Stability Control of Double Inverted Pendulum on a Cart Using Full State Feedback with H infinity and H 2 Controllers (original) (raw)
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Engineering and Technology Journal, 2018
In this work, two robust controllers, which are full state feedback, 2 and full state feedback โ controllers are proposed for the two wheeled inverted pendulum system. The nonlinear equations for the two wheeled inverted pendulum system are developed using Euler-Lagrange equation. The system parameters changes are considered to show the effectiveness of the proposed robust controllers. These controllers are proposed not only to stabilize the pendulum in upright position but also to drive the position to track a given reference input. The results show that more desirable robustness and time response specifications can be achieved using the proposed controllers. The effectiveness of the proposed controllers is verified experimentally using real two wheeled inverted pendulum system.
A new controller for the inverted pendulum on a cart
International Journal of Robust and Nonlinear Control, 2008
This paper presents a complete solution to the problem of swinging-up and stabilization of the inverted pendulum on a cart, with a single control law. The resulting law has two parts: first, an energy-shaping law is able to swing and maintain the pendulum up. Then, the second part introduces additional control to stop the cart and it is based on forwarding control with bounded input. The resulting control law is the sum of both parts and does not commute between different laws although there exist switches inside the controller.
Stability Analysis and Optimum Controller Design for an Inverted Pendulum on Cart System
IEEE, 2022
Stability analysis and control of the inverted pendulum on cart system is an important problem that has been investigated by many researchers in recent years. In this study, nonlinear modeling of the inverted pendulum on cart system is derived and free body diagram is explained. Then, the nonlinear model of the system is created in MATLAB program. In order to keep the pendulum on cart in balance, different types of controllers were designed, and stability analysis was performed by drawing root-locus curves for different controllers. The optimum controller design was obtained to keep the pendulum in balance. The impulse response of the system has been simulated and it has been proven that the designed optimum controller keeps the pendulum in balance.
Control of the Double Inverted Pendulum on a Cart Using the Natural Motion
Acta Polytechnica, 2013
This paper deals with controlling the swing-up motion of the double pendulum on a cart using a novel control. The system control is based on finding a feasible trajectory connecting the equilibrium positions from which the eigenfrequencies of the system are determined. Then the system is controlled during the motion between the equilibrium positions by the special harmonic excitation at the system resonances. Around the two equilibrium positions, the trajectory is stabilized by the nonlinear quadratic regulator NQR (also known as SDRE-the State Dependent Riccati Equation). These together form the control between the equilibrium positions demonstrated on the double pendulum on a cart.
Lyapunov-Based Controller for the Inverted Pendulum Cart System
Nonlinear Dynamics, 2005
Abstract. A nonlinear control force is presented to stabilize the under-actuated inverted pendulum mounted on a cart. The control strategy is based on partial feedback linearization, in a first stage, to linearize only the actuated coordinate of the inverted pendulum, and then, a ...
Robust Control of Double Inverted Pendulum System
Journal of Automation and Control Engineering, 2017
Double inverted pendulum system is highly nonlinear and unstable system, thus its stability is a matter of concern, particularly when the system components have parametric uncertainty. The aim is to balance the two pendulums vertically on a movable cart. This paper presents first the dynamic modeling of the system based on Euler-Lagrangian method and then uncertain model is obtained by considering the parametric uncertainty in moment of inertia of pendulums and friction coefficient of hinges and cart. In this paper, reference trajectory control, disturbance rejection and robust performance using Hโ and ยต synthesis controllers are made. Both controller shows good transient response, disturbance rejection and robust stability, but ยต synthesis controller provides the superior robust performance as compared to Hโ controller. ๏
Design and Simulation of Different Controllers for Stabilizing Inverted Pendulum System
The Inverted Pendulum system has been identified for implementing controllers as it is an inherently unstable system having nonlinear dynamics. The system has fewer control inputs than degrees of freedom which makes it fall under the class of under-actuated systems. It makes the control task more challenging making the inverted pendulum system a classical benchmark for the design, testing, evaluating and comparing. The inverted pendulum to be discussed in this paper is an inverted pendulum mounted on a motor driven cart. The aim is to stabilize the system such that the position of the cart on the track is controlled quickly and accurately so that the pendulum is always erected in its vertical position. In this paper the linearized model was obtained by Jacobian matrix method. The Matlab-Simulink models have been developed for simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using different control methods. The methods discussed in this paper are a double Proportional-Integral-Derivative (PID) control method, a modern Linear Quadratic Regulator (LQR) control method and a combination of PID and Linear Quadratic Regulator (LQR) control methods. The dynamic and steady state performance are investigated and compared for the above controllers.
State-feedback control with a full-state estimator for a cart-inverted pendulum system
International Journal of Engineering & Technology
A Cart Inverted Pendulum System is an unstable, nonlinear and underactuated system. This makes a cart inverted pendulum system used as a benchmark for testing many control method. A cart must occupy the desired position and the angle of the pendulum must be in an equilibrium point. System modeling of a cart inverted pendulum is important for controlling this system, but modeling using assumptions from state-feedback control is not completely valid. To minimize unmeasured state variables, state estimators need to be designed. In this paper, the state estimator is designed to complete the state-feedback control to control the cart inverted pendulum system. The mathematical model of the cart inverted pendulum system is obtained by using the Lagrange equation which is then changed in the state space form. Mathematical models of motors and mechanical transmissions are also included in the cart inverted pendulum system modeling so that it can reduce errors in a real-time application. The ...
European Journal of Control, 2019
In this paper we derive a modified energy based swing-up controller using Lyapunov functions. During the derivation, all effort has been made to use a more complex dynamical model for the single inverted pendulum (SIP) system than the simplified model that is most commonly used. We consider the electrodynamics of the DC motor that drives the cart, and incorporate viscous damping friction as seen at the motor pinion. Furthermore, we use a new method to account for the limitation of having a cart-pendulum system with a finite track length. Two modifications to the controller are also discussed to make the method more appropriate for real-time implementation. One of the modifications improves robustness using a modified Lyapunov function for the derivation, while the other one incorporates viscous damping as seen at the pendulum axis. We present both simulation and real-time experimental results implemented in MATLAB Simulink.