Modeling and Control of Complex Dynamic Systems: Applied Mathematical Aspects

Gao, Zhiwei; Kong, De‐Xing; Gao, Chuanhou

doi:10.1155/2012/869792

Cited by 41 publications

(39 citation statements)

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“…They can represent some natural phenomena better than ordinary differential equations, phenomena such as controlling chaos and bifurcation in engineering systems, epidemic model with impulsive birth, and modelling and control of complex dynamic systems ( [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] Some phenomena represented by an impulsive system may be perturbed by small parameters, in particular singularity perturbation. An impulsive differential equation with singularity perturbation is quite complicated and is difficult to find an exact solution, so there are not many researches in this field.…”

Section: Introductionmentioning

confidence: 99%

PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem

Witayakiattilerd

2017

Advances in Mathematical Physics

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We study singular perturbation of impulsive system with a proportional-integral-derivative controller (PID controller) and solve an optimal control problem. The perturbation system comprises two important variables, a fast variable and a slow variable. Because of the complexity of the system, it is difficult to find its exact solution. This paper presents an approximation method for solving it. The aim of the approximation method is to reduce the complexity of the system by eliminating the fast variable. The solution of the method is expressed in an integral form, and it is called an approximated mild solution of the perturbed system. An example is provided to illustrate our result.

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Section: Introductionmentioning

confidence: 99%

PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem

Witayakiattilerd

2017

Advances in Mathematical Physics

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“…On the other hand, they are also complex dynamic systems. Experience shows that the usually the conventional PID controller is not effective for complex dynamic systems [1]. A number of researchers have conducted studies to develop a hybrid fuzzy PID control logic, whose tuning parameters are provided in real time.…”

Section: Introductionmentioning

confidence: 99%

Passive Identification is Non Stationary Objects With Closed Loop Control

Dyadik

Nadezhdin

Goryunov

et al. 2016

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. Typically chemical processes have significant nonlinear dynamics, but despite this, industry is conventionally still using PID-based regulatory control systems. Moreover, process units are interconnected, in terms of inlet and outlet material/energy flows, to other neighbouring units, thus their dynamic behaviour is strongly influenced by these connections and, as a consequence, conventional control systems performance often proves to be poor. However, there a hybrid fuzzy PID control logic, whose tuning parameters are provided in real time. The fuzzy controller tuning is made on the basis of Mamdani controller, also exploiting the results coming from an identification procedure that is carried on when an unmeasured step disturbance of any shape affects the process behaviour. This paper presents procedure for identifying technological object control in a closed loop, i. e. that operates the automated control system. The variation in the controlled variable, caused by the change of the nonmeasurable disturbance, is considered the initial signal for the identification procedure. The parameters of the control object are found by optimization method Levenberg-Marquardt. IntroductionNowadays, in chemical and nuclear industries (i.e. integrated separations, extractions crystallization processes to purify U and Pu from other fusion side-components) any processing step has a high level of automation. On the one hand, all processes are high responsibility technology (HRT), i.e. high performance technology with respect of safety level. On the other hand, they are also complex dynamic systems. Experience shows that the usually the conventional PID controller is not effective for complex dynamic systems [1]. A number of researchers have conducted studies to develop a hybrid fuzzy PID control logic, whose tuning parameters are provided in real time. The fuzzy controller tuning is made on the basis of Mamdani controller, also exploiting the results coming from an identification procedure. The problem of identifying has attracted and attracts a lot of research interests and many methods are available for this problem in literature [2].A priori information about the dynamics of the controlled plant is required for the synthesis of PID-

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“…Usually the conventional PID controller is not effective for complex dynamic systems [30,31]. The complex dynamic systems are those systems with non-linear static characteristics, i.e.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy adaptive control system of a non-stationary plant with closed-loop passive identifier

Manenti

Rossi

Goryunov

et al. 2015

Resource-Efficient Technologies

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Typically chemical processes have significant nonlinear dynamics, but despite this, industry is conventionally still using PID-based regulatory control systems. Moreover, process units are interconnected, in terms of inlet and outlet material/energy flows, to other neighboring units, thus their dynamic behavior is strongly influenced by these connections and, as a consequence, conventional control systems performance often proves to be poor. This paper proposes a hybrid fuzzy PID control logic, whose tuning parameters are provided in real time. The fuzzy controller tuning is made on the basis of Mamdani controller, also exploiting the results coming from an identification procedure that is carried on when an unmeasured step disturbance of any shape affects the process behavior.In addition, this paper compares a fuzzy logic based PID with PID regulators whose tuning is performed by standard and well-known methods. In some cases the proposed tuning methodology ensures a control performance that is comparable to that guaranteed by simpler and more common tuning methods. However, in case of dynamic changes in the parameters of the controlled system, conventionally tuned PID controllers do not show to be robust enough, thus suggesting that fuzzy logic based PIDs are definitively more reliable and effective.

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Modeling and Control of Complex Dynamic Systems: Applied Mathematical Aspects

Cited by 41 publications

References 0 publications

PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem

PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem

Passive Identification is Non Stationary Objects With Closed Loop Control

Fuzzy adaptive control system of a non-stationary plant with closed-loop passive identifier

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