Milling Processes with Active Damping: Modeling and Stability

2021 ◽  
Author(s):  
David Lehotzky ◽  
Iker Mancisidor ◽  
Jokin Muñoa ◽  
Zoltan Dombovari
Keyword(s):  
Mathematical Model ◽  
Realistic Model ◽  
Active Damping ◽  
Control Parameters ◽  
Stability Prediction ◽  
Control Loop ◽  
Internal Dynamics ◽  
Measuring Device ◽  
Machine Tool Chatter ◽  
Active Damper

Abstract Active dampers are on the verge of appearing in commercial machines as devices that assist the avoidance of machine tool chatter. The adjustment of control parameters in these devices is mostly guided by models that do not consider the dynamics within the control loop of active damper. Therefore, these models neglect the dynamics of actuation, measurement and filtering, which can result in inaccurate stability predictions that hinder the efficient tuning of active dampers. To formulate a more realistic model for milling processes assisted by active damping, this paper derives a novel mathematical model that takes into account the internal dynamics of the actuator, measuring device, and discrete filtering. This study shows that accurate stability prediction requires the incorporation of actuator and filter dynamics into the model, especially at high spindle speeds and large feedback gains.

scholarly journals Delayed Trilateral Teleoperation of a Mobile Robot

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
D. Santiago ◽  
E. Slawiñski ◽  
V. Mut
Keyword(s):  
Stability Analysis ◽  
Mobile Robot ◽  
Shared Environment ◽  
Time Varying ◽  
Control Parameters ◽  
Simple Test ◽  
Control Loop ◽  
Teleoperation System ◽  
Human Operators ◽  
The Stability

This paper analyzes the stability of a trilateral teleoperation system of a mobile robot. This type of system is nonlinear, time-varying, and delayed and includes a master-slave kinematic dissimilarity. To close the control loop, three P+d controllers are used under a position master/slave velocity strategy. The stability analysis is based on Lyapunov-Krasovskii theory where a functional is proposed and analyzed to get conditions for the control parameters that assure a stable behavior, keeping the synchronism errors bounded. Finally, the theoretical result is verified in practice by means of a simple test, where two human operators both collaboratively and simultaneously drive a 3D simulator of a mobile robot to achieve an established task on a remote shared environment.

scholarly journals FULL CAR ACTIVE DAMPING SYSTEM FOR VIBRATION CONTROL

2020 ◽  
Vol 6 (4) ◽  
pp. 1-17
Author(s):  
G. Yakubu ◽  
G. Sani ◽  
S. B. Abdulkadir ◽  
A. A.Jimoh ◽  
M. Francis
Keyword(s):  
Mathematical Model ◽  
Linear Quadratic Regulator ◽  
Active Damping ◽  
Settling Time ◽  
Linear Quadratic ◽  
Body Acceleration ◽  
The Road ◽  
Road Profile ◽  
Lqr Controller ◽  
Mass Displacement

Full car passive and active damping system mathematical model was developed. Computer simulation using MATLAB was performed and analyzed. Two different road profile were used to check the performance of the passive and active damping using Linear Quadratic Regulator controller (LQR)Road profile 1 has three bumps with amplitude of 0.05m, 0.025 m and 0.05 m. Road profile 2 has a bump with amplitude of 0.05 m and a hole of -0.025 m. For all the road profiles, there were 100% amplitude reduction in Wheel displacement, Wheel deflection, Suspension travel and body displacement, and 97.5% amplitude reduction in body acceleration for active damping with LQR controller as compared to the road profile and 54.0% amplitude reduction in body acceleration as compared to the passive damping system. For the two road profiles, the settling time for all the observed parameters was less than two (2) seconds. The present work gave faster settling time for mass displacement, body acceleration and wheel displacement.

scholarly journals Study of Hydraulic Semi-Active Damper. 1st Report. Derivation of Mathematical Model and Numerical Simulation.

