Fractional-Order Model Predictive Control: Development and Application

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Numerical and Computational Methods".

Deadline for manuscript submissions: closed (28 February 2022) | Viewed by 4280

Special Issue Editor


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Guest Editor
Department of Automatic Control and Robotics, Faculty of Electrical Engineering, West Pomeranian University of Technology in Szczecin, Al. Piastów 17, 70-310 Szczecin, Poland
Interests: control theory; predictive and robust control; fractional-order systems; hybrid and switched systems; mechatronics and embedded systems; fault-tolerant control systems

Special Issue Information

Dear Colleagues,

Biological, sociocognitive, and economic phenomena, as well as transport, information, and technological systems often require the description by means of linear or nonlinear, non-integer order differential equations. As a consequence, control systems should often also realize fractional-order control algorithms.

The aim of this Special Issue is to gather a collection of papers reflecting the possibility of employing the more and more popular theory of fractional-order differential (finite difference) calculus for modern predictive control, the practical effectiveness of which has been borne out by numerous industrial applications.

The idea of predictive control, which was put forward several dozen years ago and has been intensely developed since then, is considered to be, after many years of operating experience in industry, one of the most universal and effective control methods. Predictive control enables various signal constraints and various kinds of disturbances to be taken into account and may be employed to control processes with practically any number of inputs and outputs. However, in the case of processes with particularly complex properties, its effectiveness depends on the quality of the process model. Additionally, in the case of nonlinear processes, direct nonlinear control algorithms are often too complex in order for computations to be performed online. Therefore, there is a need to develop new predictive control algorithms to cope effectively with the abovementioned difficult cases and to provide new opportunities for control performance and robustness. The introduction of fractional-order differential calculus at the stage of synthesizing the control algorithm offers an additional degree of freedom in tuning a control loop; on the other hand, it enables the specific properties of the controlled process to be better taken into account.

Articles submitted to this Special Issue may focus on research relating to fractional-order model predictive control and its applications to real dynamic systems modeled using integer- and/or fractional-order differential equations. Other important subjects, such as example numerical and computational aspects of proposed control algorithms, may also be explored.

Prof. Dr. Stefan Domek
Guest Editor

Manuscript Submission Information

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Keywords

  • model predictive control
  • fractional-order control theory
  • fractional-order dynamic models
  • fractional-order controllers and observers
  • analytical and computational methods for fractional-order systems
  • implementation of fractional-order control

Published Papers (2 papers)

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Research

14 pages, 2214 KiB  
Article
On the Linear–Quadratic–Gaussian Control Strategy for Fractional-Order Systems
by Grzegorz Bialic and Rafał Stanisławski
Fractal Fract. 2022, 6(5), 248; https://doi.org/10.3390/fractalfract6050248 - 29 Apr 2022
Cited by 2 | Viewed by 1528
Abstract
In the paper, the Linear–Quadratic–Gaussian (LQG) control strategy in regulatory mode (disturbance attenuation, zero value of the reference signal) in single-loop control is used to stabilize the system equipped in a non-integer order plant. The influence of the optimal controller design sophistication on [...] Read more.
In the paper, the Linear–Quadratic–Gaussian (LQG) control strategy in regulatory mode (disturbance attenuation, zero value of the reference signal) in single-loop control is used to stabilize the system equipped in a non-integer order plant. The influence of the optimal controller design sophistication on control quality in terms of output variance is examined. It has been shown that the optimal implementation length of fractional-order difference is relatively low (several dozen in considered examples). Therefore, further increasing the controller’s complexity in terms of approximation length does not improve the control performance. Furthermore, it is presented that, under bounded control signal variance, the optimal fractional order of the controller may be significantly different from the actual fractional order of the plant (in the examples, the difference is up to 0.66). Full article
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18 pages, 2917 KiB  
Article
Fractional Order Distributed Model Predictive Control of Fast and Strong Interacting Systems
by Chuanguo Chi, Ricardo Cajo, Shiquan Zhao, Guo-Ping Liu and Clara-Mihaela Ionescu
Fractal Fract. 2022, 6(4), 179; https://doi.org/10.3390/fractalfract6040179 - 23 Mar 2022
Cited by 3 | Viewed by 2177
Abstract
Fast and strong interacting systems are hard to control from both performance and control effort points of view. Moreover, multiple objective functions or objectives with various identifiers of varying weights can hold unfeasible solutions at times. A novel cost objective function is proposed [...] Read more.
Fast and strong interacting systems are hard to control from both performance and control effort points of view. Moreover, multiple objective functions or objectives with various identifiers of varying weights can hold unfeasible solutions at times. A novel cost objective function is proposed here to overcome both feasibility set limitations and computational burdens. An application example is used to illustrate its added value, which is a fast and strong interacting multivariable system: a landscape office lighting regulatory problem. New lighting technology and an intelligent control system have been produced to improve control accuracy and reduce power consumption. While optimizing the hardware of the lighting system, the energy consumption can be further reduced by applying advanced control strategy in the lighting system. This paper designed a fractional order distributed model predictive control (FOMPC) scheme to realize the reference tracking and stability control of multiple illuminations at the same time. In order to test the efficiency of the control strategy, an experiment was carried out on the lighting setup based on the dSPACE control system. The FOMPC scheme was analyzed through simulation and lighting experiments based on the dSPACE control system. Through a comparison with the mode predictive control (MPC) scheme, the superiority of the FOMPC scheme for the dynamic behavior and control performance of multiple lighting systems was verified. The research results provide a basis for multiple lighting control and its application. Full article
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