In this paper, we propose a Nyquist plot-based method for finite-frequency reshaping of the mechanical plant considering a low-order controller, which significantly reduces the large gap between actual robust stability and desired probability tolerance for closed-loop stability    $(1-\epsilon )$    due to linear matrix inequality conservatism. The solution region for the open-loop Nyquist plot is derived based on the simultaneous use of two Nyquist planes. The chance-constrained robust stability criterion is represented on one Nyquist plane using a square region centered at    $(-1+j0)$   , which has to be avoided over all frequencies. The other Nyquist plane contains commonly used graphical constraints from performance specifications. Our simulation results using the proposed graphical method achieves a robust stability of 97.1% based on a desired probability tolerance of    $(1-\epsilon )=0.70$    for closed-loop robust stability. As such, a high-bandwidth control system with the desired disturbance attenuation capabilities while ensuring stable zeros is achieved as compared with the existing methods in the literature.
['Yan Zhi Tan', 'Chee Khiang Pang']
Relaxing LMI Conservatism Using Nyquist Plots and Its Application to Robust Mechatronics Synthesis