On Using Nyquist Plots for Relaxing Convex Conservative Approximations in Design of Robust Mechatronic Systems*

:In this paper, a Nyquist plot-based method which reduces the conservatism associated with Linear Matrix Inequality (LMI) approximation of ambiguous chance constraints is proposed for the design of robust mechatronic systems. The mechanical plant and controller are redesigned over finite frequencies by shaping the open loop Nyquist plot to avoid an ambiguous chance-constrained robust stability disc. Commonly used graphical constraints such as the sensitivity disc are also included in order to satisfy the performance specifications. Our simulation results using the proposed graphical method achieves a robust stability of 91.8% based on a desired probability tolerance for closed-loop stability of (1 - ε) = 0.70 as compared with LMI approximation, which requires the standard deviation of the parametric uncertainties to be reduced by four times in order to satisfy an identical (1 - ε), and achieves a robust stability of 100%.