Fractional-order modeling and sliding mode control of energy-saving and emission-reduction dynamic evolution system

Abstract

A B S T R A C TThis paper proposes the fractional-order modeling for sliding mode control of a complex four-dimensional energy-saving and emission-reduction system (ESERS). In the proposed methodology, the fractional calculus techniques are employed to accurately model the dynamics of the ESERS, and the fractional-order model of the energy-saving and emission-reduction system (FOESERS) is formulated. With the proposed FOESERS, all of the equilibrium points and the corresponding eigenvalues are obtained, and the instability region and the state trajectories of FOESERS are also given. The FOESERS can represent complex dynamic behaviours with chaotic and unstable states on the energy conservation, carbon emissions, economic growth, and renewable energy development, and have a great impact on the formulation of government energy policies. Furthermore, based on the fractional Lyapunov stability and robust control theory, a sliding-mode controller is designed to control the FOESERS with model uncertainties and external disturbances to the equilibrium point in the finite time. Finally, simulation results confirm the effectiveness and robustness of the proposed scheme.

Dynamic Analysis and Suppression Strategy Research on a Novel Fractional-Order Ferroresonance System

“…On this basis, fractional-order finite-time control has attracted more and more attention. Then, all kinds of fractional-order control methods have been investigated [30,31], such as fractional-order sliding mode control [32], fractional-order PID control [33], fractional-order finite-time control combined with the frequency distributed model [34], and fractional-order adaptive fuzzy control [35]. Although the above literature present the fractional-order control method to be applied to other chaotic system rather than chaotic ferroresonance circuits, the research ideas can be used for reference.…”

Fixed-time fractional-order sliding mode control for nonlinear power systems

“…However, because of the disadvantages of the IOSMC, it would result in some unfavorable effects on the nonlinear power system, such as high amplitude, chattering phenomenon, and long convergence time (Chen et al, 2016; Mobayen, 2015). Hence, fractional calculus, which has been proven to be effective in eliminating chattering, is a generalization of the arbitrary order of ordinary integration and differentiation (Huang et al, 2018; Xiong et al, 2018). Aghababa (2013) converted the sign function of the control input on the sliding mode surface into a fractional derivative form and proposed a novel fractional-order control method which effectively restrains the chattering caused by the switch control action and achieves high precision performance.…”

Hybrid extended-unscented Kalman filters for continuous-time nonlinear fractional-order systems involving process and measurement noises

“…Also, fractional-order models are more accurate than traditional models to reveal the dynamic of complex systems. Therefore, fractional-order models have been widely applied in the economics in Tarasov and Tarasova (2018), the biotechnology in Ionescu et al (2017), the energy engineering in Huang et al (2018), the agricultural engineering in Zhang et al (2013), the automation and control in Sadeghzadeh and Momeni (2016) and so on. Besides, the fractional-order calculus has developed rapidly in the field of control engineering to produce many fractional-order controllers, such as the fractional-order sliding mode controller in Zhan and Liu (2018), the fractional-order proportional-integral- derivative (PID) controller in Hamamci (2008), the fractional-order fuzzy control in Li et al (2018) and so on.…”