Robust FOPID controller design for fractional‐order delay systems using positive stability region analysis

2019 ◽  
Vol 29 (15) ◽  
pp. 5195-5212 ◽  
Author(s):  
Shuo Zhang ◽  
Lu Liu ◽  
Xinshu Cui
Keyword(s):  
Fractional Order ◽  
Stability Region ◽  
Controller Design ◽  
Delay Systems ◽  
Region Analysis

Transient Response Control by Fractional-Order PI Controllers

2011 ◽  
Author(s):  
Serdar Ethem Hamamci ◽  
Serhat Obuz
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Transient Response ◽  
Stability Region ◽  
Control Method ◽  
Settling Time ◽  
Delay Systems ◽  
Response Control ◽  
Pi Controllers ◽  
And Control

Consideration of the transient response is one of the key topics in control system design for time delay systems. In this paper, an efficient method to control the transient response of the first order plus time delay stable (FOPTD) systems using the fractional-order PI (PIλ) controllers is presented. The main characterization of the method is first to construct the global stability region in the (kp, ki)-plane for any fixed value of λ and then to obtain ts and Mp curves corresponding to special settling time and maximum overshoot values in this region. Finally, by intersection of these curves, the Dλ-stability region in the (kp, ki)-plane is found. Changing the value of λ in the range of (0, 2), a set of Dλ-stability regions is obtained. These regions involve the controller parameters providing the closed loop settling time and maximum overshoot specifications together in the acceptable values. Therefore, the designer can easily decide to the selection of suitable values of kp, ki and λ. The simulation results indicate that the presented transient response control method is effective and practically useful in the analysis and control of the stable FOPTD systems by means of fractional-order PI controllers.

scholarly journals Disturbance Rejection for Fractional-Order Time-Delay Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Hai-Peng Jiang ◽  
Yong-Qiang Liu
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Disturbance Rejection ◽  
Controller Design ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Design Algorithm ◽  
The Stability ◽  
Disturbance Estimator

This paper presents an equivalent-input-disturbance (EID-) based disturbance rejection method for fractional-order time-delay systems. First, a modified state observer is applied to reconstruct the state of the fractional-order time-delay plant. Then, a disturbance estimator is designed to actively compensate for the disturbances. Under such a construction of the system, by constructing a novel monochromatic Lyapunov function and using direct Lyapunov approach, the stability analysis and controller design algorithm are derived in terms of linear matrix inequality (LMI) technique. Finally, simulation results demonstrate the validity of the proposed method.

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