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Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum
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作者 Guogang Gao LeiXu +2 位作者 Tianpeng Huang Xuliang Zhao Lihua Huang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第7期305-323,共19页
The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Des... The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme. 展开更多
关键词 Rotary inverted pendulum(RIP) linear quadratic regulator(LQR) reduced-order observer states estimate
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Project-Based Teaching in Control Theory Education Based on V-REP: A Cart Inverted Pendulum Case
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作者 Chao Liu Yonghuai Yang +1 位作者 Chengwei Zhang Shengyi Yang 《Journal of Contemporary Educational Research》 2023年第4期18-24,共7页
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 V-REP.Students must analyze,de... 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 V-REP.Students must analyze,design,and implement a suitable controller for the cart inverted pendulum system using their knowledge of the control theory.Different from traditional experiment and numerical simulation,virtual experiment is safe and less constrained.Moreover,the experiment results are more intuitive and obvious.This study can improve students’interest in learning the control theory and help students understand the relevant content better. 展开更多
关键词 V-REP inverted pendulum Control EDUCATION Virtual experiment
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Optimal feedback gains of a delayed proportional-derivative(PD) control for balancing an inverted pendulum 被引量:5
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作者 Qiang Wang Zaihua Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2017年第3期635-645,共11页
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 ... 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. 展开更多
关键词 inverted pendulum Time delay Stability Rightmost characteristic root Optimal feedback gain
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Numerical Study of a Novel Procedure for Installing the Tower and Rotor Nacelle Assembly of Offshore Wind Turbines Based on the Inverted Pendulum Principle 被引量:10
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作者 Wilson Guachamin Acero Zhen Gao Torgeir Moan 《Journal of Marine Science and Application》 CSCD 2017年第3期243-260,共18页
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 pract... 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. 展开更多
关键词 offshore wind turbine installation crane vessel shielding effects critical events limiting parameters inverted pendulum allowable sea states
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Mathematical modeling of elastic inverted pendulum control system 被引量:3
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作者 ChaoXU XinYU 《控制理论与应用(英文版)》 EI 2004年第3期281-282,共2页
Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering. The researches concentrate on the rigid finite dimensional models which are described... Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering. The researches concentrate on the rigid finite dimensional models which are described by ordinary differential equations (ODEs) .Complete rigidity is the approximation of practical models ; Elasticity should be introduced into mathematical models in the analysis of system dynamics and integration of highly precise controller. A new kind of inverted pendulum, elastic inverted pendulum was proposed, and elasticity was considered. Mathematical model was derived from Hamiltonian principle and variational methods, which were formulated by the coupling of partial differential equations (PDE) and ODE. Because of infinite dimensional, system analysis and control of elastic inverted pendulum is more sophisticated than the rigid one. 展开更多
关键词 Elastic inverted pendulum Hamiltonian principle Variational methods Mathematical model Coupling equation array
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Novel active fault-tolerant control scheme and its application to a double inverted pendulum system 被引量:3
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作者 Cui Ping Weng Zhengxin Patton Ron 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第1期134-140,共7页
On the basis of the gain-scheduled H∞ design strategy, a novel active fault-tolerant control scheme is proposed. Under the assumption that the effects of faults on the state-space matrices of systems can be of affine... On the basis of the gain-scheduled H∞ design strategy, a novel active fault-tolerant control scheme is proposed. Under the assumption that the effects of faults on the state-space matrices of systems can be of affine parameter dependence, a reconfigurable robust H∞ linear parameter varying controller is developed. The designed controller is a function of the fault effect factors that can be derived online by using a well-trained neural network. To demonstrate the effectiveness of the proposed method, a double inverted pendulum system, with a fault in the motor tachometer loop, is considered. 展开更多
关键词 active fault-tolerant control neural network estimator gain-scheduled controller double inverted pendulum.