1997 ◽  
Vol 28 (4) ◽  
pp. 458-465
Author(s):  
Naoto SATO ◽  
Satoru HAYASHI ◽  
Akira TANAKA ◽  
Ikuro IIMURA
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Active Damper

scholarly journals DYNAMIC SIMULATION AND COMPOSITION CONTROL IN A 10 L MIXING TANK

REAKTOR ◽  
2012 ◽  
Vol 14 (2) ◽  
pp. 95
Author(s):  
Yulius Deddy Hermawan ◽  
Gogot Haryono
Keyword(s):  
Mathematical Model ◽  
Dynamic Simulation ◽  
Closed Loop ◽  
Step Function ◽  
Open Loop ◽  
Liquid Volume ◽  
Control Parameters ◽  
Software Environment ◽  
Composition Control ◽  
Volumetric Rate

The open loop experiment of composition dynamic in a 10 L mixing tank has been successfully done inlaboratory. A 10 L tank was designed for mixing of water (as a stream-1) and salt solution (as astream-2 with salt concentration, c2 constant). An electric stirrer was employed to obtain uniformcomposition in tank. In order to keep the liquid volume constant, the system was designed overflow. Inthis work, 2 composition control configurations have been proposed; they are Alternative-1 andAlternative-2. For Alternative-1, the volumetric-rate of stream-1 was chosen as a manipulatedvariable, while the volumetric-rate of stream-2 was chosen as a manipulated variable for Alternative-2. The composition control parameters for both alternatives have been tuned experimentally. Thevolumetric-rate of manipulated variable was changed based on step function. The outlet stream’scomposition response (c3) to a change in the input volumetric-rate has been investigated. Thisexperiment gave Proportional Integral Derivative (PID) control parameters. The gain controllers Kc[cm6/(gr.sec)] for Alternative-1 and Alternative-2 are -34200 and 40459 respectively. Integral timeconstant ( tI) and Derivative time constant (tD) for both alternatives are the same, i.e. tI = 16 second,and tD = 4 second. Furthermore, closed loop dynamic simulation using computer programming wasalso done to evaluate the resulted tuning parameters. The developed mathematical model ofcomposition control system in a mixing tank was solved numerically. Such mathematical model wasrigorously examined in Scilab software environment. The results showed that closed loop responses inPID control were faster than those in P and PI controls.

scholarly journals The study of chaotic and regular regimes of the fractal oscillators FitzHugh-Nagumo

2018 ◽  
Vol 62 ◽  
pp. 02017 ◽  
Author(s):  
Olga Lipko ◽  
Roman Parovik
Keyword(s):  
Mathematical Model ◽  
Lyapunov Exponents ◽  
Nerve Impulse ◽  
Chaotic Attractors ◽  
Control Parameters ◽  
Schmidt Orthogonalization ◽  
Non Local ◽  
Explicit Finite Difference ◽  
Maximum Lyapunov Exponents ◽  
Orthogonalization Procedure

In this paper we study the conditions for the existence of chaotic and regular oscillatory regimes of the hereditary oscillator FitzHugh-Nagumo (FHN), a mathematical model for the propagation of a nerve impulse in a membrane. To achieve this goal, using the non-local explicit finite-difference scheme and Wolf’s algorithm with the Gram-Schmidt orthogonalization procedure and the spectra of the maximum Lyapunov exponents were also constructed depending on the values of the control parameters of the model of the FHN. The results of the calculations showed that there are spectra of maximum Lyapunov exponents both with positive values and with negative values. The results of the calculations were also confirmed with the help of oscillograms and phase trajectories, which indicates the possibility of the existence of both chaotic attractors and limit cycles.

Sliding Mode Control of the Human Vestibular System

2012 ◽  
Author(s):  
Rachael McCarty ◽  
S. Nima Mahmoodi ◽  
Keith Williams
Keyword(s):  
Mathematical Model ◽  
Sliding Mode Control ◽  
Vestibular System ◽  
Head Movement ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Control Parameters ◽  
Mode Control ◽  
The Mathematical Model ◽  
The Brain

An original sliding mode controller is designed, based on an existing mathematical model for response control of the human vestibular system. The human vestibular system is located in the inner ear and significantly contributes to the functions of detecting head motion, maintaining balance and posture, and realizing gaze stabilization. The vestibular system sends signals to the brain to tell it how the head and body are moving, and the brain reacts by changing eye position accordingly. The nonlinearities of the vestibular system are not completely understood. The biggest nonlinearity is the nystagmus, a bouncing of the eyes to compensate for quick head movement. Another nonlinearity is that the quick phase does not start until head movement reaches a certain frequency. Considering these nonlinearities as well as the uncertainties of the system, sliding mode control a good choice for controlling the system. Several mathematical models of the human vestibular system are considered for use in the control design. The best model of those considered is chosen based on the models’ consideration of nonlinearities and their levels of complexity. The mathematical model used in this paper is a nonlinear transfer function. The output is controlled with a robust sliding mode controller. Results demonstrate the need to increase control parameters as frequency of the sinusoidal input increases to minimize overshoot error. However, since the human head cannot tolerate an infinitely large frequency input, control parameters also will necessarily be limited. Therefore, results show that the designed sliding mode robust controller is an effective mechanism for controlling the mathematical model of the human vestibular system.

