Flexible Performance Design of Robust Control Using the Linear Matrix Technique for a Robotic Coax-Helicopter

This study introduces a parametric \({H_\infty }\) loop shaping control for a robotic coax-helicopter using linear matrix inequality and provides a flexibility design method of the performance index selection. Based on stabilizing solution of sufficient linear conditions, an alternative but simple set of solvability conditions is developed. The dynamic model of a robotic coax-helicopter was built before the design procedure of a new parametric \({H_\infty }\) loop shaping control was addressed. Therefore, the state and control matrices were computed using the small perturbation theory through the quasi-steady assumption. Performance of the resulting parametric \({H_\infty }\) controller was implemented to compare with previous works. The numerical simulations indicate effectiveness of the proposed method in step responses of the closed loop. This method reduces the complexity of appropriate selection of required performance and gives designer an additional degree of freedom to seek the appropriate close-loop performance.