On-off shaping commands for acceleration limits

In this paper, an on-off shaping command is presented for reducing the residual oscillation of flexible systems with the acceleration limits of actuators. The flexible systems might be operated with on-off actuators such as in spacecrafts, cranes and manufacturing machines. Because of limited acceleration of actuators, the on-off commands would be distorted. The non-ideal on-off commands result in residual oscillation to flexible systems which is degrading control accuracy and performance. Therefore, an analytical solution of on-off command generation with acceleration limits is developed by using a vector diagram approach with a ramp-step function to represent the actuator response due to acceleration limits. The exact solution is numerically evaluated with a benchmark system with respect to robustness and control performance in comparison to a classical shaping technique. The presented technique is experimentally validated with a mini-bridge crane.