the passive element employed in the experiments. As a starting point for more accurate simulations, a 4-dof reduced-order model (ROM) of the floating system, including a simplified piezoelectric model, is developed and the wave induced response is compared with the experimental data. The elastic connection is represented through a torsional spring and potential linear theory is employed to calculate the hydrodynamic loads. Thus, Cummins equations for the floating system are formulated in pure differential form by introducing additional equations for radiation forces. This numerical approach allows for performing in an efficient and robust way the computation of the specific response amplitude operators, characterizing the WEC’s electro-mechanical response. Introducing system modes, the electro-mechanical equations can be further simplified and, by means of their frequency-domain analytical solution, facilitate a sensitivity analysis of the system response, capture-width ratio and power output with respect to relevant parameters, highlighting optimal conditions and performance enhancements by using arrays of piezoelectric elements, both in ideal (regular waves) and realistic (irregular sea) conditions.

A passive planar model with rolling contact and its application for bounding and pronking on a quadruped robot

Abstract The development and investigation of a quadruped robot's dynamic bounding and pronking gaits using a sagittal planar model that captures the robot's natural dynamics are presented. The proposed reduced-order model, termed the Two-rolling-leg (TRL) model, is a 3-DOF planar rigid-body model consisting of two half-circular compliant legs with pure rolling contact. Throughout the non-dimensional steps-to-fall and fixed-point analysis, the model with feasible intrinsic parameters can passively perform the periodic dynamic behavior of bounding and pronking, revealing a relationship between the body parameters and the preferred dynamic behaviors. Dynamic bounding and pronking on a quadruped robot were initiated by developing a model-based control strategy based on the searched periodic dynamic behaviors of the TRL model. The experimental results showed that the robot can initiate its dynamic bounding and pronking behaviors at various forward speeds merely by causing the motor to track a preset trajectory derived from the fixed-point motion of the TRL model using position control. The higher success rate of the robot in stable bounding than in pronking is in line with the results from the analysis of the model. This paper confirms that the dynamic multi-gait locomotion of a quadrupedal robot can be initiated by utilizing a reduced-order model for control guidance and that the body configuration plays an important role in determining the characteristics of the dynamic behaviors.

Metal members stiffened by bistable components for the protection of naval architectures under periodic loading

ABSTRACT Naval architectures are required to simultaneously have high stiffness and high damping to bear periodic loading and suppress resonance that is possibly caused by ship self-excitation vibration. A protection approach, namely, metal members stiffened by bistable components, is proposed. This approach not only achieves high stiffness but also exhibits excellent energy dissipation compared to that of traditional approaches under periodic loading. A two-degree-of-freedom (2-DOF) model of a Euler beam stiffened by a bistable component is derived and characterised by two potential wells. The influence of the structural parameters and energy dissipation mechanisms of the coupled bistable-linear (CBL) beam on the laws of the potential energy wells are studied via theoretical model. In the end, a panel stiffened by optimally designed CBL beams, according to the parametric studies, effectively dissipate the dynamic energy and protect the structure by staying within the elastic range found in the finite element model (FEM).

Beyond pull-in angle control of a dual axis torsional micro-actuator considering bending effects

Torsional micro-actuators are fundamental elements in micro-system technologies. They've found several applications in optical cross connects, endoscopic optical coherence tomography and miniaturized projection displays. Effective angle control in these actuators is necessary for their acceptable performance. So, the objective of the current paper is to develop a novel fuzzy controller to extend the travel range of these actuators based on an accurate dynamic model. The degrees of freedom (DoF) of the system includes two rotational angles resulted from twist of the torsion micro-beams and two translational ones originating from their bending towards the electrodes. Using these four DoFs, Lagrange equations are employed to develop a novel dynamic model for the dual axis torsional micro-actuator. Comparing the response of the system obtained from 4-DoF and 2-DoF models with those resulted from nonlinear recursive finite element simulations reveals that the use of the 4-DoF model is critical for having accurate predictions of the system's behavior. Then dynamic simulations to step input voltages are used for proposing an expert fuzzy rule base which describes the dependence of the rotation angles to input voltages. Using this rule base along with a singleton fuzzifier, product inference engine and center average defuzzifier, an incremental fuzzy controller is designed for smooth control of the rotation angles of the actuator about the desired angles. To maximize the performance of the closed-loop system, the centers of the fuzzy sets of the THEN parts of the rules are adaptively tuned using a higher-level fuzzy system. Closed loop simulations shows that the presented novel fuzzy controller is capable of stabilizing the angles of the actuator even beyond their inherently unstable pull-in range. The proposed 4-DoF model can be used for design optimization of dual axis torsional micro-actuators. Additionally, the developed incremental fuzzy controller can be employed for controlling the response of other types of electrostatically actuated micro/nano-systems.

