Two-mass Model Research Articles

Explicit smooth/nonsmooth cosimulation using kinematic constraints

An explicit cosimulation scheme is developed to study the coupling of smooth and nonsmooth systems using kinematic constraints. Using the force-displacement decomposition, the coupling constraints are formulated at the velocity level, to preserve consistency with the impulse-momentum equations for frictional contacts in the nonsmooth solver, which however potentially leads to instability of the explicit cosimulation. To improve the stability of the cosimulation without affecting the format of the coupling constraints, guidelines for the modification of the prescribed motion are developed following the spirit of Baumgarte’s stabilization technique and the characteristics of the proposed integration scheme, which prescribes a combination of position, velocity, and acceleration to the constrained bodies. Using modified inputs, the stability of the cosimulation is tested using a rigidly connected two-mass oscillator model, which shows clear improvement compared to that with unaltered inputs. The performances of the cosimulation with modified inputs are further illustrated using a double-pendulum system and a complex flexible multibody system coupled with a particle damper. It follows that cosimulation results well agree with those obtained using monolithic simulation or simplified models, verifying the explicit smooth/nonsmooth cosimulation. The results also show a higher efficiency of the explicit cosimulation scheme, which requires much less computational time to obtain similar results, compared to the implicit smooth/nonsmooth cosimulation.

Analysis of shock absorber resistance impact on load safety, continuous wheel rolling and energy loss in vehicle suspension

Introduction. The purpose of the article is to consider the effect of damping in the shock absorber on smooth running, continuous rolling of the wheel and energy loss in the suspension of the car.Materials and methods. The review is based on the analysis of the amplitude-frequency characteristics of a two-mass car model and the dependence of the shock absorber operation during the oscillation cycle on the frequency of kinematic action.Results. The article presents a calculation scheme and equations of dynamics of a two-mass oscillatory system equivalent to an automobile suspension. The frequencies at which the amplitude-frequency characteristics intersect for different levels of damping (invariant points) in a two-mass oscillatory system are calculated. The relative operation of the shock absorber for the oscillation cycle concept is proposed and a formula for calculating the relative operation of the shock absorber in a two-mass oscillatory system is given. A comparative analysis of graphs characterizing smooth running, continuous rolling of the wheel and energy losses in the suspension is carried out.Discussion and conclusions. It is revealed that significant contradictions between these requirements arise only near the second resonance of the sprung mass, with an increase in the frequency of vibrations in the resonant zone, these contradictions are decrease.

Controlling chaotic oscillations in a symmetric two-mass model of the vocal folds

Human phonation is a highly non-linear process in which subglottal flow emanating from the lungs induces self-oscillations of the vocal folds. In normal conditions, this results in the generation of a regularly pulsating volume velocity that becomes the source of acoustic waves, which once modulated by the vocal tract, get emitted outwards as voice. However, vocal fold oscillations can become chaotic under many circumstances. For instance, even in the case of healthy symmetric vocal folds, an excess value of the subglottal pressure can trigger chaotic motion. In this paper, we derive a chaos control strategy for a two-mass model of the vocal cords to revert the situation and render the motion regular again. The approach relies on slightly altering the system energy to move it to a stable state. Given that no external control forces can be applied to the vocal cords, it is proposed to add a third mass to the original two-mass model, which is assumed to be made of an ideal smart material. The mass of the smart material is presumed negligible in comparison to the two masses of the vocal folds model, but its damping and stiffness can be tuned to evolve with time. For a fixed subglottal pressure for which the motion is chaotic, it is shown how periodicity can be recovered using adequate damping laws, by either attaching the smart material onto the larger vocal fold mass or onto the smaller one. For the latter, chaos control turns to be more difficult and the damping of the smart material has to quickly vary with time. On the other hand, given that the subglottal pressure would rarely be constant in a real situation, we also introduce a damping law to avoid chaotic motion as the subglottal pressure augments or diminishes. Finally, it is shown that control can not only be achieved by acting on the damping of the smart material but also on its stiffness. A stiffness law to prevent chaotic oscillations and get a healthy pulsating volume velocity is therefore implemented. A brief discussion on the mid-long term potential of the presented solution for practical cases is included.

