Fractional-order Systems and the Internal Model Principle

Author(s):  
Mir Shahrouz Takyar ◽  
Tryphon T. Georgiou
Author(s):  
Aymen Rhouma ◽  
Faouzi Bouani ◽  
Badreddine Bouzouita ◽  
Mekki Ksouri

This paper provides the model predictive control (MPC) of fractional order systems. The direct method will be used as internal model to predict the future dynamic behavior of the process, which is used to achieve the control law. This method is based on the Grünwald–Letnikov's definition that consists of replacing the noninteger derivation operator of the adopted system representation by a discrete approximation. The performances and the efficiency of this approach are illustrated with practical results on a thermal system and compared to the MPC based on the integer ARX model.


2018 ◽  
Vol 24 (22) ◽  
pp. 5312-5320 ◽  
Author(s):  
Ehsan Mohammadzadeh ◽  
Naser Pariz ◽  
Seyed Kamal Hosseini Sani ◽  
Amin Jajarmi

This paper aims to investigate an efficient numerical scheme for the optimal control of fractional-order dynamic systems. By using the Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations, the fractional optimal control problem under consideration is converted into a linear programming problem. Then, the internal model principle is employed in order to extend the new scheme for the fractional dynamic systems affected by the external persistent disturbances. Numerical examples and comparative results verify the validity and applicability of the new technique.


2008 ◽  
Vol 42 (6-8) ◽  
pp. 825-838 ◽  
Author(s):  
Saïd Guermah ◽  
Saïd Djennoune ◽  
Maâmar Bettayeb

Author(s):  
Yan Ti ◽  
Kangcheng Zheng ◽  
Wanzhong Zhao ◽  
Tinglun Song

To improve handling and stability for distributed drive electric vehicles (DDEV), the study on four wheel steering (4WS) systems can improve the vehicle driving performance through enhancing the tracking capability to desired vehicle state. Most previous controllers are either a large amount of calculation, or requires a lot of experimental data, these are relatively time-consuming and laborious. According to the front and rear wheel steering angle of DDEV can be distributed independently, a novel controller named internal model controller with fractional-order filter (IMC-FOF) for 4WS systems is proposed and studied in this paper. The IMC-FOF is designed using the internal model control theory and compared with IMC and PID controller. The influence of time constant and fractional-order parameters which is optimized using quantum genetic algorithms (QGA) on tracking ability of vehicle state are also analyzed. Using a production vehicle as an example, the simulation is performed combining Matlab/Simulink and CarSim. The comparison results indicated that the proposed controller presents performance to distribute the front and rear wheel steering angle for ensuring better tracking capability to desired vehicle state, meanwhile it possesses strong robustness.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aziz Khan ◽  
Hashim M. Alshehri ◽  
J. F. Gómez-Aguilar ◽  
Zareen A. Khan ◽  
G. Fernández-Anaya

AbstractThis paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.


Author(s):  
Riccardo Caponetto ◽  
Salvatore Graziani ◽  
Emanuele Murgano

AbstractIn the paper, a fractional-order RLC circuit is presented. The circuit is realized by using a fractional-order capacitor. This is realized by using carbon black dispersed in a polymeric matrix. Simulation results are compared with the experimental data, confirming the suitability of applying this new device in the circuital implementation of fractional-order systems.


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