Numerical investigation of earthquake response reduction effects by negative stiffness connection for adjacent building structures

Coupled vibration control (CVC) for adjacent buildings can mitigate the seismic response of the system by properly setting the structural parameters, including the connecting elements. However, optimization of the control effect for CVC structures may be limited when using only positive or zero stiffness at the connecting spring. The present study explores the control effectiveness by passive negative stiffness as a connecting element installed between the mainframe and subframe of CVC structures. A two-degrees-of-freedom (2DOF) model representing a coupled building, which consisted of the mainframe and subframe linked by a spring and a viscous damping element, was used. The transfer function (TF) for displacement and acceleration of the mainframe and subframe was evaluated under various structural parameters. The results showed that by setting an optimal negative stiffness and an optimal damping at the connecting portion, the peak amplitude of the TF of the mainframe was significantly reduced compared to that of reference-controlled case without negative stiffness (i.e., with only a damping element). In addition, adopting negative stiffness in CVC structures can extend the range of optimal tuning conditions. Moreover, a time history earthquake response simulation was conducted using 2DOF models with different natural periods and structural parameters subjected to various input motions, including simulated waves and observed records. The results indicate that use of the negative stiffness connection can effectively reduce the seismic response of the mainframe for passive CVC structures.

Dynamics Modeling of Bearing with Defect in Modelica and Application in Direct Transfer Learning from Simulation to Test Bench for Bearing Fault Diagnosis

In data-driven bearing fault diagnosis, sufficient fault data are fundamental for algorithm training and validation. However, only very few fault measurements can be provided in most industrial applications, bringing the dynamics model to produce bearing response under defects. This paper built a Modelica model for the whole bearing test rig, including the test bearing, driving motor and hydraulic loading system. First, a five degree-of-freedom (5-DoF) model was proposed for the test bearing to identify the normal bearing dynamics. Next, a fault model was applied to characterize the defect position, defect size, defect shape and multiple defects. The virtual bearing test bench was first developed with OpenModelica and then called in Python with OMPython. For validation of the positive effect of the dynamics model in the direct transfer learning for bearing fault diagnosis, the simulation data from the Modelica model and experimental data from the Case Western Reserve University were fed separately or jointly to train a Convolution Neural Network (CNN). Then the well-trained CNN was transferred directly to achieve the fault diagnosis under the test set consisting of experiment data. Additionally, 157 features were extracted from both time-domain and frequency-domain and fed into CNN as input, and then four different validation cases were designed. The results confirmed the positive effect of simulation data in the CNN transfer learning, especially when the simulation data were added as auxiliary to experimental data, and improved CNN classification accuracy. Furthermore, it indicated that the simulation data from the bearing dynamics model could play a part in the actual experimental measurement when the collected data were insufficient.

Analyses on Aerodynamic and Inertial Loads of an Airborne Pod of High Performance Fighter Jet

A fighter performing a reconnaissance mission is equipped with a pod that drives optical/infrared sensors for acquiring and identifying target information on the lower part of the fuselage. Due to the nature of the reconnaissance mission, the fighter performs high speed evasive maneuvers, and the resulting load should be considered importantly for the development of the pod. This paper concerns a numerical investigation into the inertial and aerodynamic loads of the airborne pod of high performance aircrafts. For the aerodynamic load analysis, the pylon and pod shapes are added to the fighter 3D model, and the commercial software was used for static and dynamic analysis. Considering the practical mission conditions, the common/extreme conditions were established respectively in the static and dynamic situations of pods and the driving torque could be tripled under dynamic conditions. In the analysis of inertia load, a 3-DOF model considering roll and turning maneuvers was derived by the Lagrangian method, and then the numerical integration method was applied to the analysis. As a results, it was conformed that the inertia load was generally induced at a low level compared to the aerodynamic load, but depending on the unbalance mass condition of the pod, the inertia load cannot be negligible.

