PID controller tuning using Bode's integrals

Abstract

A new method for PID controller tuning based on Bode's integrals is proposed. It is shown that the derivatives of amplitude and phase of a plant model with respect to frequency can be approximated by Bode's integrals without any model of the plant. This information can be used to design a PID controller for slope adjustment of the Nyquist diagram and improve the closed-loop performance.Besides, the derivatives can be also employed to estimate the gradient and the Hessian of a frequency criterion in an iterative PID controller tuning method. The frequency criterion is defined as the sum of squared errors between the desired and measured gain margin, phase margin and crossover frequency.The method benefits from specific feedback relay tests to determine the gain margin, the phase margin and the crossover frequency of the closed-loop system. Simulation examples and experimental results illustrate the effectiveness and the simplicity of the proposed method to design and tune the PID controllers.

PID Tuning Using Internal Model Controller with Tustin Model Approach

“…Selain itu, telah banyak publikasi mengenai metode penalaan kontrol PID, antara lain penalaan on-line PID menggunakan Continuous Action Reinforcement Learning Automata (CARLA) (Howell dan Best, 2000), Fuzzy PID kontroller (Jantzen, 1998), penalaan online fuzzy PID kontroller berbasis Robust Extended Kalman Filter (REKF) (Ahn dan Truong, 2009), berbasis Internal Model Controller dengan konfigurasi prediksi Smith (Kaya, 2004), fuzzy PID dengan Internal Model Controller (Kao et al, 2006), (Ho et al, 1998), algoritma Particle Swarm Optimization (PSO) (Kumar et al, 2010), self-tuning kontrol PID dengan Particle Swarm Optimization Approach (PSOA) (Kao et al, 2006), Bode's Integrals (Karimi et al, 2003), Extremum Seeking (Killingsworth dan Krstic, 2006), Immune Algorithm (Kim et al, 2002), pengembangan Genetic Algorithm (GA) (Kim et al, 2008;Kumar et al, 2008;dan Zhang et al, 2009), fuzzy neural network (Lee dan Teng, 2003), Adaptive Interaction (Lin et al, 2000), Integral of Time-weighted Absolute Error (ITAE) Criterion (Martins, 2005), Loop shaping H∞ control (Tan et al, 1998), dan Ant algorithm (Varol dan Bingul, 2004).…”

PID controller tuning for integrating processes

“…For integrating processes, the ISE criterion results in a PD controller which gives good servo response but fails to reject the load disturbances. Recently, Karimi et al [12] have used the Bode's integrals to approximate the derivatives of amplitude and phase of a system with respect to frequency at a given frequency and these derivatives are then used to adjust the slope of the Nyquist curve at the gain crossover frequency to obtain the parameters of a PID controller using the modified Ziegler-Nichols method. However, the selection of gain crossover frequency and the slope of the Nyquist curve has not been discussed in [12].…”

Pid Controller Design for Multivariable Systems Using Gershgorin Bands

“…This guarantees the desired stability robustness of the MIMO system. The problem which consists of finding the controller parameters to satisfy the specifications is then solved by minimizing iteratively a frequency criterion (Karimi et al, 2003). This one is defined as the weighted sum of squared errors between the achieved and specified values of the design parameters.…”