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 T-S Fuzzy Control of Uncertain Fractional-Order Systems with Time Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yilin Hao ◽  
Xiulan Zhang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Control Method ◽  
Fuzzy Model ◽  
Linear Structure ◽  
Adaptive Method ◽  
Delay Systems ◽  
Robust Controller ◽  
External Disturbances ◽  
Fuzzy Adaptive

In this article, the adaptive control of uncertain fractional-order time-delay systems (FOTDSs) with external disturbances is discussed. A Takagi-Sugenu (T-S) fuzzy model with if-then rules is adopted to characterize the dynamic equation of the FOTDS. Besides, a fuzzy adaptive method is proposed to stabilize the model. By utilizing the Lyapunov functions, a robust controller is constructed to stabilize the FOTDS. Due to the uncertainty of system parameters, some fractional-order adaptation laws are designed to update these parameters. At the same time, some if-then rules with linear structure based on the fuzzy T-S adaption concept are established. The designed method not only guarantees that the state of closed-loop system asymptotically converges to origin but also keeps the signal in the FOTDS bounded. Finally, the applicability of the control method is proved by simulation examples.

scholarly journals Fractional Order PIλDµ Control Design for a Class of Cyber-Physical Systems with Fractional Order Time-Delay models

2019 ◽  
Vol 1 (2) ◽  
pp. 1-18
Author(s):  
Marwa Boudana ◽  
Samir Ladaci ◽  
Jean-Jacques Loiseau
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Control Design ◽  
Cyber Physical Systems ◽  
Performance Criteria ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Physical Systems ◽  
System Configurations ◽  
And Control

The control of cyber-physical systems (CPS) is a great challenge for researchers in control theory and engineering mainly because of delays induced by merging computation, communication, and control of physical processes. Consequently, control solutions for time-delay systems can be applied efficiently for many CPS system configurations. In this article, a fractional order PIλ and PIλDµ control design is investigated for a class of fractional order time-delay systems. The proposed control design approach is simple and efficient. The controller parameter's adjustment is achieved in two steps: first, the relay approach is used to compute satisfactory classical PID coefficients, namely kp, Ti and Td. Then, the fractional orders λ and µ are optimized using performance criteria. Simulation results show the efficiency of the proposed design technique and its ability to enhance the PID control performance.

scholarly journals Analysis and Control Design for a Class of Fractional Order Time-Delay Systems

2020 ◽  
Vol 5 (1) ◽  
pp. 18-24
Author(s):  
Marwa BOUDANA ◽  
Samir LADACI ◽  
Jean Jacques LOISEAU
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Pid Control ◽  
Control Design ◽  
Performance Criteria ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Control Performance ◽  
And Control ◽  
Fractional Orders

In this paper, we consider a class of fractional order time-delay systems and propose a fractional order control design for their stabilization. The controller parameter’s adjustment is achieved in two steps: first, the relay approach is used to compute satisfactory classical PID coefficients, namely kp, Ti and Td. Then, the fractional orders ʎ and µ are optimized using performance criteria. Simulation results show the efficiency of the proposed design technique and its ability to enhance the PID control performance.

scholarly journals Fractional-Order Controller Design for Oscillatory Fractional Time-Delay Systems Based on the Numerical Inverse Laplace Transform Algorithms

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Lu Liu ◽  
Feng Pan ◽  
Dingyu Xue
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Fractional Order ◽  
Control Method ◽  
Delay System ◽  
Inverse Laplace Transform ◽  
Delay Systems ◽  
Time Delay System ◽  
Numerical Inverse Laplace Transform ◽  
Fractional Order Controller

Fractional-order time-delay system is thought to be a kind of oscillatory complex system which could not be controlled efficaciously so far because it does not have an analytical solution when using inverse Laplace transform. In this paper, a type of fractional-order controller based on numerical inverse Laplace transform algorithm INVLAP was proposed for the mentioned systems by searching for the optimal controller parameters with the objective function of ITAE index due to the verified nature that fractional-order controllers were the best means of controlling fractional-order systems. Simulations of step unit tracking and load-disturbance responses of the proposed fractional-order optimalPIλDμcontroller (FOPID) and corresponding conventional optimal PID (OPID) controller have been done on three typical kinds of fractional time-delay system with different ratio between time delay (L) and time constant (T) and a complex high-order fractional time delay system to verify the availability of the presented control method.

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