Analysis of the model-based corrector approach for explicit cosimulation

In many industries, the focus of testing is currently shifting away from classical hardware tests to the virtual verification and validation of products. To this end, cosimulation has become a common tool for the simulation and analysis of complex systems that span multiple engineering domains and usually involve multiple, heterogeneous and application-specific simulation environments. In particular, the so-called explicit cosimulation allows a widespread application since it has minimal requirements regarding the capabilities of the tool interfaces. However, explicit cosimulation also poses a numerical challenge, especially when the system includes stiff coupling loops. The model-based corrector approach presented in Haid et al. (The 5th Joint International Conference on Multibody System Dynamics, 2018) provides a method for the efficient cosimulation of such systems. In this article, this model-based corrector approach is extended to additional extrapolation methods. By modeling the cosimulation process through a linear recurrence equation and applying it to the two-mass oscillator test model, the influence of model-based correction on the underlying extrapolation methods in terms of stability, accuracy, and error convergence is analyzed. It is shown that adding model-based correction can significantly improve the overall cosimulation, allowing >10 times larger macrostep sizes or reducing the cosimulation error by a factor of 10 or more in some cases.

Balance Recoverability and Control of Bipedal Walkers With Foot Slip.

Low-friction foot/ground contacts present a particular challenge for stable bipedal walkers. The slippage of the stance foot introduces complexity in robot dynamics and the general locomotion stability results cannot be applied directly. We relax the commonly used assumption of nonslip contact between the walker foot and the ground and examine bipedal dynamics under foot slip. Using a two-mass linear inverted pendulum model, we introduce the concept of balance recoverability and use it to quantify the balanced or fall-prone walking gaits. Balance recoverability also serves as the basis for the design of the balance recovery controller. We design the within- or multi-step recovery controller to assist the walker to avoid fall. The controller performance is validated through simulation results and robustness is demonstrated in the presence of measurement noises as well as variations of foot/ground friction conditions. In addition, the proposed methods and models are used to analyze the data from human walking experiments. The multiple subject experiments validate and illustrate the balance recoverability concept and analyses.

Determining the structure and parameters of the human model subjected to vibration

This article presents results from an experimental study of the frequency properties of a sitting person. This analysis shows that in order to define the structure and parameters of a human body model, it is necessary to find the only solution to the problem of determining the model parameters. Otherwise, this model cannot be used to build vibration protection systems, which is its main purpose. This problem was solved for a two-mass human model. To do this, the total model mass and although the amplitude-frequency response and input frequency impedance for both solids in the model structure are needed to be known. In addition to this, the influence of multi-articular muscles on the frequency characteristics of a human body is found using mechanical models with an arbitrary number of degrees of freedom. In particular, the possibility of the existence additional antiresonance frequencies on the upper mass is shown.

Analyzing Gas Turbine-Generator Performance of the Hybrid Power System

Kinetic energy available from the turbomachinery may boost short-term ramp rates during load shifting between generator and fuel cell that may be exploited to optimize the performance of turbine-fuel cell hybrid systems during load following. The paper starts with modeling a gas turbine, gearbox, and generator sitting on the rigid shafts as a two-mass model primarily for estimating the rotational inertia available from the turbogenerator. The gas turbine and its environment impose constraints of available space allowances, measurements from high-speed rotating parts, lack of accessibility to the shaft of measure, making replacements and/or required installation adjustments of the torque transducer difficult. It is demonstrated that in the absence of torque measurement, the data containing only a slow excursion of the rotor motion in response to a slight load change is sufficient to determine inertia and damping coefficients from the model. Furthermore, the generator's reactive power capability was investigated because it serves as an asset in integrated hybrid systems to meet dynamic reactive power demands, reducing the burden on the fuel cell's power electronics control in generating reactive power.

Active Fault Tolerant Control of Wind Turbine Systems using Disturbance Observer-based Sliding Mode and Time Delay Estimation

In this paper, an Active Fault Tolerant Control (AFTC) based on Time Delay Estimation (TDE), sliding mode and nonlinear disturbance observer is proposed to control the pitch angle of a wind turbine system in the presence of sensor and actuator faults and uncertainties. Time Delay Estimation (TDE) is applied as a fault estimation algorithm for the detection, isolation and compensation of the actuator fault. Then, a robust control law is synthesized to nullify uncertainty and fault effects. using a combination of sliding mode disturbance observer-based and time delay control with novel adaptation laws and a nonlinear disturbance observer. In order to mitigate chattering which comes from the discontinuous control, a nonlinear disturbance observer is designed and combined with sliding mode and time delay control. Through the proposed structure, the discontinuous gain is reduced significantly which leads to chattering reduction. Stability analysis is conducted through Lyapunov Theory. Wind speed profiles are generated using TurbSim, and simulations are performed based on a nonlinear two-mass wind turbine model which is implemented in FAST environment for verification. Finally, simulation results reveal the effectiveness of the proposed controller in the presence of uncertainty and different actuator faults such as hydraulic leakage, pump wear, and high air content in the oil.

