Ball and Beam
Control Systems Lab Project
(Ball and Beam)
Ball and Beam
Abstract
The ball and beam system can usually be found in most university 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 the 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 positions 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 inherently nonlinear but may be linear around the horizontal region. This simplified linear model, however, still represents many typical real systems, such as horizontally stabilizing an airplane during landing and in turbulent airflow.
Ball and Beam (Manually)
Mathematical Modeling
Assumptions
Settling time less than 3 seconds
Overshoot less than 5%
Symbols | Description | Values | M | Mass of The Ball | 0.2 kg | R | Radius of the Ball | 2cm=0.02 m | d | Lever Arm Offset | 0.03 m | G | Gravitational Acceleration | 9.8 m/s2 | L | Length of the Beam | 1.5 m | J | Ball 's Moment of Inertia | (2/5) x M x R2 =9.99e-6 kgm2 | r | Ball Position Coordinate | | Alpha(α) | Beam Angle Coordinate | | Theta(θ) | Servo Gear Angle | |
Open loop equations
By using the langragian expression we get the equation of rolling ball.
PID
(Proportional–Integral–Derivative Controller)
The PID controller, which consists of proportional, integral and derivative elements, is widely used in feedback control of industrial processes. In applying PID controllers, engineers must design the control system: that is, they must first decide which action mode to choose and then adjust the parameters of the controller so that their control problems are
(Ball and Beam)
Ball and Beam
Abstract
The ball and beam system can usually be found in most university 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 the 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 positions 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 inherently nonlinear but may be linear around the horizontal region. This simplified linear model, however, still represents many typical real systems, such as horizontally stabilizing an airplane during landing and in turbulent airflow.
Ball and Beam (Manually)
Mathematical Modeling
Assumptions
Settling time less than 3 seconds
Overshoot less than 5%
Symbols | Description | Values | M | Mass of The Ball | 0.2 kg | R | Radius of the Ball | 2cm=0.02 m | d | Lever Arm Offset | 0.03 m | G | Gravitational Acceleration | 9.8 m/s2 | L | Length of the Beam | 1.5 m | J | Ball 's Moment of Inertia | (2/5) x M x R2 =9.99e-6 kgm2 | r | Ball Position Coordinate | | Alpha(α) | Beam Angle Coordinate | | Theta(θ) | Servo Gear Angle | |
Open loop equations
By using the langragian expression we get the equation of rolling ball.
PID
(Proportional–Integral–Derivative Controller)
The PID controller, which consists of proportional, integral and derivative elements, is widely used in feedback control of industrial processes. In applying PID controllers, engineers must design the control system: that is, they must first decide which action mode to choose and then adjust the parameters of the controller so that their control problems are
References: http://en.wikipedia.org/wiki/Ball_and_beam http://www.engin.umich.edu/group/ctm/examples/ball/ball.html http://bea.st/sight/rbbb/rbbb.pdf http://www.ctrl.cinvestav.mx/~yuw/pdf/ijeee.pdf http://www.personal.psu.edu/users/a/x/axa943/ball_on_beam_balancer.htm http://sites.mecheng.adelaide.edu.au/robotics/robotics_projects.php?wpage_id=44&title=34&browsebytitle=1 http://www.ihaltas.com/courses/fbe_elk5320/eng/projects/Project_17.pdf http://www.library.cmu.edu/ctms/ctms/examples/ball/bbpid.htm