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The Design of Inverted Pendulum System Based on Virtual Prototype Technology and PID Control 被引量:1
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作者 Hong-bo ZHENG,An-li TAO,Guo-dong XU,Lie-kun YANG,Xian-hua ZHANG (School of Information Science and Engineering,Shandong University,Qingdao,China) 《Journal of Measurement Science and Instrumentation》 CAS 2010年第S1期46-49,共4页
A design scheme of a single Inverted Pendulum Virtual Prototype based on the combination of software and hardware is introduced.It uses hardware platform of C8051F020 single chip and the software of Matlab,Visual Basi... A design scheme of a single Inverted Pendulum Virtual Prototype based on the combination of software and hardware is introduced.It uses hardware platform of C8051F020 single chip and the software of Matlab,Visual Basic and Kingview.It can simulate the force and movement of Inverted Pendulum expediently and intuitively.The combination of software and hardware makes the system closer to the reality.The concrete scheme is introduced in the paper and the result of PID control which verifies the correctness of the scheme. 展开更多
关键词 inverted pendulum VIRTUAL PROTOTYPE PID
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Multiplicity-induced optimal gains of an inverted pendulum system under a delayed proportional-derivative-acceleration feedback 被引量:2
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作者 Zisong MEI Zaihua WANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2022年第11期1747-1762,共16页
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 standing.The closed-loop system is ... 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 standing.The 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 4.Such 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 NDDEs.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 delays.Thus,the inverted pendulum can be well-stabilized with moderate delays and relatively small feedback gains.The result might be understandable that the elderly with obvious response delays can be well-stabilized with a delayed PDA feedback controller. 展开更多
关键词 human balance inverted pendulum proportional-derivative-acceleration(PDA)feedback neutral delay differential equation(NDDE) multiplicity-induced dominancy
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Optimal PID Control of Spatial Inverted Pendulum With Big Bang–Big Crunch Optimization 被引量:2
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作者 Jia-Jun Wang Tufan Kumbasar 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2020年第3期822-832,共11页
As the extension of the linear inverted pendulum(LIP) and planar inverted pendulum(PIP), this paper proposes a novel spatial inverted pendulum(SIP). The SIP is the most general inverted pendulum(IP) than any existing ... As the extension of the linear inverted pendulum(LIP) and planar inverted pendulum(PIP), this paper proposes a novel spatial inverted pendulum(SIP). The SIP is the most general inverted pendulum(IP) than any existing IP. The model of the SIP is presented for the first time. The SIP inherits all the characteristics of the LIP and the PIP, which is a nonlinear,unstable and underactuated system. The SIP has five degrees of motion freedom and three control forces. Thus, it is a multipleinput and multiple-output(MIMO) system with nonlinear dynamics. To realize the spatial trajectory tracking of the SIP,the control structure with five PID controllers will be designed.The parameter tuning of the multiple PIDs is a challenging work for the proposed SIP model. To alleviate the difficulties of the parameter tuning for the multiple PID controllers, optimal PIDs can be achieved with the help of Big Bang – Big Crunch(BBBC) optimization. The BBBC algorithm can successfully optimize the parameters of the multiple PID controllers with high convergence speed. The optimization performance index of the BBBC algorithm is compared with that of the particle swarm optimization(PSO). Simulation results certify the rightness and effectiveness of the proposed control and optimization methods. 展开更多
关键词 BIG Bang–Big Crunch(BBBC) optimal PID control SPATIAL inverted pendulum(SIP) SPATIAL TRAJECTORY tracking
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Balance control of a 12-DOF mobile manipulator based on two-wheel inverted pendulum robot 被引量:1
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作者 Gang Wang Seunghwan Choi Jangmyung Lee 《Journal of Measurement Science and Instrumentation》 CAS 2013年第1期52-57,共6页
Humanoid mobile manipulator which is based on two-wheel inverted pendulum robot has been studied.Balance control is a key problem for this kind of centroid-variable robot.Due to the principle of two wheel inverted pen... Humanoid mobile manipulator which is based on two-wheel inverted pendulum robot has been studied.Balance control is a key problem for this kind of centroid-variable robot.Due to the principle of two wheel inverted pendulum,a timely angle compensation is necessary to make the system keep balance when the centroid changes.In 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 method.Simulation and experimental results show the effectiveness of the method. 展开更多
关键词 angle compensation inverted pendulum variable centroid HUMANOID
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Performance Study of PID Controller and LQR Technique for Inverted Pendulum 被引量:1
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作者 Akhil Jose Clint Augustine +1 位作者 Shinu Mohanan Malola Keerthi Chacko 《World Journal of Engineering and Technology》 2015年第2期76-81,共6页
