H_∞Controller Design For The Ball And Beam System Based On Back-stepping

The ball-beam system is a very important control system design experimentallaboratory equipment. For its operation is relatively simple, not complicated structure,the pros and cons of the controller design can be very intuitive observation to thecommonly used ball-beam system to achieve and verify the control theory andcontrol methods known, at the same time, the ball-beam system on the newapplication and promotion of the control theory and the new control law can alsoplay the role of the inspection.The composition and control process of the ball and beam system are introducedin the paper，a mathematical model of ball and beam system based on Lagrangeequations is set up with the application of the energy balance principle concerningdynamics，and on the base of analysis on such model，the design of a controller isworked out by utilizing the techniques of back-stepping H_∞control.The object of this paper is produced and provided by the German Amira ball-beam system, laboratory equipment, the device itself can provide some controlsoftware running on the computer, but the control software can only realize the ball-beam system comes with several software fixed control algorithm, in order to achievemore control algorithm in the ball-bar system, starting from the hardware point ofview of the ball-beam system to transform them to overcome these shortcomings.The specific rehabilitation programs of the ball-beam system: leads to the positionsignal of the ball and rod angle signal from the original ball-bar equipment, afterchip analog to digital conversion, the signal sent in Matlab computing processing, butwill after a Matlab the processed signal through the digital to analog conversion tothe ball-the servo drive in the base of the lever device to drive the motor, so as toachieve the purpose of controlling the position of the ball.Underactuated system in-depth analysis and to identify the underactuatedfeatures of the ball and beam system. Back-stepping is an effective way to solve thecontrol problem of underactuated systems，but the traditional state space back-stepping design principles. There is a certain problem，the ball and beam systemdesign improved back-stepping，the back-stepping in the frequency domain，andovercome the shortcomings and deficiencies of the state space back-stepping.