Improving the Robustness of a Parallel Robot Using Predictive Functional Control (PFC) Tools

Heuristically, it was claimed in the literature that increasing the time-constant ´T_ref´ of the reference trajectory in predictive functional control (PFC) improves the closed-loop stability because the controller will be able to tolerate model mismatch which is difficult for a zero time-constant reference trajectory (a pure set-point) to tolerate. On the other hand, PFC uses ´T_ref´ as the main tuning parameter. Smaller time constants demand more aggressive control, while larger time constants result in less aggressive action. One may start with ´T_ref´ equal to the open-loop time constant of the control variable, then refine the tuning based on performance/robustness trade-offs. In this paper, the author investigates these issues analytically for an H4 robot. The analysis done shows that the system obtained is of type MGS defined in Proceedings of ACC 2006 for which it is possible by using PFC tools to find analytically a stable equilibrium point for the system and track at the same time a reference trajectory with a gain margin that increases as ´T_ref´ increases, improving that way the relative stability of the closed-loop system. The author notes that, the study done in this paper for the H4 robot could be applied to any robot whose linearised model is of MGS type. The author notes as well that the plots illustrated in this paper were obtained by simulation using Matlab/Simulink