A dynamic model used for controller design of a coal fired once-through boiler-turbine unit

Liu, Jizhen; Yan, Suying; Zeng, Deliang; Hu, Yong; Lv, You

doi:10.1016/j.energy.2015.10.077

Cited by 160 publications

(73 citation statements)

References 9 publications

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“…where a 1 and a 2 are constants, (x 1 , x 2 ) is a continuous nonlinear function, and p 1 is identified from the running data obtained from the power plant. As mentioned in the work of Liu et al, 38 the fulfillment of the constraint on the output y = x 1 is a rather important task in control design, which can be achieved by the approach developed in this paper.…”

Section: Preliminary and Assumptionsmentioning

confidence: 96%

“…Remark It is worthwhile pointing out that a number of practical systems subject to output constraints can be governed/modeled by ordinary differential equations of the form . For example, the reduced‐order dynamical model of the boiler‐turbine unit considered in the work of Liu et al has the following form:

\begin{matrix} alignleft \\ align-1 {\dot{x}}_{1} & align-2 = a_{1} x_{2}^{p_{1}} \\ align-1 {\dot{x}}_{2} & align-2 = a_{2} u + ϕ (x_{1}, x_{2}), \end{matrix}

where a 1 and a 2 are constants, ϕ ( x 1 , x 2 ) is a continuous nonlinear function, and p 1 is identified from the running data obtained from the power plant. As mentioned in the work of Liu et al, the fulfillment of the constraint on the output y = x 1 is a rather important task in control design, which can be achieved by the approach developed in this paper.…”

Section: Preliminary and Assumptionsmentioning

confidence: 99%

“…Example Consider the reduced‐order dynamical model of the boiler‐turbine unit as previously mentioned in Remark

\begin{matrix} alignleft \\ align-1 {\dot{x}}_{1} & align-2 = a_{1} x_{2}^{p_{1}} \\ align-1 {\dot{x}}_{2} & align-2 = a_{2} u + ϕ (x_{1}, x_{2}), \end{matrix}

where x 1 is the drum pressure (kg/cm 2 ), x 2 is the reheater pressure (kg/cm 2 ), u is the control valve position (cm), a 1 =1.4, a 2 =0.98, p 1 =9/7, and

ϕ false(x_{1}, x_{2} false) = 0.33 x_{1}^{1 false/ 3} x_{2}^{1 false/ 7}

. Because the parameters a 1 and a 2 are available, Assumption is directly satisfied with

{\underline{d}}_{1} = {\overset{d}{true}}_{1} = 1.4

and

{\underline{d}}_{2} = {\overset{d}{true}}_{2} = 0.98

. By choosing r 1 =1, σ 1 =0, and σ 2 =−1/3, it follows that r 2 =1/3, r 3 =2/15, and λ = μ =1.…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…It is worthwhile pointing out that a number of practical systems subject to output constraints can be governed/modeled by ordinary differential equations of the form (1). For example, the reduced-order dynamical model of the boiler-turbine unit considered in the work of Liu et al 38 has the following form:…”

Section: Preliminary and Assumptionsmentioning

confidence: 99%

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A new approach to stabilization of high‐order nonlinear systems with an asymmetric output constraint

Chen

2019

Intl J Robust & Nonlinear

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Summary This paper is concerned with the problem of state feedback stabilization for a class of high‐order nonlinear systems with an asymmetric output constraint. A novel asymmetric barrier Lyapunov function (BLF) is first proposed by deliberating the characteristics of the system nonlinearities. Then, the presented BLF, together with a skillful manipulation of sign functions, is utilized to delicately revamp the technique of adding a power integrator, thereby developing a systematic approach that guides us in constructing a continuous state feedback stabilizer and preventing the violation of a pre‐specified asymmetric output constraint during operation. The novelty of this paper is attributed to the development of a unified method that is able to simultaneously tackle the problem of stabilization for high‐order nonlinear systems with and without output constraints in a constructive fashion, without changing the controller structure. An illustrative example is presented to demonstrate the superiority of the proposed approach.

