This study explores controlling discrete fractional-order Hammerstein systems through two different approaches. The first method involves a detailed exploration of discrete sliding mode control (SMC), while the second method employs adaptive sliding mode techniques to address challenges posed by unknown time-varying system parameters. The aim is to enhance control strategies for these systems by ensuring stability and robustness amid evolving parameters. Stability analysis using Lyapunov Theory is carried out to establish the stability of the proposed control schemes. Comprehensive reachability analysis is then performed to show that the system reaches a quasi-sliding mode in finite time. The effectiveness of the proposed methods is thoroughly evaluated using simulation cases, covering three distinct scenarios. Finally, a discussion section analyzes the simulation outcomes and assesses the efficiency methodologies in handling complex system dynamics. Through comparative analysis and discussion, this study contributes to advancing control strategies tailored for systems characterized by fractional-order dynamics and varying parameters.
BaiEW (2010) Block-oriented Nonlinear System Identification. Berlin: Springer-Verlag.
2.
BingxinLZhaoX, et al (2023) Neural network-based adaptive sliding mode control for T-S fuzzy fractional order systems. IEEE Transactions on Circuits and Systems II: Express Briefs70(12): 4549–4553.
3.
DumitruBValentinaEBPraveenA (2023) Fractional Order Systems and Applications in Engineering. Amsterdam: Elsevier.
4.
DzielinskiASierociukD (2008) Ultracapacitor modelling and control using discrete fractional order state-space model. Acta Montanistica Slovaca13: 268–273.
5.
ElloumiMKamounS (2014) Parametric estimation of interconnected nonlinear systems described by input-output mathematical models. International Journal of Automation and Computing13: 1–18.
6.
EsraaMOsamaEMohammadEB, et al. (2023) Embedded adaptive fractional-order sliding mode control based on TSK fuzzy system for nonlinear fractional-order systems. Soft Computing27: 15463–15477.
7.
GaoWYufuWAbdollahH (1995) Discrete-time variable structure control systems. IEEE Transactions on Industrial Electronics42(2): 117–122.
8.
GoelsABruceALBernsteinDS, et al. (2020) Recursive least squares with variable-direction forgetting: Compensating for the loss of persistency. IEEE Control Systems Magazine40(4): 80–102.
9.
GuanghuiSLigangWZhianK, et al. (2023) Practical tracking control of linear motor via fractional-order sliding mode. Automatica94: 221–235.
10.
HammarKTounsiaDMaamarB (2019) Identification of fractional Hammerstein system with application to a heating process. Nonlinear Dynamics96: 2613–2626.
11.
JiachangWYihengWTianyuL, et al. (2022) Fully parametric identification for continuous time fractional order Hammerstein systems. Journal of the Franklin Institute357(1): 651–666.
12.
LiuYZhongyangZDongjieL (2023) Fractional order neural sliding mode control based on the FO-Hammerstein model of piezoelectric actuator. ISA Transactions142: 515–526.
13.
LopezPNouriAS (2006) Théorie Élémentaire et Pratique de la Commande par les Régimes Glissants. Berlin: Springer.
14.
MarzouguiSBedouiSAbderrahimK (2023) On the combined estimation of the parameters and the states of fractional-order systems. Journal of Systems and Control Engineering237(10): 1853–1866.
15.
MohsenVMahdiK (2019) Adaptive fractional order sliding mode control for a quadrotor with a varying load. Aerospace Science and Technology86: 737–747.
16.
PetrasI (2011) Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation. Berlin: Springer.
17.
ShengjunWXinkaiC (2019) Discrete-time fractional-order integral based sliding mode control for piezo-actuated system. In: International Conference on Advanced Mechatronic Systems (ICAMechS), Kusatsu, Japan, pp. 163–168. New York: IEEE.
18.
TarekAMMohammadEHBelalAZ, et al. (2024) Fractional-order fuzzy sliding mode control of uncertain nonlinear mimo systems using fractional-order reinforcement learning. Complex and Intelligent Systems10: 3057–3085.
19.
UtkinIV (1996) Sliding Modes in Control and Optimization. Berlin: Springer.
20.
WangC (2024) Adaptive terminal sliding-mode synchronization control with chattering elimination for a fractional-order chaotic system. Fractal and Fractional8(4): 2–14.
21.
YakoubZMessaoudAAounM, et al. (2018) On the fractional closed-loop linear parameter varying system identification under noise corrupted scheduling and output signal measurements. Transactions of the Institute of Measurement and Control41(10): 1–13.
22.
YakoubZNaifarOIvanovD (2022) Unbiased identification of fractional order system with unknown time-delay using bias compensation method. Mathematics10(16): 1–19.
23.
YanLLunZYangQuanC, et al. (2014) Fractional-order iterative learning control and identification for fractional-order Hammerstein. In: Proceeding of the world congress on intelligent control and automation, Shenyang, China, 29 June–4 July, pp. 840–845. New York: IEEE.
24.
YangLZhaoZLiD, et al. (2023) Fractional order neural sliding mode control based on the FO-Hammerstein model of piezoelectric actuator. ISA Transactions142: 515–526.
25.
YuFZhuQChenY (2023) Adaptive fractional-order fast-terminal-type sliding mode control for underwater vehicle-manipulator systems. Journal of Mechanisms Robotics15: 064501.
26.
ZnidiADehriKNouriAS (2022) Discrete adaptive second order sliding mode control for uncertain Hammerstein nonlinear systems. In: 19th international multi-conference on systems, signals and devices (SSD), Algeria, Setif, 6–10 May, pp. 1241–1247. New York: IEEE.
27.
ZnidiADehriKNouriAS (2024a) Decentralized discrete adaptive sliding mode control for interconnected nonlinear systems. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering238(5): 943–956.
28.
ZnidiAKhlifRJNouriAS (2024b) Discrete sliding mode control based on a new fractional order power reaching law. Journal of Vibration and Control. Epub ahead of print2January. DOI: 10.1177/10775463231223273.