Nonlinear Maximum Power Point Tracking Control of Wind Turbine Based on Two-Mass Model Without Anemometer

A nonlinear control without using anemometer is proposed to achieve the maximum power of the wind turbine (WT) based on two-mass model in this paper. To track the maximum power points, the optimal tip speed ratio control strategy requiring to know the optimal rotor speed of the WT (ORS) is employed. To achieve the ORS, a torque observer is designed to estimate the aerodynamic torque, then the ORS can be obtained by the corresponding calculations based on the estimated torque. Due to the high nonlinearities of the WT and time-varying wind speed, a nonlinear control based on feedback linearization control (FLC) is adopted to track the ORS. In the FLC, the WT is linearized firstly, then the rotor speed controller is designed via linear control technique. The effectiveness of the proposed control strategy is verified by simulation studies. The simulation results show that, compared with the traditional PI control based on torque estimation and FLC based on wind speed estimation, the proposed control strategy provides better dynamic performances and higher power conversion efficiency.

Адаптивное управление амортизатором с магнитореологической жидкостью в подвеске автомобиля

The disadvantages of car suspension control systems include their inability to function with uncertainty of the suspension parameters and external disturbances, as well as the impossibility of quickly countering the latter. A new suspension control algorithm is proposed, which is able to reduce the impacts on the vehicle body from the road as well as inertial forces under the uncertainty of these parameters. The algorithm is adaptive and is based on the parametric identification of the mathematical model of the controlled object, performed by the control system in real time, and also on the use of an implicit reference model. A shock absorber with a magnetorheological fluid acts as a controlled element, which is capable of changing the degree of suspension damping. On the example of a two-mass model of the "quarter car" suspension, a model study of the effectiveness of the developed algorithm in comparison with a passive suspension was carried out. The results of the study showed the ability of the proposed adaptive suspension control algorithm to function under the current a priori uncertainty, improving the properties of the suspension in the low frequency range, which is most important for ensuring comfortable conditions for the driver and passengers.

Fault tolerant control of wind turbines with simultaneous actuator and sensor faults using adaptive time delay control

In this paper, a new Active Fault Tolerant Control (AFTC) is proposed using adaptive fractional-based Terminal Back-stepping Sliding Mode (TBSM) control strategy for pitch angle control of a variable speed wind turbine in the presence of actuator and sensor faults. In order to detect, isolate and accommodate the faults, Time Delay Estimation (TDE) is used as an online fault estimation algorithm. To eliminate the chattering of conventional sliding mode, supper twisting sliding mode algorithm is applied, which also ensures finite time convergence and high precision. Moreover, wind speed profiles are generated using TurbSim, and the controller is implemented on a simplified two-mass wind turbine model. To verify the validity of the proposed scheme, the simulations are also performed in FAST environment, and finally, the simulation results are presented which reveal the effectiveness of the proposed controller in the presence of faults, uncertainties and turbulent wind fields.

Variable speed wind turbine power control: A comparison between multiple MPPT based methods

Reducing the renewable energy costs is necessary for the competition with the fossil energies and control strategies have great impact on the efficiency of wind machines. In the wind turbine industry, a practical approach is to maximize the energy capture of a wind machine by optimizing the power coefficient in the under-rated situations. In this paper, with the main objective of maximizing the energy capture in the second region, four different control strategies are compared in the presence of uncertainties. The proposed control methods are compared based on their power capture and robustness against probable uncertainties in the structural and environmental parameters. A two-mass mechanical model is used and verified by FAST simulations. The generator torque is considered as the control input and the control objective is to track the rotor angular velocity in order to achieve the optimum value of power coefficient. First, a common sliding mode controller is reviewed, then a modern PI-Neural Network controller (PI-NN) studied, and then a backstepping controller is designed; finally, a hybrid H∞ and feedback linearization controller (H∞-FL) is introduced. While all controllers demonstrate an appropriate performance in terms of the tracking and efficiency indices, backstepping method shows better efficiency, Sliding mode and PI-NN are similar in terms of power efficiency and H∞-FL controller showed the least efficiency. On the other hand, the backstepping controller suffer from the high fluctuations in control signal and H∞-FL controller has a considerably smoother torque. The proposed controllers can also come up with the disturbances so that they can tolerate the structural and environmental parameters discrepancy to some extent. The backstepping and H∞-FL controllers showed similarly the best robustness, but sliding mode controller shows less robustness. The robustness of the PI-NN performance lies between the sliding mode and backstepping controller.