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Section: Preliminary and Assumptionsmentioning

confidence: 96%

\begin{matrix} alignleft \\ align-1 {\dot{x}}_{1} & align-2 = a_{1} x_{2}^{p_{1}} \\ align-1 {\dot{x}}_{2} & align-2 = a_{2} u + ϕ (x_{1}, x_{2}), \end{matrix}

Section: Preliminary and Assumptionsmentioning

confidence: 99%

“…Example Consider the reduced‐order dynamical model of the boiler‐turbine unit as previously mentioned in Remark

\begin{matrix} alignleft \\ align-1 {\dot{x}}_{1} & align-2 = a_{1} x_{2}^{p_{1}} \\ align-1 {\dot{x}}_{2} & align-2 = a_{2} u + ϕ (x_{1}, x_{2}), \end{matrix}

where x 1 is the drum pressure (kg/cm 2 ), x 2 is the reheater pressure (kg/cm 2 ), u is the control valve position (cm), a 1 =1.4, a 2 =0.98, p 1 =9/7, and

ϕ false(x_{1}, x_{2} false) = 0.33 x_{1}^{1 false/ 3} x_{2}^{1 false/ 7}

. Because the parameters a 1 and a 2 are available, Assumption is directly satisfied with

{\underline{d}}_{1} = {\overset{d}{true}}_{1} = 1.4

and

{\underline{d}}_{2} = {\overset{d}{true}}_{2} = 0.98

. By choosing r 1 =1, σ 1 =0, and σ 2 =−1/3, it follows that r 2 =1/3, r 3 =2/15, and λ = μ =1.…”

Section: Illustrative Examplesmentioning

confidence: 99%

Section: Preliminary and Assumptionsmentioning

confidence: 99%

See 2 more Smart Citations

A new approach to stabilization of high‐order nonlinear systems with an asymmetric output constraint

Chen

2019

Intl J Robust & Nonlinear

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show abstract

“…System is the standard p ‐normal form discussed in if the power is a constant. However, in practice, the power p in fact could be varying along with the different running conditions, as shown in the following reduced‐order dynamical model of a boiler‐turbine unit in (, system (32)),

\begin{matrix} right {\dot{x}}_{1} & left = c_{1} {[x_{2}]}^{p (t)} + ϕ_{1} (x_{1}, u) & right \\ right {\dot{x}}_{2} & left = c_{2} x_{2} + ϕ_{2} (u) \end{matrix}

where c 1 and c 2 are constants, and ϕ 1 (·) and ϕ 2 (·) are continuous nonlinear functions. For different boiler‐turbine units, the power in is not fixed because it is usually identified from the operational data obtained from the power plant.…”

Section: Introductionmentioning

confidence: 99%

Smooth output feedback stabilization for a class of nonlinear systems with time‐varying powers

Chen

Qian

Lin

et al. 2017

Intl J Robust & Nonlinear

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Summary This paper investigates the global asymptotic stabilization problem for a class of nonlinear systems with time‐varying powers. First, adding a power integrator technique is revamped to design a smooth state feedback controller, which is implementable with only upper and lower bounds of the time‐varying powers. When the system state is not fully available and the time‐varying power is exactly known, a smooth output feedback controller constituted by a state feedback and a nonlinear state observer is constructed to globally stabilize the system. Copyright © 2017 John Wiley & Sons, Ltd.

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Neural network‐based decentralized adaptive fault‐tolerant control for a class of nonlinear interconnected systems with unknown input powers

Zhu

Shen

Zhang

2023

Adaptive Control & Signal

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Summary This article studies the output tracking control for a class of interconnected nonlinear systems with actuator faults, where each subsystem has unknown powers. Based on Lyapunov stability theory, a neural‐network‐based decentralized adaptive fault‐tolerant control scheme is proposed so that each tracking error can be constricted in a small adjustable neighborhood of the origin. In existing results, interconnections and actuator bias faults have been addressed. But the systems' input powers are required to be a known positive integer and preferably one. So in our article, we relax the restrictions and consider more general systems whose input powers are extended to larger than one and unknown at the same time. Finally, two numerical simulation examples are shown to explain the validity of control strategy proposed in our article.

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A dynamic model used for controller design of a coal fired once-through boiler-turbine unit

Cited by 160 publications

References 9 publications

A new approach to stabilization of high‐order nonlinear systems with an asymmetric output constraint

A new approach to stabilization of high‐order nonlinear systems with an asymmetric output constraint

Smooth output feedback stabilization for a class of nonlinear systems with time‐varying powers

Neural network‐based decentralized adaptive fault‐tolerant control for a class of nonlinear interconnected systems with unknown input powers

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