Stabilization of Double Link Inverted Pendulum Using LQR
01 Mar 2018-pp 1-6
TL;DR: The result shows and validate the comparative lead of LQR control strategy over conventional PID control strategy in double inverted pendulum-cart dynamic system.
Abstract: An double inverted pendulum on cart is an object which is a nonlinear, unstable system that is used as a standard for designing the control methods and finds most versatile application in the field of control theory. In this paper the mathematical modeling and control strategy of double inverted pendulum-cart dynamic system with disturbance input using PID and LQR have been stated. The states of the system are given to LQR controller which is obtained using linear state-feedback controller. The MATLAB-SIMULINK environment have been used for simulation of the control strategies. The aim of this work is to have a comparative study of two different control strategies and the analysis of performance of two different types of controller for double inverted pendulum on cart system have been obtained. The result shows and validate the comparative lead of LQR control strategy over conventional PID control strategy.
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09 Dec 2020
TL;DR: In this article, the authors examined the control of a double inverted pendulum (DIP) using pole placement and linear quadratic regulator (LQR) control and found the optimal parameters of the LQR control law, GA and PSO to tune and determine the proper control parameters.
Abstract: An inverted pendulum system has potential applications in different domains that motivate researchers for new innovative development. An inverted pendulum system is an underactuated, nonlinear, inherently unstable and a multivariable system. The system is modelled mainly through either Euler-Lagrange or Newtonian dynamic formulation. This paper aims to examine the control of a double inverted pendulum (DIP) using pole placement and linear quadratic regulator (LQR) control. To find the optimal parameters of the LQR control law, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are used to tune and determine the proper control parameters. Simulations are conducted using MATLAB/Simulink under different circumstances and the performance of each control technique is analyzed and compared in terms of the system rise time, settling time, peak amplitude, and steady state error.
10 citations
TL;DR: In this paper, the authors designed optimal LQR and LQG controllers for the system of ball-on-sphere and did a comparative analysis between the two controllers, and the results showed that both controllers met the desired system performance.
Abstract: With the state-space method, many controllers can be designed optimally. LQR and LQG are two of these controllers. These two controllers are covered much in the literature. Despite this, not many works cover the ball-onsphere system. Therefore, the research designed optimal LQR and LQG controllers for the system of ball-on-sphere and did a comparative analysis between the two. System dynamics were first investigated and the mathematical model was derived. After that, the system was linearized and then the state-space representation was obtained. Using this representation, the two controllers were designed and applied to the system for control. The control was done based on the specified desired system performance. Finally, the controllers' performances were analyzed and compared. Results obtained showed that both controllers met the desired system performance. With θx is 87.14% and θy is 86.43% less than their respective unregulated settling times, LQR satisfied the at least 80% performance requirement more than LQG. For LQG, θx is 82.35% and θy is 82.95% less than their respective unregulated settling times. These values are less than that of LQR. It was also observed that minimizing the total control energy leads to maximizing the total transient energy but LQG maximizes the total transient energy more than LQR. Another finding was that all states played role in regulating the controller to the desired system performance. Without regulation, LQG was found to be more efficient than LQR but in general, LQR is more efficient than LQG because, in LQG, settling time (of ball's angles) of less than 1.00 sec could not be realized. LQR is 4.79% and 3.48% more efficient than LQG in x and y directions, respectively, for the ball’s angles settling time. This research is significant because it is the first to design and do a comparative analysis of LQR and LQG controllers for the ball-on-sphere system. Therefore, bridging the existing gap in the literature is the value of this research.
5 citations
Cites methods from "Stabilization of Double Link Invert..."
...Double inverted pendulum (DIP)-cart system dynamics are modelled and mathematically represented in [23] where a control strategy with disturbance input is used using LQR and PID....
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22 Jul 2020
TL;DR: In this article, the impact of a kinematic chain in terms of a nonlinear contact force has been investigated, which has different expressions for elastic compression, elasto-plastic compression, and elastic restitution.
Abstract: This article presents a method to solve the impact of a kinematic chain in terms of a non-linear contact force. The nonlinear contact force has different expressions for elastic compression, elasto-plastic compression, and elastic restitution. Lagrange equations of motion are used to obtain the non-linear equations of motion with friction for the collision period. The kinetic energy during the impact is compared with the pre-impact kinetic energy. During the impact of a double pendulum the kinetic energy of the non-impacting link is increasing and the total kinetic energy of the impacting link is decreasing.
