Stability analysis of a three-dimensional energy demand-supply system under delayed feedback control

Yang, Kun-Yi; Zhang, Ling Li; Zhang, Jie

doi:10.14736/kyb-2015-6-1084

Cited by 4 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, all those works assume that the control action can be exerted on the plant immediately, i. e., without any latency or time lag in the control channel. Motivated by their importance in many application areas, e. g., networked structures [8,12,15,27,30], biological [39], mechanical [42], and energy [43] systems, inventory and process control [10,11,31,35], remote regulation and sensing [6,29,44], in this paper, the possibility of using soft VSC in the systems with non-negligible delay is investigated. In order to overcome the potentially destabilizing effect of the delay in the feedback loop, a dead-time compensator is incorporated.…”

Section: Related Work and Contributionmentioning

confidence: 99%

Soft variable structure control in time-delay systems with saturating input

Ignaciuk¹

2021

Kybernetika

View full text Add to dashboard Cite

show abstract

Section: Related Work and Contributionmentioning

confidence: 99%

Soft variable structure control in time-delay systems with saturating input

Ignaciuk¹

2021

Kybernetika

View full text Add to dashboard Cite

show abstract

“…The DFC method is also reformulated as a tool to stabilize equilibria embedded in chaotic attractors (see [9] and references within it). With this objective, it is implemented on known chaotic systems as Chen system [25] or Rossler system [2] and on technical applications like [10] or [26] among others. An extended version (EDFC), proposed in [24], results more effective for stabilizing highly-unstable equilibrium points and UPO's ( [19]).…”

Section: Introductionmentioning

confidence: 99%

Oscillating delayed feedback control schemes for stabilizing equilibrium points

Pastor

González

2019

Heliyon

View full text Add to dashboard Cite

Limitations of the delayed feedback control and of its extended versions have been fully treated in the literature. The oscillating delayed feedback control appears as a promising scheme to overcome this problem. Two methods based on it are dealt with in this work. It is rigorously proven that for a nonlinear scalar system, stabilization in one of its (unstable) equilibrium points is achieved if any of these methods is applied. An ad-hoc map is associated to the (continuous) controlled system and the results are derived using discrete-time system stabilization tools. Moreover, the stability parameters region is fully described and issues like control performance, rate of convergence or robustness aspects are carefully analyzed.

show abstract

“…They used synchronization theory as the regulation theory for regional coordinated development to research the system. Based on previous findings (Chen & Liu, ; Fang et al, 2017a, ; Feng, Sun, & Zhang, ; Huang et al, ; Liao, ; Niu et al, ; Ozturk & Acaravic, ; Pao & Tsai, ; Yang, Zhang, & Zhang, ; Yin et al, ), Fang et al () proposed a mathematical model of the energy‐saving and emission‐reduction system as follows, which includes energy‐saving and emission‐reduction, carbon emissions, and economic growth, and studied the chaos of the system.

\begin{matrix} right \frac{d x}{d t} & center = & left a_{1} x true(\frac{y}{M} - 1) - a_{2} y + a_{3} z - a_{4} x, \\ right \frac{d y}{d t} & center = & left - b_{1} x + b_{2} y true(1 - \frac{y}{C}) + b_{3} z true(1 - \frac{z}{E} true) - b_{4} y, \\ right \frac{d z}{d t} & center = & left c_{1} x true(\frac{x}{N} - 1 true) - c_{2} y - c_{3} z - c_{4} z . \end{matrix}

where

x (t)

is the time‐dependent variable of energy‐saving and emission‐reduction,

y (t)

the time‐dependent variable of carbon emissions, and

z (t)

the time‐dependent variable of economic growth;

a_{i}, b_{i}, c_{i} (i = 1, 2, 3, 4), M, C, E, N

are positive constants;

…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of fractional‐order energy‐saving and emission‐reduction system and its discretization

Chen

Liu

2018

Natural Resource Modeling

View full text Add to dashboard Cite

This paper attempts to explore dynamical behavior and mathematical properties of the three‐dimensional fractional‐order energy‐saving and emission‐reduction system. Theoretically, the conditions of local stability of fractional‐order system's equilibrium points are obtained. Numerical investigations on the dynamics of this system are carried out, and the existence of the asymptotically stable attractor is found. Combined with the fractional‐order subsystem, we discuss the relationship between energy‐saving and emission‐reduction and economic growth, and carbon emissions and economic growth. Furthermore, we discretize the fractional‐order system and give necessary and sufficient conditions of its stabilization. It is shown that the stability of the discretization system is impacted by the system's fractional parameter. Numerical simulations show the richer dynamical behavior of the fractional‐order system and verify the theoretical results. Recommendations for Resource Managers The impact of carbon emissions on economic growth is one of the main reasons for energy‐saving and emission‐reduction. Control measures on people's low‐carbon life through government intervention are required to protect the natural environment. New energy‐saving and emission‐reduction technologies should be implemented to achieve sustainable social and economic development.

show abstract

Stability analysis of a three-dimensional energy demand-supply system under delayed feedback control

Cited by 4 publications

References 9 publications

Soft variable structure control in time-delay systems with saturating input

Soft variable structure control in time-delay systems with saturating input

Oscillating delayed feedback control schemes for stabilizing equilibrium points

Dynamical behavior of fractional‐order energy‐saving and emission‐reduction system and its discretization

Contact Info

Product

Resources

About