Individual Pitch Angle Control of a Variable Speed Wind Turbine Using Adaptive Fractional Order Non-Singular Fast Terminal Sliding Mode Control

Pitch angle control strategy has been applied to mitigate the influence of mechanical load and also output power control at above-rated wind speeds. In this paper, a wind turbine is modeled based on simplified two-mass model and an adaptive fractional-order non-singular fast terminal sliding mode controller (AFO-NFTSMC) is proposed based on individual pitch control strategy to control pitch angle of wind turbine against uncertainties and external disturbances. To do this, the single-blade approach is used and the wind turbine is divided into aerodynamics and mechanical subsystems and governing equations of each subsystem are derived. By designing and applying the AFO-NFTSMC to the two-mass model, system behavior is observed and simulated in terms of step and turbulent wind speed inputs. In addition, to verify the validity of the AFO-NFTSMC, the proposed controller is implemented in the FAST environment in which the wind speed profiles are generated using TurbSim. In order to analyze the environmental effects on the dynamic behavior of the system, the controller performance is explored in presence of parametric uncertainties. Simulation results reveal the priority and high-precision performance of the controller compared to conventional adaptive and adaptive sliding mode controller. Moreover, rotor speed tracking error is evaluated and demonstrated through different criteria.

Estimation of Design Parameters of the Crank-Connecting Rod Mechanism of Engines for Mobile Agricultural Machines

An accurate choice of the design model of the crank-connecting rod mechanism of piston internal combustion engines affects the accuracy of the calculation results and their complexity. At present, most of scientists and technicians choose a two-mass design model to analyze the operation of the crankconnecting rod mechanism. The model considers only the rotational and reciprocating movements of two masses, which are connected by a rigid weightless rod. This model significantly simplifies the calculations, neglects the elastic deformations of the parts of the crank-connecting rod mechanism, and eliminates the need for compiling the equations of dynamics in partial derivatives. However, the model has a number of drawbacks. The calculation results obtained using the two-mass model exhibit significant errors, which mainly depend on the design features of the connecting rod assembly. The paper discusses multi-mass design models, where the connecting rod assembly can comprise several lumped masses located along its length. In this case, the plane-parallel motion of these masses is added. The masses have weightless and absolutely rigid bonds. Forces and moments acting on the piston assembly and the crank are calculated according to the equations compiled. Comparison of the calculation results with the results obtained for a two-mass model can be used to determine errors and choose a design model that provides the required accuracy. The considered design model is of interest to engineers and technicians engaged in the design and calculation of the crank-connecting rod mechanism of piston internal combustion engines.

Command Filter Adaptive Power Capture Control Based on Fuzzy Rules Emulated Networks for Variable Speed Wind Turbines With Flexible Shaft

This paper considers the power capture control problem of variable-speed wind turbine (VSWT) systems with flexible shaft. The control objective is to optimize the capture of wind energy by tracking the desired power output. A novel command filter based adaptive power signal feedback (PSF) control method is proposed to design the PSF controller for the non-affine nonlinear VSWT systems with a two-mass model for which the parameters are totally unknown. A compensation dynamic with adaptable parameters is designed to compensate the errors caused by command filtering and the unknown control gains. The unavailable aerodynamic torque is approximated by introducing fuzzy rules emulated networks (FRENs) and estimations of the unknown parameters and their learning laws are established to derive the virtual and actual control laws. Meanwhile, it is proved that all the signals in the closed-loop system are uniformly ultimately bounded (UUB) via Lyapunov synthesis. Finally, the feasibility of the proposed controllers is demonstrated on a 5-MW variable-speed wind turbine.

