| Discontinuities in the motion control profiles generated by off-line trajectory planning for industrial machinery produce high levels of acceleration and jerk. These translate into audible noise and mechanical vibrations on the structural frame that supports the moving parts. These, in turn, reduce the life expectancy of the machine, the quality of the end product, and the overall machine productivity.; In this Dissertation, an on-line trajectory planning strategy for real-time applications is developed. To do this, the kinematics of the motion is modeled using three states; namely, position, velocity, and acceleration. Jerk is used as the control input. Then, optimal control is applied to this model to find optimal state trajectories that best observe position and velocity requirements while minimizing jerk and acceleration. A performance index that penalizes both the states and the control input is chosen. The Two Point Boundary Value Problem (TPBVP) that results from applying optimal control theory to the kinematic plant model is solved, on-line, using relaxation techniques with a variable time step. The on-line implementation of the trajectory planning strategies also allow the rejection of plant disturbances. To implement the proposed strategy an open-control architecture (PC-based control) for real-time applications, including hardware and software, is developed.; The on-line trajectory planning strategy developed here is successfully being used on a real-world real-time industrial application that has 5 moving axes. However, only simulation results are presented in this Dissertation. These simulation results clearly demonstrate the advantages of the proposed trajectory planner over conventional approaches that use off-line trajectory planning. |
