Input shaping for vibration-free positioning of flexible systems

Abstract

Input shaping is a simple method for reducing the residual vibration in positioning lightly damped systems. For controlling part, a continuous and differentiable function is introduced to define the desired motion and the input is shaped by inverse dynamic analysis. The shaped input function is derived from the specified output function so that the designer can choose the speed and shape of the motion within the limitations of the drive system. Third order exponential function will be used as the desired output due to its asymptotic behavior. The simulation has been done to the spring-mass-damper system which is a second order system to study the application of the technique to the system. The effects of errors in damping ratio and natural frequency are also discussed. Next, the same technique is applied to a gantry crane system which is fourth order system. In the proposed method the parameters that need to be defined is the position of the trolley and sway angle of the mass. Simulated responses of the position of the trolley and sway angle of the mass are presented using MATLAB. The performance of the Bang-bang input technique and the inverse dynamic analysis are compared. From the simulation results, satisfactory vibration reduction of a crane system has been achieved using the proposed method