Ziegler-Nichols frequency response method for high-order adaptive optics system of the Advanced Technology Solar Telescope

We present the study and results on automatic tuning and optimizing the closed-loop control gains of the Proportional Integral (PI) controller for the high-order adaptive optics (HOAO) system. The Ziegler-Nichols frequency response (ZNfr) method is examined using the Nyquist stability criterion to implement the automatic tuning of PI controller by determining the ultimate gain, K-u, and ultimate period, T-u, of a process model, which consists of components from adaptive optics (AO) system. The maximum magnitude criterion, 0.5 <= dB <= 2.3, is identified and considered as the optimization method, which also established the stability of the PI controller. MATLAB scripts are developed to execute iterative calculation of control algorithm, which automates real-time simulation of the Simulink high-order adaptive optics (Sim-HOAO) models. Simulink block diagrams are used to represent transfer functions, which described the frequency-domain behavior of the AO system.