State space control using LQR method for a cart-inverted pendulum linearised model (original) (raw)
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LQR Controller Design for Stabilization of Cart Model Inverted Pendulum
2015
Optimal response of the controlled dynamical systems is desired hence for that is the optimal control. Linear Quadratic Regulator (LQR), an optimal control method, and PID control which are generally used for control of the linear dynamical systems have been used in this paper to control the nonlinear dynamical system. The inverted pendulum, a highly nonlinear unstable system is used as a benchmark for implementing the control methods. In this paper the modeling and control design of nonlinear inverted pendulum-cart dynamic system with disturbance input using PID control & LQR have been presented. The nonlinear system states are fed to LQR which is designed using linear state-space model. Here PID & LQR control methods have been implemented to control the cart position and stabilize the inverted pendulum in vertically uprightposition. The MATLAB-SIMULINK models have been developed for simulation of the control schemes. The simulation results justify the comparative advantages of LQR...
Linear quadratic regulator and pole placement for stabilizing a cart inverted pendulum system
Bulletin of Electrical Engineering and Informatics, 2020
The system of a cart inverted pendulum has many problems such as nonlinearity, complexity, unstable, and underactuated system. It makes this system be a benchmark for testing many control algorithm. This p aper presents a comparison between 2 conventional control methods consist of a linear quadratic regulator (LQR) and pole placement. The comparison indicated by the most optimal steps and results in the system performance that obtained from each method for stabilizing a cart inverted pendulum system. A mathematical model of DC motor and mechanical transmission are included in a mathematical model to minimize the realtime implementation problem. From the simulation, the obtained system performance shows that each method has its advantages, and the desired pendulum angle and cart position reached.
Stabilization Of Inverted Pendulum On Cart Based On Pole Placement and LQR
IEEE, 2018
An inverted pendulum on cart is an object which is a nonlinear, unstable system, is used as a standard for designing the control methods and finds most versatile application in the field of control theory. To achieve the stabilization of a inverted pendulum system pole placement method is used to design a state feedback controller and then optimal linear quadratic regulator has been applied to the system. The results shown that are the comparison between the performance of two controllers, first the state feedback controller, which is designed by pole placement method and the optimal LQR controller. Both controller stabilizes the inverted pendulum system but deviates in their performance. Simulation has been carried out to show two different approaches for comparative study of their performance.
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.
Robust LQR Controller Design for Stabilizing and Trajectory Tracking of Inverted Pendulum
This paper describes the method for stabilizing and trajectory tracking of Self Erecting Single Inverted Pendulum (SESIP) using Linear Quadratic Regulator (LQR). A robust LQR is proposed in this paper not only to stabilize the pendulum in upright position but also to make the cart system to track the given reference signal even in the presence of disturbance. The control scheme of pendulum system consists of two controllers such as swing up controller and stabilizing controller. The main focus of this work is on the design of stabilizing controller which can accommodate the disturbance present in the system in the form of wind force. An optimal LQR controller with well tuned weighting matrices is implemented to stabilize the pendulum in the vertical position. The steady state and dynamic characteristics of the proposed controller are investigated by conducting experiments on benchmark linear inverted pendulum system. Experimental results prove that the proposed LQR controller can guarantee the inverted pendulum a faster and smoother stabilizing process with less oscillation and better robustness than a Full State Feedback (FSF) controller by pole placement approach.
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.
Stabilization of Inverted Pendulum on Cart Based on LQG Optimal Control
IEEE, 2018
An inverted pendulum on cart is an object which is a nonlinear, unstable system, is used as a standard for designing the control methods and finds most versatile application in the field of control theory. To achieve the stabilization of an inverted pendulum system state observer based linear quadratic Gaussian optimal control has been applied. As the separation principal of LQG states, first the control law has been obtained to design a state feedback controller and when the system’s all states are not measurable as well as system is affected by process and measurement noise, Kalman Filter has been designed for the inverted pendulum system. The results shown that the new designed controller stabilizes the inverted pendulum system as well as eliminates process and measurement noise. Simulation has been carried out to show the approach.
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 ...
2014
The double-pole inverted pendulum system on a cart is highly nonlinear and unstable system which invoke the researchers to find the ways of stability with different controllers. In this paper we have demonstrated the mathematical modeling and by applying the controllability principle we found this system is inherently unstable and then we applied a modern LQR approach with different Q and R matrices weightage to check the stability.
Stabilization of Three Links Inverted Pendulum with Cart Based on Genetic LQR Approach
Journal européen des systèmes automatisés, 2022
This academic paper demonstrates the implementation of a Linear Quadratic Regulator (LQR) controller design for optimal controlling a three connected links in an inverted pendulum form that attached to a moving cart to realize the stability of making a pendulum in a straight vertical line via translation of the cart left and right. To maintain a triple link inverted pendulum (TLIP) vertical, genetic algorithm has been employed to adjust and tune the parameters of LQR, which are the weighting matrices Q and R instead of the approach of try and error. In this article, a hybrid control algorithm (GA-LQR) proposed to select the optimal values of weighting matrices to overcome LQR design difficulties, which gives the best transient response requirements such as percentage overshoot and steady state error. The triple link inverted pendulum is model mathematically modelled in MATLAB platform to simulate the actual system where the results from the simulation gives acceptable and adequate performance of LQR controller in making the system stable.