Simplified Adaptive Nonlinear Robust Controller for Linearized Pantagraph-Type Manipulator

1995 ◽  
Vol 7 (3) ◽  
pp. 242-249 ◽  
Author(s):  
Kiyotaka Izumi ◽  
◽  
Keigo Watanabe ◽  
Masatoshi Nakamura ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Physical Parameters ◽  
Additional Mass ◽  
Robust Controller ◽  
End Effector ◽  
Linear Controller ◽  
The Mathematical Model ◽  
Nonlinear Robust

If physical parameters are adjusted suitably in the pantagraph-type manipulator, the mathematical model becomes linear so that we can apply a linear controller. However, when the manipulator has an additional mass as an end-effector, the linear controller does not work well because the resultant model becomes nonlinear. In this paper, we propose a simplified adaptive nonlinear robust controller which we can apply to the manipulator, irrespective of the system linearity or nonlinearity. The effectiveness of the controller is illustrated by some simulations.

Force tracking control of grinding end effector based on backstepping + PID

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shijie Dai ◽  
Shining Li ◽  
Wenbin Ji ◽  
Zhenlin Sun ◽  
Yufeng Zhao
Keyword(s):  
Mathematical Model ◽  
Linear System ◽  
Control Strategy ◽  
Grinding Force ◽  
Constant Force ◽  
End Effector ◽  
Content Type ◽  
Modeling And Analysis ◽  
The Mathematical Model ◽  
Automobile Wheel

Purpose This study aims to realize the constant force grinding of automobile wheel hub. Design/methodology/approach A force control strategy of backstepping + proportion integration differentiation (PID) is proposed. The grinding end effector is installed on the flange of the robot. The robot controls the position and posture of the grinding end actuator and the grinding end actuator controls the grinding force output. First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. Finally, the feasibility of the proposed method is verified by simulation and experiment. Findings The simulation and experimental results show that the backstepping + PID strategy can track the expected force quickly, and improve the dynamic response performance of the system and the quality of grinding and polishing of automobile wheel hub. Research limitations/implications The mathematical model is based on the pneumatic system and ideal gas, and ignores the influence of friction in the working process of the cylinder, so the mathematical model proposed in this study has certain limitations. A new control strategy is proposed, which is not only used to control the grinding force of automobile wheels, but also promotes the development of industrial control. Social implications The automatic constant force grinding of automobile wheel hub is realized, and the manpower is liberated. Originality/value First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. The nonlinear model of the system is controlled by backstepping method, and in the process, the linear system composed of errors is obtained, and then the linear system is controlled by PID to realize the combination of backstepping and PID control.

Analysis of Vibrating Natural Frequency of Pressure Pipeline

2011 ◽  
Vol 421 ◽  
pp. 98-101
Author(s):  
Ting Yue Hao
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Critical Flow ◽  
Physical Parameters ◽  
Beam Model ◽  
Instability Condition ◽  
Coupling Vibration ◽  
Critical Flow Velocity ◽  
Pressure Pipeline ◽  
The Mathematical Model

The pressure pipeline is simplified as the beam model with two simple supported ends. The mathematical model is established, considering influence of the fluid-solid coupling vibration. Then the critical flow velocity is obtained by calculation and solving. By analyzing the practical numerical example，the influence of physical parameters on the first three-order natural frequency is discussed. Using Matlab software for programming, the instability condition of pressure pipeline is obtained, which is consistent with the result of numerical calculation.

Vibration Analysis of a Vertical Roller Mill: Modeling and Validation

2014 ◽  
Author(s):  
Engin H. Çopur ◽  
Metin U. Salamci ◽  
Selahattin Gülbeyaz
Keyword(s):  
Mathematical Model ◽  
Vibration Analysis ◽  
Compressive Force ◽  
Vibration Characteristics ◽  
Physical Parameters ◽  
Roller Mill ◽  
Vibration Tests ◽  
Working Parameters ◽  
The Mathematical Model ◽  
Vertical Roller

In this paper, vibration characteristics of a Vertical Roller Mill (VRM) are studied by using physical parameters of an operating VRM. The mathematical model is derived and simulated for a set of working parameters. Mechanical properties of the grinding material and the physical properties of the mechanical construction are used in the vibration model in order to obtain more realistic results. Simulation results are presented which give critical frequencies of the VRM. The effects of the hydraulic compressive force to the vibration characteristics are investigated. The effects of the material feeding rate (which affects the mineral thickness to be grinded) to the vibration characteristics are also simulated. In order to validate the mathematical model, a set of experimental vibration tests are performed on the VRM. Vibrations are measured during the run-down procedure of the VRM in order to determine natural frequencies of the mill as well as excitation frequencies of the system. The measurements showed the validity of the proposed mathematical model for the vibration analysis of the VRM.

