In this paper, a proportional–integral–derivative (PID) controller design method for stable and integrating time-delay systems with and without non-minimum phase zero (inverse response) using the direct method is proposed. The PID controller gains are obtained by matching the frequency response of the closed-loop control system to that of the reference model with a minimum weighted integral squared absolute error in the bandwidth region. The reference model is chosen to satisfy the desired maximum sensitivity Ms. As a result, three linear algebraic equations in three unknowns are obtained and the solution of them gives the PID controller gains. The proposed method can be applied to low- and high-order systems, and the Pade approximation of the time-delay term e−Ls is not required.
Fractional-Order PID Controller Design for Time-Delay Systems Based on Modified Bode’s Ideal Transfer Function
