In this study,a dynamic model for an inverted pendulum system(IPS)attached to a car is created,and two different control methods are applied to control the system.The designed control algorithms aim to stabilize the p...In this study,a dynamic model for an inverted pendulum system(IPS)attached to a car is created,and two different control methods are applied to control the system.The designed control algorithms aim to stabilize the pendulum arms in the upright position and the car to reach the equilibrium position.Grey Wolf Optimization-based Linear Quadratic Regulator(GWO-LQR)and GWO-based Fuzzy LQR(FLQR)control algorithms are used in the control process.To improve the performance of the LQR and FLQR methods,the optimum values of the coefficients corresponding to the foot points of the membership functions are determined by the GWO algorithm.Both a graphic and a numerical analysis of the outcomes are provided.In the comparative analysis,it is observed that the GWO-based FLQR method reduces the settling time by 22.58% and the maximum peak value by 18.2% when evaluated in terms of the angular response of the pendulum arm.Furthermore,this approach outperformed comparable research in the literature with a settling time of 2.4 s.These findings demonstrate that the suggested GWO-based FLQR controlmethod outperforms existing literature in terms of the time required for the pendulum arm to reach equilibrium.展开更多
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
This paper mainly focuses on stability analysis of the nonlinear active disturbance rejection control(ADRC)-based control system and its applicability to real world engineering problems.Firstly,the nonlinear ADRC(NLAD...This paper mainly focuses on stability analysis of the nonlinear active disturbance rejection control(ADRC)-based control system and its applicability to real world engineering problems.Firstly,the nonlinear ADRC(NLADRC)-based control system is transformed into a multi-input multi-output(MIMO)Lurie-like system,then sufficient condition for absolute stability based on linear matrix inequality(LMI)is proposed.Since the absolute stability is a kind of global stability,Lyapunov stability is further considered.The local asymptotical stability can be deter-mined by whether a matrix is Hurwitz or not.Using the inverted pendulum as an example,the proposed methods are verified by simulation and experiment,which show the valuable guidance for engineers to design and analyze the NL ADRC-based control system.展开更多
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 sy...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 decisions.The 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.展开更多
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
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
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
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
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
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
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
An inverted pendulum is a sensitive system of highly coupled parameters, in laboratories, it is popular for modelling nonlinear systems such as mechanisms and control systems, and also for optimizing programmes before...An inverted pendulum is a sensitive system of highly coupled parameters, in laboratories, it is popular for modelling nonlinear systems such as mechanisms and control systems, and also for optimizing programmes before those programmes are applied in real situations. This study aims to find the optimum input setting for a double inverted pendulum（DIP）, which requires an appropriate input to be able to stand and to achieve robust stability even when the system model is unknown. Such a DIP input could be widely applied in engineering fields for optimizing unknown systems with a limited budget. Previous studies have used various mathematical approaches to optimize settings for DIP, then have designed control algorithms or physical mathematical models.This study did not adopt a mathematical approach for the DIP controller because our DIP has five input parameters within its nondeterministic system model. This paper proposes a novel algorithm, named Uni Neuro, that integrates neural networks（NNs） and a uniform design（UD） in a model formed by input and response to the experimental data（metamodel）. We employed a hybrid UD multiobjective genetic algorithm（HUDMOGA） for obtaining the optimized setting input parameters. The UD was also embedded in the HUDMOGA for enriching the solution set, whereas each chromosome used for crossover, mutation, and generation of the UD was determined through a selection procedure and derived individually. Subsequently, we combined the Euclidean distance and Pareto front to improve the performance of the algorithm. Finally, DIP equipment was used to confirm the settings. The proposed algorithm can produce 9 alternative configured input parameter values to swing-up then standing in robust stability of the DIP from only 25 training data items and 20 optimized simulation results. In comparison to the full factorial design, this design can save considerable experiment time because the metamodel can be formed by only 25 experiments using the UD. Furthermore, the proposed algorithm can be applied to nonlinear systems with multiple constraints.展开更多
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
