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Applied Mathematics and Mechanics(English Edition) 2022年第11期43卷 1747-1762页

作者： Zisong MEI Zaihua WANG Department of Basic Courses Army Engineering UniversityNanjing 211101China

This paper studies the stabilization to an inverted pendulum under a delayed proportional-derivative-acceleration(PDA)feedback,which can be used to understand human balance in quiet *** closed-loop system is described by a neutral delay differential equation(NDDE).The optimal feedback gains(OFGs)that make the exponential decaying rate maximized are determined when the characteristic equation of the closed-loop has a repeated real root with multiplicity *** a property is called multiplicity-induced dominancy of time-delay systems,and has been discussed intensively by many authors for retarded delay differential equations(RDDEs).This paper shows that multiplicity-induced dominancy can be achieved in *** addition,the OFGs are delay-dependent,and decrease sharply to small numbers correspondingly as the delay increases from zero and varies slowly with respect to moderate ***,the inverted pendulum can be well-stabilized with moderate delays and relatively small feedback *** result might be understandable that the elderly with obvious response delays can be well-stabilized with a delayed PDA feedback controller.

关键词： human balance inverted pendulum proportional-derivative-acceleration(PDA)feedback neutral delay differential equation(NDDE) multiplicity-induced dominancy

Optimal feedback gains of a delayed proportional-derivative(PD) control for balancing an inverted pendulum

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Acta Mechanica Sinica 2017年第3期33卷 635-645页

作者： Qiang Wang Zaihua Wang Institute of Science PLA University of Science and Technology State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and Astronautics

In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a systematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost characteristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial values around the origin are fixed. The main results are checked by numerical simulation.

关键词： inverted pendulum Time delay Stability Rightmost characteristic root Optimal feedback gain

Optimal Control of Nonlinear inverted pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input

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International Journal of Automation and computing 2014年第6期11卷 661-670页

作者： Lal Bahadur Prasad Barjeev Tyagi Hari Om Gupta Department of Electrical Engineering Indian Institute of Technology Roorkee Uttarakhand 247667 India

Linear quadratic regulator(LQR) and proportional-integral-derivative(PID) control methods, which are generally used for control of linear dynamical systems, are used in this paper to control the nonlinear dynamical system. LQR is one of the optimal control techniques, which takes into account the states of the dynamical system and control input to make the optimal control *** nonlinear system states are fed to LQR which is designed using a linear state-space model. This is simple as well as robust. The inverted pendulum, a highly nonlinear unstable system, is used as a benchmark for implementing the control methods. Here the control objective is to control the system such that the cart reaches a desired position and the inverted pendulum stabilizes in the upright position. In this paper, the modeling and simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using PID controller and LQR have been presented for both cases of without and with disturbance input. The Matlab-Simulink models have been developed for simulation and performance analysis of the control schemes. The simulation results justify the comparative advantage of LQR control method.

关键词： inverted pendulum nonlinear system proportional-integral-derivative (PID) control optimal control linear quadratic regulator (LQR)

Unfalsified control research and its application in inverted pendulum system

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Unfalsified control research and its application in inverted...

inverted pendulum Teaching Experiment Platform Based on MATLAB-DSP

第25届中国控制与决策会议

作者： Lei Cui Yu Xiang Lv Gang Xie College of Physics and Optoelectronics Taiyuan University of Technology College of Information Engineering Taiyuan University of Technology

ISBN: (纸本)9781467355322

The traditional control theory is based on the assumption model. which leads to the subjectivity weaknesses in control process. In this paper, we introduced a model-free and data-driven control method - unfalsified control method and described its basic theory in details. This algorithm is applied to the straight line inverted pendulum system. It has simple controller and does not depend on the system model, so it’s suitable for real-time online application. The simulation results verified the validity and efficiency of this theoretical approach.

关键词： inverted pendulum model-free unfalsified control

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Inverted Pendulum Teaching Experiment Platform Based on MATL...

Numerical Study of a Novel Procedure for Installing the Tower and Rotor Nacelle Assembly of Offshore Wind Turbines Based on the inverted pendulum Principle

2013教育技术与信息系统国际会议

作者： Shaoqiang Yuan Songsong Zhang School of Automation Science and Electrical Engineering Beihang University

This paper presents a new teaching platform for the inverted pendulum based on MATLAB-DSP integrated development environment. The teaching platform shows some advantages, including high efficiency, low cost, friendly interface and the function of testing dynamic process and rework parameters on line. It plays an important role in the teaching of modern control theory. The experiment platform can convert Simulink model to DSP executable code automatically, so the students can specialize in the study control algorithm. After finish this experiment, students not only learn a lot of knowledge, but also lay a good foundation for the future research work.