Design Tension Controller of Unwinding System Based on LMI-Based H∞ Robust Control

2012 ◽  
Author(s):  
Shanhui Liu ◽  
Xuesong Mei ◽  
Fanfeng Kong ◽  
Jian Li ◽  
Zhihui Liu
Keyword(s):  
Mathematical Model ◽  
Tension Control ◽  
Linear Matrix ◽  
Robust Controller ◽  
Printing Quality ◽  
Time Varying Parameters ◽  
Working Principle ◽  
The Stability ◽  
The Mathematical Model ◽  
Printing Machine

The unwinding system is the most important section for tension generating of the gravure printing machine, and how to maintain the stability of the tension in unwinding system is a key problem to ensure the printing quality. In this paper, an H∞ controller based on Linear Matrix Inequality (LMI) method is presented to strengthen the stability of the tension in unwinding section, and the controller is analyzed and verified by the simulation. Firstly, a nonlinear mathematical model is established according to unwinding system’s working principle, and a linear mathematical model is constructed by analyzing the uncertain and time-varying parameters. Secondly, based on the mathematical model and LMI framework, a H∞ robust controller is designed. Finally, the performance of the H∞ controller is verified by the simulation, and the results show that the proposed tension controller has better robustness and disturbance rejection than traditional PID controller in tension control of the unwinding system.

Multi-objective storage location allocation optimization and simulation analysis of automated warehouse based on multi-population genetic algorithm

2018 ◽  
Vol 26 (4) ◽  
pp. 367-377 ◽  
Author(s):  
Yu-ling Jiao ◽  
Xiao-cui Xing ◽  
Peng Zhang ◽  
Liang-cheng Xu ◽  
Xin-Ran Liu
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Dynamic Simulation ◽  
Population Genetic ◽  
Physical Parameters ◽  
Location Allocation ◽  
Multi Objective ◽  
Storage Location ◽  
Population Genetic Algorithm ◽  
The Mathematical Model

Aiming at the requirement of working efficiency and security of automated warehouse and taking the operation time of outbound–inbound, the equivalent center of gravity of overall shelf and the degree of relative accumulation of related products as the multi-objective functions, the mathematical model is constructed for multi-objective storage location allocation optimization. According to the simple weighted genetic algorithm, it is easily prone to the problem of immature convergence when solving multi-objective programming problems. So, the multi-population genetic algorithm is proposed to solve the mathematical model of storage location allocation optimization. Combining with the experiment data of toy car assembly and automated warehouse, the results of the automated warehouse storage location allocation are obtained. FlexSim dynamic simulation model is established based on the storage location allocation solution, the physical parameters of automated warehouse and the experimental requirements plan of vehicle model assembly. The operation effect of the model and the utilization rate of the equipment are analyzed. The result of multi-population genetic algorithm is more reasonable and effective. It is proved that the result of multi-population genetic algorithm is superior to the result of simple weighted genetic algorithm, which provides an effective method for storage location allocation optimization and outbound–inbound dynamic simulation.

Mathematical model used for predicting arc-flash protective performance of fabrics based on physical parameters

2021 ◽  
pp. 004051752110226
Author(s):  
Wen Zhu ◽  
Hong Tang ◽  
Qilong Sun ◽  
Zhen Huang ◽  
Chengjiao Zhang
Keyword(s):  
Mathematical Model ◽  
Raw Materials ◽  
Principal Component ◽  
Thermomechanical Properties ◽  
Physical Parameters ◽  
Weave Structure ◽  
Arc Flash ◽  
Protective Fabrics ◽  
Protective Performance ◽  
The Mathematical Model

In this study, parameters that may affect the performance of arc-flash protective fabrics were systematically analyzed. Sixteen different commonly used fabrics with different configurations and grammage were produced and investigated, namely four raw materials with different configurations (93:0:5:2, 70:23:5:2, 46:47:5:2, and 23:70:5:2) and four with different grammage (180, 210, 240, and 270 g/m2). It was found that factors had different effects on the arc protective performance. Principal component analysis showed that the four plain weave fabrics of 180 g/m2 behaved differently compared with other samples, which was ascribed to the related differences in weave structure. In addition, a predicting mathematical model was developed based on the parameters that have the greatest influence on arc protective performance. The prediction parameters were not added to the structure, but replaced with physical parameters such as air permeability and thermomechanical properties. The adjusted R2 was 0.867, which demonstrated the rationality of using multiple linear regression to accurately predict arc protective performance. It was hypothesized that the construction of the mathematical model could contribute to the arc protective fabric evaluation and future researches in this field.

scholarly journals NUMERICAL METHOD OF VIBRATIONS RESEARCH IN LARGE FLEXIBLE SYSTEMS

2014 ◽  
pp. 52-59
Author(s):  
Olena Mul ◽  
Delfim Torres
Keyword(s):  
Mathematical Model ◽  
Communication Network ◽  
Numerical Method ◽  
Frequency Spectrum ◽  
Elastic System ◽  
Physical Parameters ◽  
Flexible Systems ◽  
The Real ◽  
Fundamental Systems ◽  
The Mathematical Model