The Spring-Loaded Inverted Pendulum(SLIP)has been regarded as a canonical model for hopping and running dynamics of legged robots.This paper presents a novel control of the actuated-SLIP hopping on unknown terrains.We...The Spring-Loaded Inverted Pendulum(SLIP)has been regarded as a canonical model for hopping and running dynamics of legged robots.This paper presents a novel control of the actuated-SLIP hopping on unknown terrains.We propose that in the neighborhood of the desired stable hybrid limit cycle,the local dynamical behavior of a hybrid system can be expressed by a set of phase coordinates and transverse coordinates.Under some acceptable assumptions,the hybrid averaging theorem is applied on the SLIP non-integrable dynamics to simplify the controller design.Using the inherent symmetry of SLIP dynamics,a control Lyapunov function-based hybrid averaging controller is developed to ensure the exponential stability of the desired gait orbit.This results in a set of linear constraints on the control signal,which can be readily solved by a quadratic programming optimization.Furthermore,a novel method is introduced to improve the robustness against unknown disturbances through the online constraint adjustment.The proposed controller is evaluated in various simulations,demonstrating the SLIP hopping on diverse terrains,including flat,sin-wave,and unregular terrains.The performance of the approach is also validated on a quadruped robot SCIT Dog for generating dynamic gaits such as pronking.展开更多
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
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
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
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
The inverted pendulum is a classic problem in dynamics and control theory and is widely used as a benchmark for testing control algorithms. This paper studies the use of fuzzy control method to study the stability con...The inverted pendulum is a classic problem in dynamics and control theory and is widely used as a benchmark for testing control algorithms. This paper studies the use of fuzzy control method to study the stability control problem of a triple inverted pendulum system. By the linear model of the system, the feedback weight matrix of the LQR optimal control and the feedback parameters of the linear optimal control are designed to determine the parameters of the fuzzy controller. The simulation results show that the proposed method can achieve the stability control of the three stage inverted pendulum, and has good dynamic performance with simple parameter selection.展开更多
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
文摘In this study,a dynamic model for an inverted pendulum system(IPS)attached to a car is created,and two different control methods are applied to control the system.The designed control algorithms aim to stabilize the pendulum arms in the upright position and the car to reach the equilibrium position.Grey Wolf Optimization-based Linear Quadratic Regulator(GWO-LQR)and GWO-based Fuzzy LQR(FLQR)control algorithms are used in the control process.To improve the performance of the LQR and FLQR methods,the optimum values of the coefficients corresponding to the foot points of the membership functions are determined by the GWO algorithm.Both a graphic and a numerical analysis of the outcomes are provided.In the comparative analysis,it is observed that the GWO-based FLQR method reduces the settling time by 22.58% and the maximum peak value by 18.2% when evaluated in terms of the angular response of the pendulum arm.Furthermore,this approach outperformed comparable research in the literature with a settling time of 2.4 s.These findings demonstrate that the suggested GWO-based FLQR controlmethod outperforms existing literature in terms of the time required for the pendulum arm to reach equilibrium.
基金supported in part by the Youth Foundation of China University of Petroleum-Beijing at Karamay(under Grant No.XQZX20230038)the Karamay Innovative Talents Program(under Grant No.20212022HJCXRC0005).
文摘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.
基金supported by the National Natural Science Foundation of China(61836001).
文摘This paper mainly focuses on stability analysis of the nonlinear active disturbance rejection control(ADRC)-based control system and its applicability to real world engineering problems.Firstly,the nonlinear ADRC(NLADRC)-based control system is transformed into a multi-input multi-output(MIMO)Lurie-like system,then sufficient condition for absolute stability based on linear matrix inequality(LMI)is proposed.Since the absolute stability is a kind of global stability,Lyapunov stability is further considered.The local asymptotical stability can be deter-mined by whether a matrix is Hurwitz or not.Using the inverted pendulum as an example,the proposed methods are verified by simulation and experiment,which show the valuable guidance for engineers to design and analyze the NL ADRC-based control system.
文摘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 decisions.The 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.
基金financially supported by the Research Council of Norway granted through the Department of Marine Technologythe Centre for Ships and Ocean Structures(CeSOS) and the the Centre for Autonomous Marine Operations and Systems(AMOS) from the Norwegian University of Science and Technology(NTNU)the financial support from Escuela Politécnica Nacional(EPN)through the project PIMI-15-03"Investigación y evaluación de sistemas innovadores de propulsión distribuida con ingestión de capa límite para mejorar la eficiencia propulsiva y térmica de vehículos aéreos no tripulados aplicados en los sectores:agrícola,medicina y vigilancia"
文摘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.
基金supported by the National Natural Science Foundation of China (Grant 11372354)the Fund of the State Key Lab of Mechanics and Control of Mechanical Structures (Grant MCMS-0116K01)
文摘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.
