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.

Mikhailov's criterion states that a real Hurwitz polynomial) (s  of degree n satisfies the monotonic phase increase, that is to say the argument of) (jw  goes through n quadrants as w runs from zero to infinity. In this paper, we utilize the generalized Mikhailov criterion presented in [1] to give a solution to the problem of finding the stabilizing feedback gains for a given linear-time invariant plant having a P controller, a PI controller and a PID controller.

This paper considers a design method for PID controllers to achieve the robustness to the uncertainty of the time delay for the first-order plus time delay system (FOPTD). Initially, the stabilizing regions of the PID controller gains are determined by a graphical stability method. Then, we specify two simultaneous design specifications: gain margin and phase crossover frequency. These specifications give a set of stabilizing PID controllers. To get a unique PID controller, we introduce an additional constraint which is finding the smallest absolute value of the slope of the open-loop system magnitude at the specified phase crossover frequency. The obtained PID controller is located in the stability region, and also robust to system time delay variation due to the proposed constraint.

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This paper considers the problem of controlling a given linear time invariant (LTI) system described by a rational transfer function using a PI controller. A method based on graphical and computational tools has been proposed. This method specifies a PI controller) (i p K and K that satisfies both frequency domain specifications (a specified gain or phase margin) and minimum integral time absolute error (ITAE).