Block-pulse functions method for solving three-dimensional fractional Poisson type equations with Neumann boundary conditions

Xie, Jiaquan; Yao, Zhibin; Wu, Runlong; Ding, Xiaofeng; Zhang, Jun

doi:10.1186/s13661-018-0945-7

Cited by 2 publications

(2 citation statements)

References 31 publications

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“…Podlubny [17] first proposed the model of fractional order proportional-integral-differential controller. The basic knowledge of the definition, properties, Laplace transformation, and application of fractional order calculus is introduced in [18][19][20][21][22]. Compared with the integer , the expression of fractional controller has two parameters , , which increases the adjustment range of parameters.…”

Section: Introductionmentioning

confidence: 99%

Study on the Control Method of Mine-Used Bolter Manipulator Based on Fractional Order Algorithm and Input Shaping Technology

Jun

Huang

2018

Mathematical Problems in Engineering

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Mine-used bolter is the main equipment to solve the imbalance of excavation and anchor in well mining, and the manipulator is the main working mechanism of mine bolt drilling rig. The manipulator positioning requires high rapidity and stability. For this reason, this paper proposes a composite control method of “input shaping + fractional order PDμ control”. According to the mathematical model of the valve-controlled cylinder, the fractional-order controller PDμ is developed. At the same time, the input shaping is used to feed forward the accurate positioning and path planning of the manipulator, which not only improves the robustness of the system, but also shortens the stability time of the system and restrains the maximum amplitude of the system vibration. In this paper, the control effects of fractional order PDμ controller and integer order PD controller are compared. The results show that the maximum amplitude of the control system is reduced by 75% and the stabilization time is reduced by 60% after using the fractional order PDμ controller, which fully reflects the superiority of the fractional order controller in response speed, adjusting time, and steady-state accuracy. Finally, the control effects of “input shaping + fractional order PDμ control” and fractional order PDμ controller on the stability of the system are compared. The maximum amplitude of the system was reduced by 50% by using “input shaping + fractional order PDμ control”. Numerical simulation confirms the feasibility and effectiveness of the composite control method. This composite control method provides theoretical support for the precise positioning of the manipulator, and the high stability and high safety of the manipulator also expand the application scope and depth of the composite control method.

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Section: Introductionmentioning

confidence: 99%

Study on the Control Method of Mine-Used Bolter Manipulator Based on Fractional Order Algorithm and Input Shaping Technology

Jun

Huang

2018

Mathematical Problems in Engineering

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“…The effect of traditional control is not ideal. Even if the parameters are reset, it still can not achieve the expected control goal, which can not essentially overcome the defects of integer order control technology, and it is difficult to achieve the accurate spatial positioning.Therefore, it is necessary to introduce intelligent optimization Fractional Order PID [25][26][27][28][29][30] controller technology. The expression of fractional order controller has two more parameters than that of integral order PID.…”

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confidence: 99%

Motion Strategy of Drilling Anchor Manipulator Based on Intelligent Optimization Algorithm

Che

Jun

2023

J. Phys.: Conf. Ser.

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The drilling and anchoring robot is an important equipment to realize the intellectualization of fully mechanized coal mining. The control effect of its manipulator directly affects the safety and efficiency of the support operation of the drilling and anchoring robot. The control of drilling anchor manipulator usually adopts PID controller, but due to the limitation of integer order PID control algorithm and traditional empirical parameter adjustment, it is difficult to find a group of parameters with the best control effect in a short time, resulting in the failure of timely and accurate positioning of the end of the manipulator. In this paper, the combination of numerical modeling and simulation analysis is used to adjust the parameters of fractional order PIλDμ controller by using search algorithm (GPS) and applied to the motion control of manipulator; Based on the independent joint control theory, the single input single output system model of hydraulic cylinder at the joint of manipulator is established by using Matlab-Simulink software and fractional PIλDμ control technology. The fractional order control system is regulated by input shaping feedforward control technology(IS). The step response effect of the hydraulic system is further analyzed by setting input feedforward controllers with different gain ratios. The numerical simulation results show that the control strategy of “Input Shaping(IS) + Intelligent optimization algorithm (GPS) parameter adjustment + Fractional PIλDμ control technology” can effectively improve the spatial accurate positioning of mining manipulator. The research expand the application of intelligent control technology in the field of mining equipment.

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Block-pulse functions method for solving three-dimensional fractional Poisson type equations with Neumann boundary conditions

Cited by 2 publications

References 31 publications

Study on the Control Method of Mine-Used Bolter Manipulator Based on Fractional Order Algorithm and Input Shaping Technology

Study on the Control Method of Mine-Used Bolter Manipulator Based on Fractional Order Algorithm and Input Shaping Technology

Motion Strategy of Drilling Anchor Manipulator Based on Intelligent Optimization Algorithm

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