基金This worie was supported by Ningbo Institute of Technology, Zhejiang University (No. 1051157G301).
文摘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.
文摘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.
基金supported by the China Scholarship Council(CSC)the National Natural Science Foundation of China(92067106)。
文摘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.
基金supported by the National Natural Science Foundation of China(No.12072370)。
文摘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.
文摘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.
基金supported by Indonesian Government(No.BPPLN DIKTI 3+1)
文摘An inverted pendulum is a sensitive system of highly coupled parameters, in laboratories, it is popular for modelling nonlinear systems such as mechanisms and control systems, and also for optimizing programmes before those programmes are applied in real situations. This study aims to find the optimum input setting for a double inverted pendulum（DIP）, which requires an appropriate input to be able to stand and to achieve robust stability even when the system model is unknown. Such a DIP input could be widely applied in engineering fields for optimizing unknown systems with a limited budget. Previous studies have used various mathematical approaches to optimize settings for DIP, then have designed control algorithms or physical mathematical models.This study did not adopt a mathematical approach for the DIP controller because our DIP has five input parameters within its nondeterministic system model. This paper proposes a novel algorithm, named Uni Neuro, that integrates neural networks（NNs） and a uniform design（UD） in a model formed by input and response to the experimental data（metamodel）. We employed a hybrid UD multiobjective genetic algorithm（HUDMOGA） for obtaining the optimized setting input parameters. The UD was also embedded in the HUDMOGA for enriching the solution set, whereas each chromosome used for crossover, mutation, and generation of the UD was determined through a selection procedure and derived individually. Subsequently, we combined the Euclidean distance and Pareto front to improve the performance of the algorithm. Finally, DIP equipment was used to confirm the settings. The proposed algorithm can produce 9 alternative configured input parameter values to swing-up then standing in robust stability of the DIP from only 25 training data items and 20 optimized simulation results. In comparison to the full factorial design, this design can save considerable experiment time because the metamodel can be formed by only 25 experiments using the UD. Furthermore, the proposed algorithm can be applied to nonlinear systems with multiple constraints.
基金The MKE(the Ministry of Knowledge Economy),Korea,under the Human Resources Development Program for Robotics Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2012-H1502-12-1002)the MKE,Korea,under the ITRC(Information Technology Research Center)Support Program supervised by the NIPA(NIPA-2012-H0301-12-2006)
文摘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.
基金supported by HeilongJiang Touyan Innovation Team Program.
文摘The Spring-Loaded Inverted Pendulum(SLIP)has been regarded as a canonical model for hopping and running dynamics of legged robots.This paper presents a novel control of the actuated-SLIP hopping on unknown terrains.We propose that in the neighborhood of the desired stable hybrid limit cycle,the local dynamical behavior of a hybrid system can be expressed by a set of phase coordinates and transverse coordinates.Under some acceptable assumptions,the hybrid averaging theorem is applied on the SLIP non-integrable dynamics to simplify the controller design.Using the inherent symmetry of SLIP dynamics,a control Lyapunov function-based hybrid averaging controller is developed to ensure the exponential stability of the desired gait orbit.This results in a set of linear constraints on the control signal,which can be readily solved by a quadratic programming optimization.Furthermore,a novel method is introduced to improve the robustness against unknown disturbances through the online constraint adjustment.The proposed controller is evaluated in various simulations,demonstrating the SLIP hopping on diverse terrains,including flat,sin-wave,and unregular terrains.The performance of the approach is also validated on a quadruped robot SCIT Dog for generating dynamic gaits such as pronking.
文摘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.
文摘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.
文摘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.
文摘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]
文摘The inverted pendulum is a classic problem in dynamics and control theory and is widely used as a benchmark for testing control algorithms. This paper studies the use of fuzzy control method to study the stability control problem of a triple inverted pendulum system. By the linear model of the system, the feedback weight matrix of the LQR optimal control and the feedback parameters of the linear optimal control are designed to determine the parameters of the fuzzy controller. The simulation results show that the proposed method can achieve the stability control of the three stage inverted pendulum, and has good dynamic performance with simple parameter selection.
基金supported by the 2021 Higher Education Teaching Reform Research Project of SEAC(No.221057)2021 Ministry of Education Collaborative Education Project(No.202102646007)2022 Guizhou Province Gold Course Construction Project.
文摘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.