The dynamic loads of mobile continuous earthmoving machine during the working body lock

working body is locked significant dynamic loads appear that influence the drive shaft and might lead to the machine breakdown. Preliminary approximate calculation of these loads is made according to oneor two-mass dynamic loads. For more detailed and precise analysis of dynamic load in drive shaft elements of the earth moving machines it is necessary to review the multimass model machine element movement. Goal. The aim of research is definition of the dynamic load and working out methodology that appears in the continuous earth digging machine elements during working body lock. Methodology. The discreet dynamic system dynamic and mathematical model construction is performed by means of the programming language Modelica. The model relevance is assessed via a two-mass model analytical solution. Results. Drive shaft element loading is assessed via the dynamic coefficient, which depends on kinematic, flexible and inertial machine parameters. Originality For the first time the continuous earth digging machine dynamic model that enables the automobile chassis drive shaft to interact with the continuous digging chain is constructed. It was determined that the drive shaft dynamic loading parameter correlation change upon the earth digging machine working body meaningful parameters. With designed model usage, the input data for transmission element engineering calculation was defined and the automobile basic chassis construction, equipped with the continuous digging chain. Practical value. The obtained dynamic factor value and developed methodology can be applied during continuous earth moving machine designing and calculation. Dynamic load decrease is possible through shaft stiffness and rotating mass inertia adjustment, and also by introducing elastic protecting frictional coupling with a controlling device.

Influence of Nonlinear Fluid Viscous Dampers on Seismic Response of RC Elevated Storage Tanks

The numerical investigation on the seismic response of RC elevated liquid storage tanks installed with viscous dampers is presented. A discrete two-mass model for the liquid and multi-degree of freedom system for staging, installed with the dampers are developed for Reinforced Concrete (RC) elevated liquid storage tanks. The elevated tank is assessed for seismic response reduction when provided with Linear Viscous Damper (LVD) and Nonlinear Viscous Damper (NLVD), installed in the staging. The RC elevated liquid storage tanks are analyzed for two levels of liquid containment in the tank, 100% and 25% of the tank capacity. Three Configurations of placements of dampers viz. dampers at alternate levels (Configuration I and Configuration II) and dampers at all the panels of the staging of the tank (Configuration III) are considered. To study the effect of peak ground acceleration, eight real earthquake time histories with accelerations varying from 0.1 g to 0.93 g are considered. The nonlinearity in the viscous damper is modified by taking force proportional to various velocity exponents. It is found that the nonlinear viscous dampers with lower damping constant result in a comparable reduction in the response of RC elevated liquid storage tank, to that of linear viscous dampers with higher damping constant. A lower damping constant signifies compact the size of the damper. Doi: 10.28991/cej-2020-SP(EMCE)-09 Full Text: PDF

Modelling sagittal and vertical phase differences in a lumped and distributed elements vocal fold model

The quality and timbre of disordered voices heavily rely on the vibration properties of the vocal folds. We discuss the representation of sagittal phase differences in vocal fold oscillations through a numerical biomechanical model involving lumped elements as well as distributed elements, i.e., delay lines. A dynamic glottal source model is proposed in which the fold displacement along the vertical and the sagittal dimensions is modelled using delay lines. In contrast to other models, with which the reproduction of sagittal phase differences is impossible (e.g., in two-mass models) or not easy to control (e.g., in 3D 16-mass and multi-mass models in general), the one proposed here provides direct control over the amount of phase delay between folds’ oscillations at the posterior and anterior part of the glottis, i.e., the sagittal axis, and at the superior and inferior part of the glottis, i.e., the vertical axis, while keeping the dynamic model simple and computationally efficient. The model is assessed by addressing the reproduction of oscillatory patterns observed in high-speed videoendoscopic data, in which sagittal phase differences are observed. Also, timing asymmetry parameters observed in hemi glottal area waveforms (GAWs) are used for fitting.

The study of damping control in semi-active car suspension

Paper discusses apparently opposing goal functions in terms of car’s comfort and handling. Short descriptions of passive, semi-active and active suspensions with their features are included. Thereafter, employing a two-mass quarter car model, an idea of damping control strategy in semi-active car suspension is presented. The results of performed simulation tests for various inputs are depicted and thoroughly discussed with comparison to classical passive suspension’s response. On the grounds of obtained results, conclusions are formulated. What is more, a layout of further work is outlined, with the aim of system’s response optimization in terms of comfort and handling features, as well as reliable validation of efficiency of proposed damping control strategy.

Optimal Landing Strategy for Two-Mass Hopping Leg With Natural Dynamics

It is necessary for a robotic leg to behave like a spring to realize a periodic hopping, since it can be efficient and does not require complicated control algorithm. However, the impact force makes the realization of periodic hopping more challenging. In this letter, an optimal landing strategy for a hopping leg is proposed, which can realize continuous hopping motion only by natural dynamics. The proposed strategy can reduce the foot landing velocity to zero and thus minimize the impact force. The formulation to derive the optimal condition is derived theoretically based on two-mass leg model, and its effectiveness is verified through various simulations and experiments using a series elastic actuator-driven robot leg.