The mathematical model of the real flexible elastic system is considered with the distributed and discrete parameters, which presents the equation at derivative parts with non-classical maximum terms. Complication of maximum terms makes impossible finding of exact analytical decision of such maximum task, in connection with what for researches the numerical method of the normal fundamental systems of decisions is used. Dependence of frequencies of possible vibrations is explored on different physical parameters of system. It is shown, that introduction to reverse communication network after speed with the defined values of the reverse communication coefficient allows controling the frequency spectrum in which excitation of vibrations are possible.

scholarly journals Measurement of low frequency mechanical vibrations based on an inverted magnetic pendulum

2019 ◽  
Vol 9 (5) ◽  
pp. 3480
Author(s):  
Susana V. Awad ◽  
Joaquin F Orozco ◽  
Fredy E Hoyos
Keyword(s):  
Mathematical Model ◽  
Friction Force ◽  
Low Frequency ◽  
Physical Parameters ◽  
Model Design ◽  
Frequency Meter ◽  
Adjustable Range ◽  
The Mathematical Model ◽  
Considerable Period ◽  
The Magnetic Field

<span>In this paper is presented the mathematical model, design and construction of a prototype of a  vibration frequency meter in an adjustable range of 2 Hz to 30 Hz; The experimental results and their analysis are also presented, making a comparative evaluation with the theoretical model. The device is based on the principle of resonance applied in an inverted magnetic pendulum whose natural frequency can be modified by variations of physical parameters. The oscillation of the pendulum is recorded detecting variations in the magnetic field using hall effect sensors; the data recorded with a microprocessor is analyzed and the results are simultaneously plotted in a computer interface. The data obtained were processed to be plotted in the frequency domain, facilitating its analysis. It was proved that the prototype can be used as a frequency meter and that the adjustable character of the device works according to the mathematical model. Finally, The effect of the friction force was studied, it was concluded that the friction force affects the measurement after a considerable period of time of oscillation, but not in the first moments.</span>

scholarly journals Modeling and Analysis of Energy/Exergy for Absorber Pipes of Linear Parabolic Concentrating Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Reza Alayi ◽  
Mahdi Mohkam ◽  
Hossein Monfared ◽  
Alibek Issakhov ◽  
Nima Khalilpoor
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Numerical Solutions ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
Solar Collectors ◽  
Matlab Software ◽  
Modeling And Analysis ◽  
Parabolic Collector ◽  
The Mathematical Model

In this paper, the physical parameters of the absorber pipe of a linear parabolic collector have been investigated. The types of solar collectors, specifically the linear parabolic collector, have been comprehensively studied. Then, the mathematical model of heat transfer in the absorber pipe of the collector has been presented based on valid references. Numerical solutions of the equations related to the absorber pipe were performed by MATLAB software, and the effects of the physical parameters of the absorber pipe on its efficiency were investigated. The results show that increasing the length of the absorber pipe causes a nonlinear decrease in the efficiency of the absorber pipe. One of the important results is the increase in fluid temperature due to the increase in the diameter of the adsorbent tube, which increases the diameter of the fluid temperature by 60 K, in which the parameter increases the efficiency by 0.38%.

Analysis of Radiative Magneto-Nanofluid over an Accelerated Plate in a Rotating Medium with Hall Effects

2017 ◽  
Vol 11 ◽  
pp. 129-145 ◽  
Author(s):  
Rohit Sharma ◽  
Syed Modassir Hussain ◽  
Hitesh Joshi ◽  
Gauri Shenkar Seth
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Shear Stress ◽  
Convective Flow ◽  
Research Work ◽  
Secondary Flows ◽  
Physical Parameters ◽  
Rotating Medium ◽  
Laplace Transform Technique ◽  
The Mathematical Model

Present research work has been undertaken to analyze the effects of Hall current on natural convective flow of radiative, incompressible, viscous and electrically conducting magneto-nanofluid over a uniformly accelerated moving vertical ramped temperature plate in a rotating medium. Three types of water based nanofluids containing the nanoparticles of alumina, copper and titanium oxide have been accounted. The mathematical model of the problem has been presented using the nanoparticle volume fraction model. The Laplace transform technique has been employed to solve the mathematical model. The closed-form expressions of nanofluid velocity, temperature, shear stress and rate of heat transfer at the plate have been obtained for both the conditions of ramped temperature and isothermal plates. The effects of various physical parameters on the nanofluid velocity due to primary and secondary flows and temperature have been exemplified using various graphs whereas, the numerical values of shear stress and rate of heat transfer at the plate have been reported in tabular form for different values of physical parameters of interest. Moreover, the numerical results have been compared for the natural convective flow near ramped temperature plate with the corresponding flow near isothermal plate. It has been noted that both the nanofluid velocity and temperature are higher in magnitude in the case of isothermal plate than that of ramped temperature plate. The results of present research work have been validated with the earlier published work.

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