5 citations
04 Mar 2021
TL;DR: An attempt to produce a robust and expected walking gait is made by using an ALO (ant lion optimization) tuned linear inverted pendulum model plus flywheel (LIPM plus fly wheel) to provide the stabilized dynamic walking.
Abstract: PurposeHumanoid robots have complicated dynamics, and they lack dynamic stability. Despite having similarities in kinematic structure, developing a humanoid robot with robust walking is quite difficult. In this paper, an attempt to produce a robust and expected walking gait is made by using an ALO (ant lion optimization) tuned linear inverted pendulum model plus flywheel (LIPM plus flywheel).Design/methodology/approachThe LIPM plus flywheel provides the stabilized dynamic walking, which is further optimized by ALO during interaction with obstacles. It gives an ultimate turning angle, which makes the robot come closer to the obstacle and provide a turning angle that optimizes the travel length. This enhancement releases the constraint on the height of the COM (center of mass) and provides a larger stride. The framework of a sequential locomotion planer has been discussed to get the expected gait. The proposed method has been successfully tested on a simulated model and validated on the real NAO humanoid robot.FindingsThe convergence curve defends the selection of the proposed controller, and the deviation under 5% between simulation and experimental results in regards to travel length and travel time proves its robustness and efficacy. The trajectory of various joints obtained using the proposed controller is compared with the joint trajectory obtained using the default controller. The comparison shows the stable walking behavior generated by the proposed controller.Originality/valueHumanoid robots are preferred over mobile robots because they can easily imitate the behaviors of humans and can result in higher output with higher efficiency for repetitive tasks. A controller has been developed using tuning the parameters of LIPM plus flywheel by the ALO approach and implementing it in a humanoid robot. Simulations and experiments have been performed, and joint angles for various joints are calculated and compared with the default controller. The tuned controller can be implemented in various other humanoid robots
4 citations
TL;DR: A linear quadratic regulator model tuning and control was applied to the inverted pendulum using internet of things (IoT) and the system's conditions and performance could be monitored and controlled via personal computer (PC) and mobile phone.
Abstract: This research proposes control method to balance and stabilize an inverted pendulum. A robust control was analyzed and adjusted to the model output with real time feedback. The feedback was obtained using state space equation of the feedback controller. A linear quadratic regulator (LQR) model tuning and control was applied to the inverted pendulum using internet of things (IoT). The system's conditions and performance could be monitored and controlled via personal computer (PC) and mobile phone. Finally, the inverted pendulum was able to be controlled using the LQR controller and the IoT communication developed will monitor to check the all conditions and performance results as well as help the inverted pendulum improved various operations of IoT control is discussed.
2 citations
References
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01 Jan 2012
TL;DR: Main focus is to introduce how to built the mathematical model and the analysis of it's system performance, then design and performance analysis of the double inverted pendulum and simulation of Linear Quadratic Regulator (LQR) controller.
Abstract: Double Inverted Pendulum is a nonlinear system, unstable and fast reaction system. Double Inverted Pendulum is stable when its two pendulums allocated in vertically position and have no oscillation and movement and also inserting force should be zero. The aim of the paper is to design and performance analysis of the double inverted pendulum and simulation of Linear Quadratic Regulator (LQR) controller. Main focus is to introduce how to built the mathematical model and the analysis of it's system performance, then design a LQR controller in order to get the much better control. Matlab simulations are used to show the efficiency and feasibility of proposed approach.
24 citations
"Stabilization of Double Link Invert..." refers background or methods in this paper
...Difficulties are faced in finding out the right weighting matrices, which limits the application of the LQR Controller design [5]....
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...In the control strategy a feedback gain matrix is obtained which aids to minimize the quadratic performance index and makes the system stable[5]....
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01 Jan 2012
TL;DR: In this paper, a comparison of the time specification performance between two type of controller for a Double Inverted Pendulum system is presented, the objective is to determine the control strategy that to deliver better performance with respect to pendulum angle's and cart position.
Abstract: this paper presented comparison of the time specification performance between two type of controller for a Double Inverted Pendulum system. Double Inverted Pendulum is a non-linear ,unstable and fast reaction system. DIP is stable when its two pendulums allocated in vertically position and have no oscillation and movement and also inserting force should be zero. The objective is to determine the control strategy that to delivers better performance with respect to pendulum angle's and cart position. In this paper simple multi PD controller designed on the theory of pole placement and its performance is compared with Linear Quadratic Regulator controller using MATLAB and Simulink.
18 citations