The inverted pendulum is a classic problem in dynamics and control theory and is widely used as a benchmark for testing control algorithms. It is unstable without control. The process is non linear and unstable with o... The inverted pendulum is a classic problem in dynamics and control theory and is widely used as a benchmark for testing control algorithms. It is unstable without control. The process is non linear and unstable with one input signal and several output signals. It is hence obvious that feedback of the state of the pendulum is needed to stabilize the pendulum. The aim of the study is to stabilize the pendulum such that the position of the carriage on the track is controlled quickly and accurately. The problem involves an arm, able to move horizontally in angular motion, and a pendulum, hinged to the arm at the bottom of its length such that the pendulum can move in the same plane as the arm. The conventional PID controller can be used for virtually any process condition. This makes elimination the offset of the proportional mode possible and still provides fast response. In this paper, we have modelled the system and studied conventional controller and LQR controller. It is observed that the LQR method works better compared to conventional controller. 展开更多
关键词 Control System LQR TECHNIQUE CONVENTIONAL Controller inverted pendulum
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Designing Discrete Predictor-Based Controllers for Networked Control Systems with Time-varying Delays:Application to A Visual Servo Inverted Pendulum System 被引量:1
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作者 Yang Deng Vincent Léchappé +4 位作者 Changda Zhang Emmanuel Moulay Dajun Du Franck Plestan Qing-Long Han 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2022年第10期1763-1777,共15页
A discrete predictor-based control method is developed for a class of linear time-invariant networked control systems with a sensor-to-controller time-varying delay and a controller-to-actuator uncertain constant dela... A discrete predictor-based control method is developed for a class of linear time-invariant networked control systems with a sensor-to-controller time-varying delay and a controller-to-actuator uncertain constant delay,which can be potentially applied to vision-based control systems.The control scheme is composed of a state prediction and a discrete predictor-based controller.The state prediction is used to compensate for the effect of the sensor-to-controller delay,and the system can be stabilized by the discrete predictor-based controller.Moreover,it is shown that the control scheme is also robust with respect to slight message rejections.Finally,the main theoretical results are illustrated by simulation results and experimental results based on a networked visual servo inverted pendulum system. 展开更多
关键词 Discrete predictor-based control inverted pendulum system networked control system time-varying delay vision-based control
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Using Adaptive Gain Scheduling LQR Method Control of Arm Driven Inverted Pendulum System Based on PIC18F4431 被引量:1
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作者 Huu Chan Thanh Nguyen An-Wen Shen 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2013年第4期85-92,共8页
The arm driven inverted pendulum system is a highly nonlinear model, muhivariable and absolutely unstable dynamic system so it is very difficult to obtain exact mathematical model and balance the inverted pendulum wit... The arm driven inverted pendulum system is a highly nonlinear model, muhivariable and absolutely unstable dynamic system so it is very difficult to obtain exact mathematical model and balance the inverted pendulum with variable position of the ann. To solve this problem, this paper presents a mathematical model for arm driven inverted pendulum in mid-position configuration and an adaptive gain scheduling linear quadratic regulator control method for the stabilizing the inverted pendulum. The proposed controllers for arm driven inverted pendulum are simulated using MATLAB-SIMULINK and implemented on an experiment system using PIC 18F4431 mieroeontroller. The result of experiment system shows the control performance to be very good in a wide range stabilization of the arm position. 展开更多
关键词 Arm Driven inverted pendulum (ADIP) adaptive gain scheduling LQR control LQR control swing up pendlum
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Swinging up a Real-Time Inverted Pendulum System 被引量:1
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作者 Maher Mohammed AlOmari Saeb Farhan Al Ganideh 《Journal of Mechanics Engineering and Automation》 2011年第5期407-411,共5页
In this study, a real-time control of the cart inverted pendulum system was developed using Mamdani type Fuzzy Logic Controller. Swing-up and stabilization of the inverted pendulum were implemented directly in a Fuzzy... In this study, a real-time control of the cart inverted pendulum system was developed using Mamdani type Fuzzy Logic Controller. Swing-up and stabilization of the inverted pendulum were implemented directly in a Fuzzy Logic Controller. The fuzzy logic controller was designed in the Matlab-Simulink environment and applied into in a Quasar controller board. Swing-up algorithm brings the pendulum near to its inverted position in 5 seconds from downward position. External forces were applied on the inverted pendulum to test the robustness of the fuzzy logic controller under internal as well as external disturbances. The inverted pendulum system showed an acceptable robustness to the external and internal disturbances. 展开更多
关键词 FUZZY CONTROL inverted pendulum.