Design of Static Output Feedback Controllers for an Active Suspension System

This paper presents a method by which to design linear quadratic (LQ) static output feedback (SOF) controllers with a 2-DOF quarter-car model for an active suspension system. Generally, it is challenging to implement linear quadratic regulator (LQR), designed with a full-car model, in actual vehicles because doing so requires 14 state variables to be precisely measured. For this reason, LQR has been designed with a quarter-car model and then applied to a full-car model. Although this requires far fewer state variables, some of them are still difficult to measure. Thus, it is necessary to design a LQ SOF controller which uses available sensor signals that are relatively easily measured in real vehicles. In this paper, a LQ SOF controller is designed with a quarter-car model and applied to a full-car model for ride comfort. To design the controller, an optimization problem is formulated and solved by a heuristic optimization method. A frequency domain analysis and a simulation with a simulation package show that the proposed LQ SOF controllers effectively improve the ride comfort with an active suspension system.

Modeling of Pantograph under Sliding Friction using FMBD and Stability Analysis

Sliding of the pantograph head and contact wire causes frictional force acting on traveling pantograph head in horizontal direction. If the coefficient of friction between the pantograph head and contact wire is large, unstable vibration of the traveling pantograph could be observed. To analyze this vibration, a 2-dof pantograph model considering frictional force acting on the pantograph head based on the multi-body dynamics (MBD) has been proposed. However, elastic deformation of each element of the pantograph is not studied in this model. Therefore, this study proposes a pantograph model that considers friction characteristics of the pantograph based on the flexible multi-body dynamics (FMBD) approach. In this paper, a single-arm pantograph for shinkansen train is modeled using the FMBD technique. In addition, a stability analysis method based on the complex eigenvalue analysis for the pantograph model is proposed. Furthermore, excitation test of actual pantograph for Shinkansen train is carried out to identify its dynamic characteristics. Then mode shapes and natural frequencies of the pantograph are identified. Moreover, the stability analysis based on the complex eigenvalue analysis is carried out using identified parameters.

Design and control of 2-DoF joystick using MR-fluid rotary actuator

The purpose of this paper is to design a control algorithm for a 2-DoF rotary joystick model. Firstly, the structure of the joystick, which composes of two magneto-rheological fluid actuators (shorten MRFA) with optimal configuration coupled perpendicularly by the gimbal mechanism to generate the friction torque for each independent rotary movement, is introduced. The control strategy of the designed joystick is then suggested. Really, because of two independent rotary movements, it is necessary to design two corresponding controllers. Due to hysteresis and nonlinear dynamic characteristics of the MRFA, controllers based an accurate dynamic model are difficult to realize. Hence, to release this issue, the proposed controller (named self-turning fuzzy controllers-STFC) will be built through the fuzzy logic algorithm in which the parameters of controllers are learned and trained online by Levenberg-Marquardt training algorithm. Finally, an experimental apparatus will be constructed to assess the effectiveness of the force feedback controls. Herein, three experimental cases are performed to compare the control performance of open-loop and close-loop control method, where the former is done through relationship between the force at the knob and the current supplied to coil while the latter is realized based on the proposed controller and PID controller. The experimental results provide strongly the ability of the proposed controller, meaning that the STFC is robust and tracks well the desirable force with high accuracy compared with both the PID controller and the open-loop control method.

Optimal calibration of a tuned liquid column damper (TLCD) for rotating wind turbine blades

