Analytical approach determines stability domain of PID parameters for nonlinear systems, suggesting effective tuning methods.
An analytical method is presented to find the stability domain of PID controller parameters for nonlinear time-delay systems by utilizing the Volterra series and its generalized frequency response function (GFRF), and all the parameters in the derived region can stabilize the system. According to the conditions for closed-loop L 2 stabilization, the procedures are derived to determine the PID controller stabilization region. The simulation results show the accuracy of the stability domain. Meanwhile, this proposed method preserves the nonlinear characteristics and is suitable for nonlinear time-delay systems with arbitrary-order nonlinearity. It also brings convenience to the tuning of PID parameters, providing a new idea for the practical design of nonlinear time-delay systems.
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Chen et al. (2025) studied this question.
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