Ball And Beam: Controller Design

The ball and beam system is a classical mechanical system consisting of a ball that moves over a beam in a planar movement. The beam can rotate around its center of gravity, and an elastic belt attached to the beam extremities (and an electric motor) allows the transmission of control forces to the beam in order to cause the movement. The ball translates and rolls, always maintaining a contact with the beam. The ball's rolling movement can be without or with slipping, and this last kind of rolling movement is more likely to occur in high beam's angles (in relation to a horizontal line) and in higher ball's velocities. The friction model between the ball and the beam (and the beam and its bearing) is also complex, involving possibly dry and viscous friction together. We present the modeling, control and implementation of a closed loop control system for a ball and beam system. Firstly, we present and compare the mathematical model, considering rolling without and with slipping. A closed loop controller is then designed and implemented in the real system in order to do a comparative analysis. Despite of being a didactical system, the ball and beam presents a complex dynamics, with several nonlinearities, with an infinite number of equilibrium points (if we apply a torque in the beam) and a difficult-to-determine friction model. Finally, conclusion for the modeling, simulation and control techniques are drawn, and future research directions are pointed out.

2014

A PID controller allows for precise control of the dynamics of a system during transitory and stationary states; a feature that can be useful to extend the motors life in a little robot or to equilibrate the liquid within containers in a huge cargo ship. This work describes the design of a Ball and Beam platform for testing control algorithms, and the implementation of a particular PID controller for it. The platform is made out of 2D-wooden parts, an Arduino UNO, a PING ultrasonic sensor, a standard servo motor and screws. The controller is implemented in Arduino language and includes proportional, integrative and derivative terms. The system is successfully stabilized; the ball can be positioned at any point within a range of distance. The platform is cheap, easy to replicate and allows for further testing of alternative control algorithms.

International Journal of Engineering Research and Technology (IJERT), 2015

https://www.ijert.org/mathematical-modeling-simulation-and-control-of-ball-and-beam-system https://www.ijert.org/research/mathematical-modeling-simulation-and-control-of-ball-and-beam-system-IJERTV4IS030879.pdf The ball and beam system can usually be found in most control labs since it is relatively easy to build, model and control theoretically. The system includes a ball, a beam, a motor and several sensors. The basic idea is to use the torque generated from motor to control the position of the ball on the beam. The ball rolls on the beam freely. By employing linear sensing techniques, the information from the sensor can be taken and compared with desired position values. The difference can be fed back into the controller, and then into the motor in order to gain the desired position. The mathematical model for this system is nonlinear but may be linearized around the horizontal region. This simplified linearized model, however, still represents many typical real systems, such as horizontally stabilizing an airplane during landing and in turbulent airflow. By considering real plant problems such as the sensor noise and actuator saturation, the controllers of the system become more efficient and robust. There are number of alternative controller design theories that can be used to stabilize the ball and beam system. In the system, to stabilize the ball and beam system modified PD controller is designed and system responses of modified PD controller and modified PD-PSO controller are compared.

International journal of engineering research and technology, 2015

The ball and beam system can usually be found in most control labs since it is relatively easy to build, model and control theoretically. The system includes a ball, a beam, a motor and several sensors. The basic idea is to use the torque generated from motor to control the position of the ball on the beam. The ball rolls on the beam freely. By employing linear sensing techniques, the information from the sensor can be taken and compared with desired position values. The difference can be fed back into the controller, and then into the motor in order to gain the desired position. The mathematical model for this system is nonlinear but may be linearized around the horizontal region. This simplified linearized model, however, still represents many typical real systems, such as horizontally stabilizing an airplane during landing and in turbulent airflow. By considering real plant problems such as the sensor noise and actuator saturation, the controllers of the system become more efficient and robust. There are number of alternative controller design theories that can be used to stabilize the ball and beam system. In the system, to stabilize the ball and beam system modified PD controller is designed and system responses of modified PD controller and modified PD-PSO controller are compared. I.

The purpose of this project was to control ball position on a beam by varying the angle of a servo gear connected to the beam through a lever arm. A linear differential equation describing the dynamic of the ball and beam to model (transfer function) the relation between input (θ) and output (r) was first derived using basic laws of physic. This transfer function was used to analyze the performance of the system and to design proper controllers (Lead compensator and PID) to meet the design criteria. The locations of the desired poles were found from the design criteria (settling time, percent overshoot). Using root locus, it was found that a lead compensator is required to meet this design criteria and to place poles in the desired locations. The result of the lead compensator on the closed loop response of the system is shown in figure 2. Using this controller, settling time of 1.59 seconds and percent overshoot of 4% and zero steady state error were achieved. PD controller was also used in this problem to meet the design criteria. Using a trial and error approach, PD gains were first tuned and implemented. The closed loop response of the PD controller is shown in figure 3. A settling time of 1.43 seconds with 3.74% percent overshoot and zero steady state error were achieved with PD controller. Details of the design procedure and MATLAB code are shown in the following pages.

