Low‐gain internal model control PID controller design based on second‐order filter

Abstract

A design method is proposed for low-gain internal model control (IMC) proportional-integral-derivative (PID) controllers based on the second-order filter. The PID parameters are obtained by approximating the feedback form of the IMC controller with a Maclaurin series, in which the second-order filter is applied using the IMC approach to achieve a low-gain PID controller that is suitable for model mismatch problems. Analytical PID tuning rules based on the second-order filter are derived for several common-use process models.The second-order filter is designed from the desired time domain performances of maximum overshoot and settling time. Furthermore, the robustness of the IMC PID controller based on the second-order filter is analyzed, and results show that its robustness performance is better than the first-order filter under certain conditions. Finally, three categories of models divided by the ration of time constant and time delay are presented in the comparative numerical simulations to validate the effectiveness and generality of the proposed PID controller design method.

Advanced Flowrate Control of Petroleum Products in Transportation: An Optimized Modified Model Reference PID Approach

“…However, the Ziegler-Nichols method may not result in optimal parameters for a transportation lag system due to its linear and time-invariant nature [15]- [19]. To overcome these limitations, several studies have explored PID controller design methods for transportation lag systems with first order plus time delay [20] [21], such as the PID controller based on Ziegler-Nichols tuning, Internal Model Control tuning, and Shams Internal Model Control tuning [22], PID controller design based on the minimum error tunning rules [23] [24], enhanced fractional filter PID controller design [25], PID controller design based on fractional order tuning [26], directly synthesized parallel PID controller [27], active disturbance rejection PID controller [28], optimized PID controller based on linear programming [29], PI-PD controller design by considering both the maximum sensitivity principles and the Routh-Hurwitz stability criteria [30], particle swarm optimization-based PID controller [31], PID controller design based on disturbance observer [32], and filter-based PID with low-gain internal model control [33]. However, these methods come with many limitations and challenges, such as suboptimal tuning, lack of robustness, and inadequate handling of system complexities.…”