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Harvesting base vibration energy by a piezoelectric inverted beam with pendulum
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作者 Jia-Nan Pan Wei-Yang Qin +1 位作者 Wang-Zheng Deng Hong-Lei Zhou 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第1期594-607,共14页
We proposed a two-degrees-of-freedom inverted piezoelectric beam with pendulum to promote the performance of vibration energy harvesting. This configuration is composed of an inverted elastic beam and a pendulum attac... We proposed a two-degrees-of-freedom inverted piezoelectric beam with pendulum to promote the performance of vibration energy harvesting. This configuration is composed of an inverted elastic beam and a pendulum attached to its free end. The electromechanical equations governing the nonlinear system were derived. The harmonic balance method(HBM)is applied to solve the equation and the results prove that there exists a 1:3 super-harmonic resonance. The simulation results show that owing to the particular nonlinearity, there appears a special bending effect in the amplitude-frequency response, i.e., bending right for the first natural frequency and left for the second natural frequency, which is beneficial for harvesting vibration energy. The HBM results are verified by the entity simulations. Furthermore, over a relatively wide range of power spectral density, it could reach a dense jumping and give a dense high pulse voltage. 展开更多
关键词 stochastic EXCITATION energy HARVESTING inverted PIEZOELECTRIC BEAM pendulum bi-stable state
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Intelligent Control on Three-Stage Inverted Pendulums
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作者 Lin Ruisen Lu Liang (School of Automation) 《Advances in Manufacturing》 SCIE CAS 1998年第4期26-31,共6页
In this paper, a new intelligent control method is introduced, which combines stipulations, optimal control method with knowledge based control. Using nonlinear programming method and expert experience for the compli... In this paper, a new intelligent control method is introduced, which combines stipulations, optimal control method with knowledge based control. Using nonlinear programming method and expert experience for the complicated nonlinear object, the good control result can be achieved. The effect of this method is shown by a simulation of three stage inverted pendulums. 展开更多
关键词 intelligent control stipulations principle pattern search inverted pendulum
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Design and implementation of 2DOF spherical inverted pendulum
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作者 GongShuang ZhangDongjun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2005年第1期123-127,共5页
The dynamics of 2DOF spherical inverted pendulum system is analyzed. The motion of the pendulum may be projected onto the orthogonal planes in the Cartesian Space. In this way the system can be decoupled into two clas... The dynamics of 2DOF spherical inverted pendulum system is analyzed. The motion of the pendulum may be projected onto the orthogonal planes in the Cartesian Space. In this way the system can be decoupled into two classical cart-pendulum systems and the design of controllers aimed at each subsystem separately are proposed. The linear quadratic optimal control strategy is applied in order to balance the pendulum system at the 'inverted' status. The method proposed is verified by the simulation and actual system experiments and the performance of the controller is discussed. 展开更多
关键词 DOF spherical inverted pendulum nonlinear system optimal control LQY.
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Modeling Walking with an Inverted Pendulum Not Constrained to the Sagittal Plane. Numerical Simulations and Asymptotic Expansions
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作者 Guillermo H. Goldsztein 《Applied Mathematics》 2017年第1期57-76,共20页
Inverted pendulum models are commonly used to study the bio-mechanics of biped walkers. In its simplest form, the inverted pendulum consists of a point mass attached to two straight mass-less legs. Most works constrai... Inverted pendulum models are commonly used to study the bio-mechanics of biped walkers. In its simplest form, the inverted pendulum consists of a point mass attached to two straight mass-less legs. Most works constrain the motion of the mass to the sagittal plane, i.e. the plane perpendicular to the ground that contains the direction toward the biped is walking. In this article, we remove this constrain to study the oscillations, the mass experiences in the direction perpendicular to the sagittal plane as the biped walks. While small, these lateral oscillations are unavoidable and of importance in the understanding of balance and stability of walkers, as well as walkers induced oscillations in pedestrian bridges. 展开更多
关键词 Mathematical MODELING inverted pendulum Mechanics of WALKING SAGITTAL Plane OSCILLATIONS
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Steering performance of an inverted pendulum vehicle with pedals as a personal mobility vehicle
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作者 Chihiro Nakagawa Kimihiko Nakano +1 位作者 Yoshihiro Suda Yuki Hirayama 《Theoretical & Applied Mechanics Letters》 CAS 2013年第1期71-76,共6页
From the viewpoints of environmental protection, support for the aged and ensuring the right to mobility, there is a need to develop a new type of mobility vehicle that provides more effective transportation. The auth... From the viewpoints of environmental protection, support for the aged and ensuring the right to mobility, there is a need to develop a new type of mobility vehicle that provides more effective transportation. The authors propose an inverted pendulum vehicle with pedals as one of the forms of personal mobility vehicles (PMVs). In this paper, the steering performance of the inverted pendulum vehicle with pedals is discussed based on experiments on a prototype. From the experimental results, it was confirmed that the errors from the five subjects for the target trajectory and the five-grade evaluation of the maneuverability were similar. Finally, we created an inverted pendulum vehicle with pedals to which was added a reaction actuator for the steering system. From the experimental results, it was found that setting appropriate feedback gains for the handle steering angle and its rate of rotation, which control the right and left wheel driving torques, resulted in greatly improved maneuverability. C 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi:10.1063/2.1301309] 展开更多
关键词 steering control STABILITY inverted pendulum vehicle
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LQG Control Design for Balancing an Inverted Pendulum Mobile Robot 被引量:1
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作者 Ragnar Eide Per Magne Egelid +1 位作者 Alexander Stamso Hamid Reza Karimi 《Intelligent Control and Automation》 2011年第2期160-166,共7页
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 ... 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. 展开更多
关键词 LQG Control inverted pendulum Mobile Robot
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