The ball and beam control system usually defined as non-linear control system which basically derived and implemented to observe the controller performance. One important step in this design process is to develop a mathematical model of the system. The main purpose of this project is to balance ball on beam using proportional– integral-derivative (PID) controller design with MATLAB and related control algorithm to adjust the angle of beam with real time sensory feedback. A constant angle of beam causes the ball to slide in axial direction due to gravity. Based on closed loop real time control system and well-tuned parameter, it will necessarily adjust angle of the beam to minimise the error, namely the distance between the actual position and set-point position of the ball. The system includes a ball, a beam, a motor and ultrasonic sensor for position sensing of ball. The basic idea is to use the torque generated from motor to the control the position of the ball on the beam by actuating the beam in desired angle. The information from the ultrasonic sensor can be taken and compared with desired set values and the difference can be fed back to Arduino used as controller that is PID controller design in it. Servo Motor will be interfaced with Arduino Uno board which in turn actuate the beam in desired angle in order to attain the set-point requirement.

Jomard Publishing, 2019

The commonest benchmark for testing control algorithms in control engineering laboratories is the ball and beam system. It is vastly unstable as well as nonlinear. An example of its application is found in balancing the ball on the beam, which is analogous to stabilizing an airplane horizontally during landing and or in turbulent air-flow. In this paper, pole placement (PP) and proportional integral derivative (PID) controllers were designed to control the ball position on the beam. Comparative analysis was presented. The performance indices used were the Integral absolute error, time response analysis, and integral square error. Based on the analysis and simulation results, better performances were recorded with PP. Introduction 1 The ball and beam system, because of its significance in control applications, is one of the most popular laboratory design experiment. It is a common feedback control system due mostly to its ease of construction and its use in learning. The basic components of this system is a motor, attached to the beam such that the shaft of the motor can help to manipulate the positions of the ball on the beam by controlling the angle of tilt of the beam. This is done with the use of a lever arm attached to the end of the beam. These types of systems have wide areas of applications in industries including passengers' platform balancing for comfort, control of rocket and aircraft takeoff and landing. This system is an open-loop system which is unstable since for a given a constant angle of tilt on the beam, the ball position changes without limit. Due to the instability of the system and non-linearity property in the system's model, there is, therefore, need for some forms of a feedback loop to control the ball's positions and to design a robust controller for the system's model so as to have the best performance in real-time applications. Many researchers have taken this upon themselves to design different controllers to improve the performance of the system. Taifour et al. (2017) designed a PID controller for a ball and beam system to control the ball position. These controllers are designed based on two feedback loops: the inner and the outer loops. The inner loop controls the motor gear angle position while the outer loop uses the inner loop feedback to control the ball position. Keshmiri et al.

The practical implementation of advanced controlled system for an industrial application involves a wide variety of integrated field such as control electronics, power electronics, electric machine and drives. The ball and beam educational tool presented here allows student to work with all different fields. The system includes a ball, a beam, a motor, several sensors, intelligent drive and PC as a host. This educational tool involves the modelling process, analysis and control of the ball and beam system using Matlab/Simulink and experimental hardware. The control is designed in closed-loop system using PID tuning method. This research presents the very useful and influential laboratory system that provides PC-based control software that enable student to compare the simulation and experiment. Thus, it is easier for students to relate the theoretical concepts that they have learned in class.

This paper presents the development of a dynamic ball-and-plate system successfully completed for a one-semester Senior Capstone Design project. A group of five undergraduate students developed the project concept and constructed a prototype within a semester, integrating major mechatronics engineering concepts learned in classes. The three-degree-of-freedom system consists of sensors, actuators, and controls to keep a free rolling ball in a desired position on a flat plate, accounting for any possible external disturbances. Due to its complexity, multiple steps were taken to solve the design challenges and develop the system. The major works were mathematical modeling, kinematic constraints and dimensional analysis, simulations, and construction of the system. The control system required an effective control strategy and a thorough analysis of system parameters. The system's feasibility and optimal operation were fully considered in the design phase. The design was then validated by simulations using Simulink/MATLAB™ and experimental testing. The completion of the system development provided the understanding of analyzing different control designs on various system parameters based on multidisciplinary mechatronics design principles. Lastly, the class outcomes confirmed the effectiveness of students' learning on multidisciplinary mechatronics engineering through this hands-on project as an assessment of the design project presented.