Nonlinear Dynamics of Upright Human Balance While Using a Passive-Cane

2016 ◽  
Author(s):  
James R. Chagdes ◽  
Joao P. Freire ◽  
Amit Shukla
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Assistive Technology ◽  
Treatment Plan ◽  
Assistive Technologies ◽  
Feedback Gain ◽  
Control Parameters ◽  
Human Posture ◽  
Inverted Pendulum Model ◽  
Potential Applications

Recent mathematical models of human posture have been explored to better understand the space of control parameters that result in stable upright balance. These models have demonstrated that there are two types of instabilities — a leaning instability and an instability leading to excessive oscillation. While these models provide insight into the stability of upright bipedal stance, they are not sufficient for individuals that require the aid of assistive technologies, such as a passive-cane or a walker. Without a valid model one is unable to understand the control parameters required for maintain upright posture or if similar instabilities even exist when assistive technologies are used. Therefore in this study, we developed a mathematical model of human posture while using a passive-cane to examine the nonlinear dynamics of stance. First, we developed a simple mathematical model of cane assisted human stance by adapting the inverted pendulum model of Chagdes et al., [1]. We modeled the human body, upper arm, forearm, cane, and ground as a two-degree-of-freedom, five-bar-linkage with pin joints representing the ankle, shoulder, elbow, and wrist joints. Second, we investigate upright stability in the parameter space of feedback gain and time-delay. We hypothesize that the analysis will show similar instabilities compared to that of a human standing without assistive technology. We also hypothesize that the space of control parameters which stabilize upright equilibrium posture will increase when a cane is incorporated. This study has two potential applications. First, the developed mathematical model could allow clinicians to better assess technology assisted balance and if needed help clinicians to customize a treatment plan for an individual that allows them to avoid unstable postural dynamics. Second, the mathematical model can be used to design customized assistive technology for people of difference physical properties and impairments.

scholarly journals POSSIBILITY OF THE MATHEMATICAL MODEL OF COUNTERACTION APPLICATION TO THE ASSESSMENT OF TRANSPORT INFRASTRUCTURE SECURITY LEVEL

2018 ◽  
Vol 21 (3) ◽  
pp. 67-77
Author(s):  
A. V. Dormidontov ◽  
L. V. Mironova ◽  
V. S. Mironov
Keyword(s):  
Mathematical Model ◽  
Classical Model ◽  
State Level ◽  
Security System ◽  
Transport Infrastructure ◽  
Security Level ◽  
Assessment Procedure ◽  
Control Parameters ◽  
Predator Prey Model ◽  
Danger Level

The air transport infrastructure objects security is the state level problem as the part of national and public security of the country. One of the directions in this field is the vulnerability assessment procedure for transport infrastructure objects and on the basis of this procedure the elaboration of ensuring their safety recommendations takes place. The mathematical substantiation of recommendations and their possible implementation is an important part of the marked problem. The possibility of mathematical model of counteraction application, which assesses the offender’s potential and the security’s potential based on evaluative dimensions of the offender and the security system, is under consideration. Assume as a basis the mathematical description model of interaction nature between defender-offender system components, the model known as the competition predator-prey model with quantitative qualitative characteristic parameters of the two systems is taken. The model is modified classical model of Lotka-Volterra competition, which allows us to estimate changes in the danger level formation with reference to the transport infrastructure object and the object security level. The analysis of possible model states is made. The control parameters of the model are described. The mathematical apparatus, which is able to evaluate the danger level, the level of transport infrastructure objects protection, to reveal parameters reducing security system potential and to perform the control parameters data is given. The presented mathematical model identifies the parameters which reduce the security system potential and controls these parameters. The management can be carried out for the purpose of system transfer from one steady state to another, preservation of its operability, increase of its operation cycle and compliance to modern safety requirements. The system of Defender-offender equations correct usage allows us to justify the configurable security system of transport infrastructure objects on the basis of the specified security level.

scholarly journals Rapidly Accelerated Synchronous Generators in CAES Systems for Frequency Support in Power Grids

