EXPONENTIAL INPUT SHAPING FOR VIBRATION FREE POSITIONING OF LIGHTLY DAMPED MULTI-MODE SYSTEMS

Input shaping provides a simple and effective method for vibration-free positioning of a load driven through a lightly damped transmission mechanism. In a carefully calibrated system, input shaping can provide open loop vibration free movement of a lightly damped system. It can also be used in conjunction with a closed loop controller, acting on the reference signal. The most popular approach to input shaping is based on the convolution of impulses with carefully calculated magnitude and time intervals. The motion speed or the travel time is determined by the system dynamics (i.e. the natural frequency and the damping ratio), and the signal generated by the input shaping has infinite jerk. Different filters are suggested in the literature to limit the jerk. An alternative command shaping techniques based on a third order exponential function has been developed by the author. The technique is based on an inverse dynamic analysis. The exponential command signal can be used to drive the system as fast as the actuators capability, and the motion speed is controlled by a single speed parameter giving the user complete control of the motion speed. For speeds slower than a certain critical value, the input shaping signal can be simplified and no knowledge of the natural frequency and damping ratio of the system is required. The low sensitivity of the technique to errors in specifying the natural frequency and damping ratio of the system makes it applicable to multi mode systems without any knowledge of the higher modes. It is a smooth continuous function starting with zero first and second derivatives with low jerk requirements. Therefore, no additional jerk control measures are necessary. The paper demonstrates the application of the technique to multi-mode systems. Two versions of the suggested shaped input function are applied to simulated systems, one requires no knowledge of the system parameters, and the other requires only the first natural frequency for higher speed applications