Linear quadratic regulator and pole placement for stabilizing a cart inverted pendulum system (original) (raw)
Related papers
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.
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...
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 space control using LQR method for a cart-inverted pendulum linearised model
The Cart-Inverted Pendulum System (CIPS) is a classical benchmark control problem. Its dynamics resembles with that of many real world systems of interest like missile launchers, pendubots, human walking and segways and many more. The control of this system is challenging as it is highly unstable, highly non-linear, non-minimum phase system and underactuated. Furthermore, the physical constraints on the track position also pose complexity in its control design. This paper presents a control method to stabilise the unstable CIPS within the different physical constraints such as in track length and control voltage. A novel cart-inverted pendulum model is proposed where mechanical transmission and a dc motor mathematical model have been included which resembles the real inverted pendulum. Therefore problems emerged in realtime implementation can be minimised. A systematic the state feedback design method by choosing weighting matrices key to the Linear Quadratic Regulator (LQR) design is presented. Simulation experiments have been conducted to verify the controller's performances. From the obtained simulation and experiments it is seen that the proposed method can perform well stabilising the pendulum at the upright angle position while maintaining the cart at the desired position.
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.
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.
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.
Comparative analysis of inverted pendulum control
The Scientific Temper
The main motive of this paper is to balance the inverted pendulum system (non-linear model) using controllers and to compare the results obtained from using different controllers. The aim is to determine which controller provides best results with respect to cart’s position and pendulum’s angle. The controllers used in this paper are PI, PD, PID. The inverted pendulum model is modeled using Simscape and the simulation results are obtained using MATLAB
Comparison of LQR and Pole Placement Design Controllers for Controlling the Inverted Pendulum
In this paper an inverted pendulum is modeled firstly by using Euler – Lagrange energy equation for stabilization of the pendulum. To control the modeled system, both full-state feedback and Linear Quadratic Regulator controller methods are applied and the results are compared. After that, a pre-compensator is implemented to eliminate the steady-state error. Linear Quadratic Regulator is an optimal technique of pole placement method which defines the optimal pole location based on a definite cost function. The investigated system develops classical inverted pendulum by forming two moving masses. The motion of two masses in the pendulum which slide along the horizontal plane is controllable.
CONTROLLER DESIGN OF INVERTED PENDULUM USING POLE PLACEMENT AND LQR
IJRET, 2012
In this paper modeling of an inverted pendulum is done using Euler – Lagrange energy equation for stabilization of the pendulum. The controller gain is evaluated through state feedback and Linear Quadratic optimal regulator controller techniques and also the results for both the controller are compared. The SFB controller is designed by Pole-Placement technique. An advantage of Quadratic Control method over the pole-placement techniques is that the former provides a systematic way of computing the state feedback control gain matrix.LQR controller is designed by the selection on choosing.The proposed system extends classical inverted pendulum by incorporating two moving masses. The motion of two masses that slide along the horizontal plane is controllable .The results of computer simulation for the system with Linear Quardatic Regulator (LQR) & State Feedback Controllers are shown in section 6.