2021 ◽  
Author(s):  
◽  
Efim Sturov
Keyword(s):  
Mathematical Model ◽  
Renewable Energy Sources ◽  
Synchronous Generator ◽  
Power Grids ◽  
Small Scale ◽  
Rotational Inertia ◽  
Control Parameters ◽  
Electrical Networks ◽  
Hydraulic Motor ◽  
Synchronous Generators

<p>Modern electrical networks are transformed through the use of intermittent sources of energy, such as small-scale photovoltaic installations and wind turbines. By reducing the carbon footprints associated with centralised power grids, they are made more vulnerable to contingent under-frequency events. The renewable energy sources can't provide the required rotational inertia to make the power grid's frequency stable and to be able to assist in restoring the frequency. In New Zealand, Transpower (system operator) is responsible for normalising the frequency in case of contingent events to avoid blackouts in the networks.    In case of contingent events in power grids, additional power must be delivered to the networks with the use of primary frequency support systems. Internationally these systems are represented by under loaded power plants, where power output can be adjusted by controlling the primary governor output. This approach incurs no-load running costs and to avoid these costs generation units should be maintained at rest. The most efficient and technically feasible solution is to use synchronous generators that are already present in the power grids or can be additionally delivered to the grids as stand-alone units. However, with the use of the traditional synchronisation method, the generators cannot be synchronised with power grids in a short timeframe (up to 10 s in some countries).   To overcome this disadvantage, a novel synchronisation approach should be designed to synchronise synchronous generators from rest of the electrical networks. This thesis proves that it can be achieved by a ballistic synchronisation approach (and then the improved 2-stage ballistic approach), which computes and follows an acceleration trajectory which simultaneously synchronises both phase and frequency. To achieve this fast acceleration a novel environmentally friendly small-scale compressed air energy storage (ss-CAES) system has been designed. This system utilises a hydraulic drivetrain which transmits very high torque directly to the shaft of a synchronous generator, thus enabling its rapid acceleration.  The hydraulic drivetrain is composed of a proportional throttle valve and a variable-displacement hydraulic motor. The central controller from National Instruments outputs a voltage that controls the opening of the proportional valve. It changes the flowrate in the main hydraulic circuit, meaning that it is possible to control the output torque and velocity of the hydraulic motor. Since it is coupled to a synchronous generator, the control system can control the dynamics of the drivetrain by changing its voltage output.   Computer simulations indicate that this approach enables very rapid synchronisation of a model system to the grid in < 1.5 s at a 100-kW scale. The modelling of the prototype helped to verify the control parameters of the system before the implementation of the algorithm built into the hardware. It should be noted that this model was simulated with the use of the corresponding manufacturer's data. To increase the accuracy of the mathematical model and verify the control parameters, the system components were experimentally characterised with the use of a ubiquitous high-speed data acquisition system.  It resulted in a realistic and accurate mathematical model of the complex electro-hydraulic system, despite the well-known challenges of modelling the hydraulic domain. This model was utilised for the tuning of the control parameters of the system before its experimental testing. Experimental runs confirmed the feasibility of the proposed acceleration and synchronisation approach for synchronisation from the rest of the generator in < 4 s.</p>

Feasibility Study of Using Simultaneous Motion of Two Rotary Axes to Evaluate Machining Center: Simulation

2011 ◽  
Author(s):  
K. M. Muditha Dassanayake ◽  
Masaomi Tsutsumi ◽  
Ohta Katsunori
Keyword(s):  
Mathematical Model ◽  
Feasibility Study ◽  
Radial Direction ◽  
Rotary Table ◽  
Measuring Device ◽  
Rotary Axes ◽  
Machining Center ◽  
Double Ball Bar ◽  
Ball Bar ◽  
The Mathematical Model

In this paper, a new motion: the two rotary axes simultaneous motion was proposed and the mathematical model which was used to carryout simulations was described. The effect of each deviation on the proposed motion was identified and described one by one. A methodology to estimate all the eight deviations which inherent to tilting rotary table type machining centers was described step by step. This methodology consists of two motions: the proposed motion and C axis radial direction motion. Both the two motions used only the rotary axes. All the motions can be run on one setup. The simulations were carried out by considering that the double ball bar as the measuring device. Furthermore, number of settings which can be used for the new motion were discussed. From this study, it was confirmed that this method can be used for estimate all the eight deviations, accurately.

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