2 inverted pendulums
Design of an LQG controller for two inverted pendulums
Objective:
The objective of this paper is to design linear quadratic controllers for a system with two inverted pendulums on 2-d Plane. To this goal, it has to be determined which control strategy delivers better performance with respect to pendulum’s angle and the cart’s position. The inverted pendulums represents a challenging control problem, since it continually moves toward an uncontrolled state.
Introduction:
Inverted pendulum has been the subject of numerous studies in automatic control since the forties. The inverted pendulum is a typical representative of a class of high-order nonlinear and non-minimum phase systems [1]. Since the system is inherently nonlinear, it is useful to illustrate some of the ideas in nonlinear control.
Many different control methods are proposed for the inverted pendulum problem. The Proportional-Integral-Derivative (PID) and Proportional-Derivative (PD) controllers, Model Predictive Control (MPC), and fuzzy control to mention a few. However one of the obstacles by using the PID and PD controllers are that they alone cannot effectively control all of the pendulum state variables (modes) since they are of lower order than the pendulum itself. Hence, they are usually replaced by a full-order controller. A linear state feedback controller based on the linearized inverted pendulum model can instead be used, and may also be extended with a disturbance observer (Kalman filter) to improve the disturbance rejection performance.
The proposed method is to balance an inverted pendulum placed on top of a cart by use of LQR/LQG control methods. Our solution implements an LQG controller with comparison to a simple LQR controller. The controller found by means of a more analytical approach will be tested with implementation of the controller in the MATLAB/Simulink environment.
Inverted Pendulum:
Objective:
The objective of this paper is to design linear quadratic controllers for a system with two inverted pendulums on 2-d Plane. To this goal, it has to be determined which control strategy delivers better performance with respect to pendulum’s angle and the cart’s position. The inverted pendulums represents a challenging control problem, since it continually moves toward an uncontrolled state.
Introduction:
Inverted pendulum has been the subject of numerous studies in automatic control since the forties. The inverted pendulum is a typical representative of a class of high-order nonlinear and non-minimum phase systems [1]. Since the system is inherently nonlinear, it is useful to illustrate some of the ideas in nonlinear control.
Many different control methods are proposed for the inverted pendulum problem. The Proportional-Integral-Derivative (PID) and Proportional-Derivative (PD) controllers, Model Predictive Control (MPC), and fuzzy control to mention a few. However one of the obstacles by using the PID and PD controllers are that they alone cannot effectively control all of the pendulum state variables (modes) since they are of lower order than the pendulum itself. Hence, they are usually replaced by a full-order controller. A linear state feedback controller based on the linearized inverted pendulum model can instead be used, and may also be extended with a disturbance observer (Kalman filter) to improve the disturbance rejection performance.
The proposed method is to balance an inverted pendulum placed on top of a cart by use of LQR/LQG control methods. Our solution implements an LQG controller with comparison to a simple LQR controller. The controller found by means of a more analytical approach will be tested with implementation of the controller in the MATLAB/Simulink environment.
Inverted Pendulum: