Ball and beam position control using quarc student manual. Engineering 58control theory and design final projectball. Scribd is the worlds largest social reading and publishing site. The basic idea is to use the torque generated from motor to the control the position of the ball on the beam. Thomann stairville beam ball 100 quad led user manual pdf. Based on the equations of motion, you will build the theoretical nonlinear model in simulink. Pdf design and implementation of ball and beam system using. The ball and beam balance problem is a classic open loop unstable system. The ball and beam balance is a safe way to investigate control design for unstable systems. The track is fitted with a linear transducer to measure the position of the ball, i. Description the quanser ball and beam module, pictured in figure 1, consists a track on which the metal ball is free to roll. As the servo gear turns by an angle theta, the lever changes the angle of the beam by alpha. The apparatus has a steel ball which is free to roll on two parallel tensioned wires positioned on a beam that pivots at its centre.
The process the ball and beam model consists of a horizontal beam and a dc motor mechanically attached at the centre of the beam. Its distance to the beam center is counted positively to the right. Join 7,200,000 engineers with over 4,000 free cad files join the community. The ball and beam system consists of a motor driven beam with a ball free to roll on the beam.
The apparatus has a steel ball which is free to roll on two parallel tensioned wires. Modelling the ballandbeam system from newtonian mechanics. Stairville beam ball 100 quad led light fixture pdf manual download. Pdf ball and beam balance final report semantic scholar. The ball has a mass, a radius and a moment of inertia. Free body diagram of the beam summing torques acting on the beam yields free to roll. Modelling and control of ball and beam system using. The purpose of the project was to build a robotic platform that will allow a user to balance a ball on a beam by altering the tuning parameter kp, ki, and. Among the interesting challenges of such a system is the indirect control of the ball using the angles of the plate. The angle in turn influences the position of the ball. Free body diagram of the beam summing torques acting on the beam yields beam.
The incomplete free body diagram of the ball on a beam is illustrated in figure 2. The ball and beam system shown in the video is a work in progress and performs poorly at this point. The ball and beam module consists of a steel rod in parallel with a nickelchromium, wirewound resistor forming the track on which the metal ball is free to roll. 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. For the purpose of simplification, the ball can only move in the horizontal direction.
This paper presents the design of an optimal control strategy for a 2 degree of freedom standard laboratory system ball and beam. By doing this we are essentially controlling a torque applied at the center of the beam by a motor. Applying newtons law of motion, the sum of the forces acting on the ball. The main ideas of the paper are to model the ball and beam system considering nonlinear factors and coupling effect and to design proportional integral derivative pid controller to control the ball position. Optimal control of a ball and beam system through lqr and. Rolling ball on a beam free body diagram the inclination is considered the xcoordinate. Modelling and control of ball and beam system using pid. The aims of this research are to model the ball and beam system considering nonlinear factors and coupling effect and to design controllers to control the ball position. Many simple and present day control methods have been used to balance the ball and beam system.
A ball is placed on a beam, see figure below, where it is allowed to roll with 1 degree of freedom along the length of the beam. The ball conveyor solution is one example of many possible solutions for the make a system that moves a ball project. Quanser srv02 ball and beam user manual pdf download. Ball and beam control system simulation with simulink ball and beam control system simulation with simulink.
A ball is placed on the beam and is free to roll under. A linear quadratic regulator lqr is designed and implemented with an objective to control the position of ball on the beam by varying the angular position of beam. Modelling and control of ball and beam system using pid controller abstract. Kanpur, india modelling and control of ball and beam system using coefficient diagram method cdm based pid controller b. Pdf the commonest benchmark for testing control algorithms in control engineering laboratories is the ball and beam system.
A free body diagram of the physical ball and beam system. When the angle is changed from the horizontal position. Jan 17, 2016 use pdf download to do whatever you like with pdf files on the web and regain control. Pdf the ball and beam system is a classical mechanical system consisting of a ball that moves over a beam in a. The ball and beam system is open loop unstable since for a given constant angle of tilt on the beam, the ball s position changes without limit. The ball and beam module consists of a steel rod in parallel with a nickelchromium wire wound resistor forming the track on which the metal ball is free to roll. This information is analysed on the myrios embedded processor and an appropriate control algorithm is run to provide feedback to the system. The advantage of this system is 64 design and implementation of an embedded ball beam controller using pid algorithm that relatively small motor can be used due to the existing of gear box 1. The controller seeks to balance the ball on the beam.
Make a system that moves a ball ev3 design engineering. In particular, changing the control algorithms is simply done by flashing the codes for the. Idiots tree felling fails with chainsaw machine tree falls on head and house duration. Stairville beam ball 100 quad led user manual pdf download. The system is an open loop and nonlinear system, which is inherently unstable.
The position of the ball is obtained by measuring the voltage at the steel rod. The ball and beam system shown below in figure 1 has the control objective of placing the ball anywhere along the beam by varying the motor voltage. Summing forces acting on the ball in the j direction yields free body diagram of the beam shown in figure 5. Because of its attentiongrabbing nature, educational hardware companies such. In this paper, a complete physical system and controller design is.
In this first go at the ball and beam system design and control, many lessons were learned that can be used to create a much more stable system and controller. Adaptive embedded control for a ball and plate system jun xiao informatics institute. Pdf ball and beam educational tool for advanced control system. We created three different pd controllers, one was underdamped, one was optimally damped 7, and one was overdamped. Control of a ball and beam system mechanical engineering. The ball and beam system is laboratory equipment with high nonlinearity in its dynamics. Design and implementation of ball and beam system using pid. The ball is left free on a bar where its position is detected or measured by an ultrasonic. The ball and beam is a system commonly used to expose undergraduate students to. Since the poles are not strictly in the left half plane, the open loop system will be unstable as seen in the step response below. Mathematical modeling, simulation and control of ball and beam. Pdf design and implementation of ball and beam system. The beam has a length, a moment of inertia and its deflection from the horizontal line is the angle. This section will present an overview of the control strategy to be used, describe the ball and beam model, and discuss controller design.
The ball and beam apparatus shows the control problems of unstable systems, for example a rocket or missile during launch, which needs active control to prevent the missile going unstable and toppling over. The ball and beam system is a type ii system which has two poles at the origin, as seen in the polezero map below. Web to pdf convert any web pages to highquality pdf files while retaining page layout, images, text and. The statespace representation of the ball and beam example is given below. Ball and beam dynamics introduction this report does not omit any mathematical steps in order to reflect upon details of the mechanical operation of the process. Ball balancing table with resistive touch screen functionality video duration. The track is effectively a potentiometer, outputting a voltage thats proportional to the position of the ball. Figure 1 below depicts the ball and beam module coupled to the srv02 plant in the correct configuration. The ball and beam is a basic reference point system with high nonlinearity and unstable system in its dynamics.
Design and implementation of ball and beam system using. Consider the free body diagram of the ball and beam system shown in figure 4. The ball and beam system can usually be found in most university control labs since it is relatively. The beam consists of a steel rod in parallel with a nickelchromium wirewound resistor forming the track on which the metal ball is free to roll. The linear sensor measures the position of the ball on the track by measuring. In this system, a constant beam angle causes the ball to accelerate due to the force of gravity and the balls position increases nonlinearly. Srv02 2d ball balancer laboratory instructor manual solution. It is also possible to set a desired position or motion for the. The system includes a ball, a beam, a motor and several sensors. The complete free body diagram of the ball on the beam is pictured in figure 4. System modeling and simulation provide useful and safe mechanisms for initial controller design.
Mathematical modeling, simulation and control of ball and. The significance of the ball and beam system is that. A servo motor controls the beam angle and sensors measure the beam angle and ball position. Optimal state feedback control ball and beam by carion pelton 1 objective in this experiment you will build and control a ball and beam system. Design and realization of ball and beam balancing mechanism. Ball and beam apparatus ce106 control engineering tecquipment.
A lever arm is attached to the beam at one end and a servo gear at the other. Pdf the commonest benchmark for testing control algorithms in control engineering laboratories is the ball. Ball and beam balance final report tom trapp and wil selby department of mechanical engineering massachusetts institute of technology 2. Design, fabrication and control of a ball on beam balancer system also known as the ball and beam system was my b. In order to design a controller for the ball and beam system, a transfer function for the system was derived. Embedded controller building for ball and beam system using optimal. Ball and beam control system simulation with simulink grabcad. The significance of the ball and beam system is that it is a simple system which is openloop unstable. The main ideas of the paper are to model the ball and beam system considering nonlinear factors and coupling effect and to design proportional integral. Join the grabcad community today to gain access and download.
The ball and beam body consists of a vgrooved steel bar and a free rolling ball. The lqr is designed considering two degreesoffreedom and coupling dynamics. Third international conference on advances in control and optimization of dynamical systems march 15, 2014. The aims of this research are to model the ball and beam system. Control of a ball and beam system the university of adelaide. The basic control problem is to vary the beam angle to control the ball position. View and download thomann stairville beam ball 100 quad led user manual online. 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. It is a popular textbook example in control theory. Kongregate free online game beam ball deflect an onslaught of laser beams and advance through 40 increasingly challenging levels in play beam ball. The ball and beam system consists of a long beam which can be tilted by a servo or electric motor together with a ball rolling back and forth on top of the beam. Adaptive embedded control for a ball and plate system.
As the servo gear turns by an angle, the lever changes the angle of the beam by. Pdf design and realization of ball and beam balancing. As illustrated above in figure 4, the force acting in the positive x direction when the incline is positive is fx,t mb g sin. For a constant input there is a nonconstant output.