Blade edgewise vibration is a growing concern for modern megawatt wind turbines, as it may significantly shorten the blade lifetime. In this paper, optimal calibration (tuning) of a blade-mounted tuned liquid column damper (TLCD) using closed-form formulas is investigated. A 2-DOF model for the blade-TLCD system is first established, acting as the basis for analytical derivation of the optimal tuning formulas. Two different frequency-tuning criteria are employed, one based on the equal dynamic amplification at two neutral frequencies and the other one based on the equal modal damping ratio of the two free vibration modes. Two optimal frequency-tuning (frequency ratio) formulas having similar expressions are derived based on these two criteria, and both formulas are dependent on the rotational speed, the mounting position, the blade edgewise eigenfrequency and the TLCD prescribed parameters. Next, an explicit expression for the optimal equivalent TLCD damping ratio is obtained by equalizing the dynamic amplification at three excitation frequencies, and it also exhibits dependence on the rotational speed and the edgewise eigenfrequency. A closed-form formula for the optimal TLCD head loss coefficient is then proposed, providing a straightforward method to determine the optimal value without resorting to iteration. Comparisons of the two optimal frequency-tuning formulas are conducted in terms of the dynamic amplification, the root loci of the 2-DOF system, and the parametric sensitivity, using data from the NREL 5MW reference wind turbine. The results indicate that these two formulas lead to very similar optimal design of the blade-mounted TLCD as well as the damper performance, although the 1st formula only guarantees the equal dynamic amplification while the 2nd one only guarantees the equal modal damping ratio. The set of closed-form formulas developed in this study facilitates a convenient and robust design of blade-mounted-TLCD for suppressing edgewise vibrations, and forms the basis for developing semi-active control algorithms.

Modeling and Dynamics Analysis of a Dual-Mass Flywheel with the Conformal Contact Action of Friction Damping Ring and Pressure Plate

To study the nonlinear dynamic characteristics of the dual-mass flywheel (DMF) under the conformal contact action between the friction damping ring and primary flywheel pressure plate, the contact action model is established and analyzed based on Winkler model. Through analysis and calculation, the contact deformation, contact pressure at different contact positions, and equivalent torsional contact stiffness are obtained. The nonlinear dynamic analysis model of three-degree-of-freedom (3DOF) which takes the conformal contact into account and two-degree-of-freedom (2DOF) without considering conformal contact is established. The approximate analytical solution of the nonlinear frequency characteristics of the system at steady state is derived. By comparing with the results obtained from numerical method, the theoretical analysis process is proved to be valid. And it is found that the overall amplitude and angular displacement transmissibility of the 3DOF model are smaller than the 2DOF model, especially at resonance frequency. The effects of the friction damping ring moment inertia, stiffness of DMF, and axial friction torque on the frequency characteristics of system and angular displacement transmissibility are analyzed. The forced vibration response analysis of the 3DOF model is conducted, through which the torsional angle variations of the primary flywheel, friction damping ring, and secondary flywheel with time are obtained. The results show that the amplitude of the secondary flywheel is much smaller than that of the primary flywheel, indicating that the DMF has prominent damping performance.

Design of a vibration damping robot and force evaluation in intraoperative robotic-assisted femoral shaft repair using a modified soft damper.

Closed intra-medullary nailing fixation is a method for treating fractured femurs with minimal invasiveness. However, this method lacks safety and precision. To avert prevailing problems such as extended cracks in the already broken bone, the design of a vibration damping robot and force evaluation system is essential. This paper presents a sensor-based clamping robot system embedded with a regulated pressurised air balloon. Drilling forces were monitored by a force sensor attached to the end robot effector, while the reduced vibration result was measured by a non-contact laser displacement sensor. A 2 degree-of-freedom (2DOF) model was developed. Force and vibration data were obtained using a data acquisition module (EMS 309) and analysed using MATLAB software (Version R2015b). The results obtained show that both the frequencies and amplitudes of the vibration is reduced at 6bar with effector's spindle speed of 1500rpm. This proposed concept shows that drilling force and vibration can be reduced simultaneously using a robot effector coupled with a damper.

Vibration Isolation of Railway Vehicle Car body using Semi-active Suspension

In the past, the magnetorheological (MR) suspension for railway vehicle has obtained great attention for the isolation of vibrations. This work presents a numerical approach to analyse skyhook and ground hook semi-active control methods for railway vehicle suspension. A 10 DoF model of the railway vehicle system is formulated for the comparative analysis between conventional passive and semi-active suspension control in the present study. The non-linear analysis is investigated in time and frequency domain for the sinusoidal excitations from the track.

