Jerk-constrained time-optimal control of a positioning servo

This paper presents a jerk-constrained time-optimal control (JCTOC) method for a positioning servo. While high jerk, the derivative of acceleration with respect to time, can cause problems such as vibrations and high wear to mechanical parts, it is then important to limit the maximum jerk in many control applications. Many trajectory planning methods have been proposed, limiting the maximum jerk during the optimized planning of the desired path. Distinct from the previous path-planning methods that yield jerk-constrained ideal trajectories only, the approach proposed in this paper directly controls the jerk of the plant while guaranteeing minimum-time performance under the specified jerk constraint. Simulation studies of the JCTOC compared with the conventional PD controller have been conducted, demonstrating that the proposed control requires less control effort and also offers the time-optimal response with admissible jerk.