COMPUTER CONTROL OF A DOUBLE INVERTED PENDULUMf (original) (raw)
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In this paper an inverted pendulum is presented using state space modeling method. And full state feedback controller is developed using pole placement and LQR (Linear Quadratic Regulation) methods. After that, tracking problem is addressed by designing a steady state error controller. Then, considering the reality conditions, first assuming by some of the state variables are measurable, a reduced state observer is designed and then for a worst scenario a full order state observer is designed. Finally, the state feedback controller and the state observer are summed up to give a precompensator and an overall steady state error controller is added to that new system. All mathematical modeling are presented clearly and simulations together with their analysis were done using MATLAB software. For clear view on what is going on with the control method and the system, an animation GUI is also presented.
Design and Implementation of Controllers in an Inverted Pendulum
2015
Control of the Inverted Pendulum system in both simulated and physical laboratory is possible as the stability of the system can be attained. Finding or calculating the vectors of gains K using pole placement method and performing the closed loop simulations for the non-linear simulink model with a full state feedback controller of gains calculated makes the implementation possible. The controller is implemented by using the gain calculated on the laboratory physical inverted pendulum system. The stability of the simulated and physical laboratory inverted pendulum system was attained. The variations in time taken for the system to attain the upright position may be due to high K value of gains which make the system approach the stability.
Design of State Feedback Controller for Inverted Pendulum
This paper, present the design and simulation of a complete control system for the stabilization of an inverted pendulum using state feedback algorithms The full-state feedback controller was first design on the assumption that the entire state vector is available for feedback. The state feedback controller was designed based on the following requirements, Settling time, Rise time, peak overshoot and steady state error. The power of modern state-space techniques for the analysis and control of Multiple Input Multiple Output (MIMO) systems is also investigated using MATLAB/SIMULINK. This simulation environment supports the development of real time applications in an easy way.
An Overview of Control Technics for Inverted Pendulum
2022
Stabilization of Inverted Pendulum is defined as a very basic classical control problem. The Dynamics Inverted Pendulum is related to many real life applications such as robot and human walking. Objective of this thesis is giving an overview of the most used control technics of inverted pendulum. After presenting and describing the inverted pendulum system, we have built the non-linear model then linearized it around equilibrium point of the system to obtain the linear model. A state model has represented and the transfers functions have been computed. Two control types have been designed. The first one is linear such as PID, Feedback State and LQR controllers. The second one is nonlinear such as Fuzzy logic, sliding mode and Feedback Linearization controllers. all controllers design have been implemented using MATLAB. A comparative study of performance and robustness between different design technics has been carried out.
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 Based Linear Controller Design for the Inverted Pendulum
Acta Technica Jaurinensis
In a previous survey paper the detailed PID controller design to stabilize the inclination angle as well as the horizontal movement of an inverted pendulum system has been presented. In this paper the linear controller design based on the state space representation is shown step by step. Pendulum model is based on EulerLagrange modeling, and the nonlinear state space model is linearized in the unstable upward position, finally pole placement by Ackermann formula and Bass–Gura equation, moreover linear quadratic optimal control are presented. The pendulum has been inserted into a virtual reality laboratory, which is suitable to use in model based control teaching.
Comparison of a Triple Inverted Pendulum Stabilization using Optimal Control Technique
Preprints, 2020
In this paper, modelling design and analysis of a triple inverted pendulum have been done using Matlab/Script toolbox. Since a triple inverted pendulum is highly nonlinear, strongly unstable without using feedback control system. In this paper an optimal control method means a linear quadratic regulator and pole placement controllers are used to stabilize the triple inverted pendulum upside. The impulse response simulation of the open loop system shows us that the pendulum is unstable. The comparison of the closed loop impulse response simulation of the pendulum with LQR and pole placement controllers results that both controllers have stabilized the system but the pendulum with LQR controllers have a high overshoot with long settling time than the pendulum with pole placement controller. Finally the comparison results prove that the pendulum with pole placement controller improve the stability of the system.
Inverted pendulum control is one of the fundamental problems in the field of control theory. The present work consists of comparative aspects and result analysis of various control methods like LQR, PID and state space analysis. State space method and LQR method is used for determining the stability of pendulum. It is found that LQR controller has the best performance among all these controllers. AI techniques and fuzzy logic can be applied so that a robust controller and better response can be achieved for future work.
Modeling and controller design for an inverted pendulum system
2007
The Inverted Pendulum System is an under actuated, unstable and nonlinear system. Therefore, control system design of such a system is a challenging task. To design a control system, this thesis first obtains the nonlinear modeling of this system. Then, a linearized model is obtained from the nonlinear model about vertical (unstable) equilibrium point. Next, for this linearized system, an LQR controller is designed. Finally, a PID controller is designed via pole placement method where the closed loop poles to be placed at desired locations are obtained through the above LQR technique. The PID controller has been implemented on the experimental set up.
2013 IEEE International Conference on Control System, Computing and Engineering, 2013
This paper focuses on implementation of swing-up, switching and stabilizing controllers for rotary inverted pendulum. An energy based method to swing-up the pendulum and a state feedback controller to keep the pendulum in the upright position are employed. The mixed / state feedback controller is used to stabilize the pendulum with reduced oscillations. The results have been compared with the standard full state feedback and LQR. The Quanser rotary inverted pendulum is used as the testbed. All controllers are implemented in real-time using Microstick II with dsPIC33FJ128MC802 and Simulink embedded target for Microchip®.