Resonant passive energy balancing of morphing helicopter blades with bend\u2013twist coupling

With increasing demand for rotor blades in engineering applications, improving the performance of such structures using morphing blades has received considerable attention. Resonant passive energy balancing (RPEB) is a relatively new concept introduced to minimize the required actuation energy. This study investigates RPEB in morphing helicopter blades with lag–twist coupling. The structure of a rotating blade with a moving mass at the tip is considered under aerodynamic loading. To this end, a three-degree-of-freedom (3DOF) reduced-order model is used to analyse and understand the complicated nonlinear aeroelastic behaviour of the structure. This model includes the pitch angle and lagging of the blade, along with the motion of the moving mass. First, the 3DOF model is simplified to a single-degree-of-freedom model for the pitch angle dynamics of the blade to examine the effect of important parameters on the pitch response. The results demonstrate that the coefficient of lag–twist coupling and the direction of aerodynamic moment on the blade are two parameters that play important roles in controlling the pitch angle, particularly the phase. Then, neglecting the aerodynamic forces, the 3DOF system is studied to investigate the sensitivity of its dynamics to changes in the parameters of the system. The results of the structural analysis can be used to tune the parameters of the blade in order to use the resonant energy of the structure and to reduce the required actuation force. A sensitivity analysis is then performed on the dynamics of the 3DOF model in the presence of aerodynamic forces to investigate the controllability of the amplitude and phase of the pitch angle. The results show that the bend–twist coupling and the distance between the aerodynamic centre and the rotation centre (representing the direction and magnitude of aerodynamic moments) play significant roles in determining the pitch dynamics.

Probability of Hitting the Target with an Imperfectly Manufactured Projectile

AbstractThe effect of individual projectile production errors on the probability of hitting a target is analyzed. The intensity of errors is linked to the level of production quality. The consequences of manufacturing errors are estimated by a comprehensive Monte Carlo (MC) simulation where a 3D CAD model of a missile and a modified 6DOF model of its flight are coupled. A 122 mm rocket is selected as a case study. The MC simulation gives the estimation of the probability that rocket will destroy the target.

Performance Improvement of Suspension Characteristics by Implementation of Active Suspension System in Two Wheelers

New and better two-wheel models have increased demand today, with increased protection, comfort and performance. The human body gets exhausted, which contributes to back pain and neck pain because of the excessive use of bikes, wrong riding positions, poor weather and suspension system issues. The systems engineer would focus on the design of the vehicle suspension mechanism to minimise human discomfort. This research aims to study the feasibility of implementing a suspension system with active suspension for a two-wheeler by way of numerical modelling, simulation and analysis. First of all, the active suspension system for a 2 DOF system is modelled and analysed. The analysis done is frequency response analysis and time-domain analysis. The time-domain analysis is done using two road inputs; one is a bump input, which is designed according to the standards, and the other is a random road input. Then the two-wheelers were modelled as a 4 DOF model. The controller is modelled using optimal control theory. A linear quadratic regulator (LQR) controller is used because the system is assumed to have linear characteristics and the cost function of the system is quadratic. It is observed that suspension characteristics are improved by using the active suspension system in two-wheelers.

Modeling and Design of an Aircraft-Mode Controller for a Fixed-Wing VTOL UAV

Vertical takeoff and landing (VTOL) is an essential feature of unmanned aerial vehicles (UAVs). On the one hand, VTOL can expand and enhance the applications of UAVs; yet, on the other hand, it makes the design of control systems for UAVs more complicated. The most challenging demand in designing the control system is to achieve satisfactory response sharpness of fixed-wing UAVs to control commands and ensure that the aircraft mode channels are effectively decoupled. In this work, a six-degree-of-freedom (6-DoF) model with forces and moments is established based on the aerodynamic analysis, which is carried out through computational fluid dynamics (CFD) numerical simulation. The improved proportional derivative (PD) controller based on the extended state observer (ESO) is proposed to design the inner-loop attitude control, which increases the anti-interference ability for internal and external uncertainty of the UAV system. The motion equations of the UAV are established and divided into independent components of longitudinal and lateral motion to design the outer loop control law under minor disturbance conditions. A total energy control system (TECS) for the longitudinal height channel is proposed, which separates speed control and track control. L1 nonlinear path tracking guidance algorithm is used for lateral trajectory tracking so as to improve curve tracking ability and wind resistance. Effectiveness of this approach is proved by actual flight experiment data. Finally, a controller based on angular velocity control is designed to prevent the attitude and head reference system (AHRS) from malfunctioning. Its effectiveness is verified by the response test of the control system.