关键词： inverted pendulum MATLAB-DSP LQR simulation model

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Journal of Marine Science and Application 2017年第3期16卷 243-260页

作者： Wilson Guachamin Acero Zhen Gao Torgeir Moan Department of Marine Technology Norwegian University of Science and Technology Trondheim NO-7491 Norway Departamento de Ingenieria Mecanica Escuela Politecnica Nacional Quito 17-01-2 759 Ecuador Centre for Ships and Ocean Structures Norwegian University of Science and Technology Trondheim NO-7491 Norway Centre for Autonomous Marine Operations and Systems Norwegian University of Science and Technology Trondheim NO-7491 Norway

Current installation costs of offshore wind turbines(OWTs) are high and profit margins in the offshore wind energy sector are low, it is thus necessary to develop installation methods that are more efficient and practical. This paper presents a numerical study(based on a global response analysis of marine operations) of a novel procedure for installing the tower and Rotor Nacelle Assemblies(RNAs) on bottom-fixed foundations of OWTs. The installation procedure is based on the inverted pendulum principle. A cargo barge is used to transport the OWT assembly in a horizontal position to the site, and a medium-size Heavy Lift Vessel(HLV) is then employed to lift and up-end the OWT assembly using a special upending frame. The main advantage of this novel procedure is that the need for a huge HLV(in terms of lifting height and capacity) is eliminated. This novel method requires that the cargo barge is in the leeward side of the HLV(which can be positioned with the best heading) during the entire installation. This is to benefit from shielding effects of the HLV on the motions of the cargo barge, so the foundations need to be installed with a specific heading based on wave direction statistics of the site and a typical installation season. Following a systematic approach based on numerical simulations of actual operations, potential critical installation activities, corresponding critical events, and limiting(response) parameters are identified. In addition, operational limits for some of the limiting parameters are established in terms of allowable limits of sea states. Following a preliminary assessment of these operational limits, the duration of the entire operation, the equipment used, and weather-and water depth-sensitivity, this novel procedure is demonstrated to be viable.

关键词： offshore wind turbine installation crane vessel shielding effects critical events limiting parameters inverted pendulum allowable sea states

Project-Based Teaching in Control Theory Education Based on V-REP: A Cart inverted pendulum Case

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Journal of Contemporary Educational Research 2023年第4期7卷 18-24页

作者： Chao Liu Yonghuai Yang Chengwei Zhang Shengyi Yang School of Physics and Mechatronic Engineering Guizhou Minzu UniversityGuiyang 550025Guizhou ProvinceChina

This paper provides a teaching concept for control theory education based on Virtual Robot Experimentation Platform(V-REP).A cart inverted pendulum virtual physical model is developed on *** must analyze,design,and implement a suitable controller for the cart inverted pendulum system using their knowledge of the control *** from traditional experiment and numerical simulation,virtual experiment is safe and less ***,the experiment results are more intuitive and *** study can improve students’interest in learning the control theory and help students understand the relevant content better.

关键词： V-REP inverted pendulum Control Education Virtual experiment

Balance control of a 12-DOF mobile manipulator based on two-wheel inverted pendulum robot

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Journal of Measurement Science and Instrumentation 2013年第1期4卷 52-57页

作者： Gang Wang Seunghwan Choi Jangmyung Lee Dept.of Electrical Engineering Pusan UniversityBusan 609-735Korea

Humanoid mobile manipulator which is based on two-wheel inverted pendulum robot has been *** control is a key problem for this kind of centroid-variable *** to the principle of two wheel inverted pendulum,a timely angle compensation is necessary to make the system keep balance when the centroid *** this paper,a method based on coordinate transformation is introduced to get the compensatory angle and a 12-DOF mobile manipulator is also used to check the *** and experimental results show the effectiveness of the method.

关键词： angle compensation inverted pendulum variable centroid humanoid

Hierarchical Sliding-mode Control Method for an inverted pendulum System

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Journal of Systems Science and Information 2007年第4期5卷 347-351页

作者： Nuo Jia Hui Wang Mathematics Department Harbin Normal University Harbin 150025 China

This paper addresses a hierarchical sliding-mode control method for an inverted pendulum system. In this method, the system states are divided into two groups and a kind of two-layer sliding plane is constructed. We can derive the sliding-mode control law which includes the equivalent control of every sub-sliding plane by using Lyapunov law, therefore the total sliding-mode control law can drive every subsystem to move along its own sub-sliding plane, then the asymptotical stability of all the sliding planes is proved.

关键词： inverted pendulum sliding-mode control hierarchical

LQG Control Design for Balancing an inverted pendulum Mobile Robot

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Intelligent Control and Automation 2011年第2期2卷 160-166页

作者： Ragnar Eide Per Magne Egelid Alexander Stamso Hamid Reza Karimi Department of Engineering Faculty of Engineering and ScienceUniversity of AgderGrimstadNorway

The objective of this paper is to design linear quadratic controllers for a system with an inverted pendulum on a mobile robot. To this goal, it has to be determined which control strategy delivers better performance with respect to pendulum’s angle and the robot’s position. The inverted pendulum represents a challenging control problem, since it continually moves toward an uncontrolled state. Simulation study has been done in MATLAB Simulink environment shows that both LQR and LQG are capable to control this system successfully. The result shows, however, that LQR produced better response compared to a LQG strategy.

关键词： LQG Control inverted pendulum Mobile Robot