Control of coupled PDEs–ODEs using input–output linearization: Application to a cracking furnace

Panjapornpon, Chanin; Limpanachaipornkul, Patara; Charinpanitkul, Tawatchai

doi:10.1016/j.ces.2012.03.014

Cited by 18 publications

(11 citation statements)

References 10 publications

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“…Proposition 3 For the functions ϕ 1 (·), ϕ 2 (·) and ϕ 3 (·) de¿ned in (11), there exists a positive constant M such that…”

Section: Lemmamentioning

confidence: 99%

“…As a matter of fact, the controls of coupled PDE-ODE systems have received continuous investigation over the last decades (see e.g., [7][8][9][10][11] and the references therein). Recently, the stabilization of ODE systems coupled by a parabolic PDE has been investigated in [7,8], but the systems considered are required to be precisely known, i.e., no uncertainties/unknowns exist in the systems.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive stabilization for a class of coupled PDE-ODE systems with multiple unknown parameters

Liu

2014

Proceedings of the 33rd Chinese Control Conference

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This paper investigates the adaptive stabilization for a class of coupled PDE-ODE systems with multiple unknown parameters. The systems under investigation are more general and representative, due to the presence of multiple unknown parameters and coupling between the sub-systems which makes the conventional methods on this topic ineffective. Motivated by the existing results, a reversible in¿nite-dimensional backstepping transformation with new kernel functions is ¿rst introduced to change the original system into a target system, which makes the control design and performance analysis of the original system quite convenient. Then, by certainty equivalence principle and Lyapunov method, an adaptive stabilizing controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converging to zero.

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“…Proposition 3 For the functions ϕ 1 (·), ϕ 2 (·) and ϕ 3 (·) de¿ned in (11), there exists a positive constant M such that…”

Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive stabilization for a class of coupled PDE-ODE systems with multiple unknown parameters

Liu

2014

Proceedings of the 33rd Chinese Control Conference

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“…However, when applied to a highly nonlinear process, the formulated linear controller always needs to be redesigned in order to fully guarantee the stability of the whole control system; this often significantly degrades the control performance. To overcome this performance degradation problem, there has been increasing interest in the development of various nonlinear controller design methods by involving input-output (I=O) linearization techniques (Henson and Seborg, 1997;Hassanzadeh et al, 2008;Ranjan and Gomes, 2009;Damour et al, 2011;Panjapornpon et al, 2012). This great emphasis is attributed to the fact that the I=O linearizing techniques provide an advantage of exactly canceling the nonlinear terms of a process model through the use of a state-feedback law.…”

Section: Introductionmentioning

confidence: 98%

A Direct Adaptive Control Strategy for Nonlinear Process Control Using a Shape-Tunable Nonlinear Controller

Chen

2014

Chemical Engineering Communications

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This paper proposes a novel model-based direct adaptive control (DAC) strategy for a class of nonlinear processes whose nominal model is input-output linearizable but may not be accurate enough to represent the actual process. The proposed DAC scheme is composed of two parts: the first is a model based part that makes use of the available process model for a nominal performance, and the second is an adaptive, nonlinear shape-tunable controller (STC) that is used to compensate for the model errors. To update the STC's shape parameters such that the modeling errors can be accommodated adaptively, a simple and effective parameter tuning algorithm is devised. The offset-free control performance and the stability of the resultant nonlinear control system are guaranteed by a Lyapunov-based approach, which involves two distinctive performance indices to relate, respectively, the process output error and a specially designed auxiliary signal. Furthermore, by simply manipulating the output range of the STC, the proposed DAC scheme is further extended to one that is able to handle nonlinear processes in the presence of hard input constraints. The effectiveness and applicability of the proposed DAC control scheme were examined through the regulatory control of a nonlinear, continuous stirred-tank reactor and the temperature trajectory tracking control of an input-constrained batch reactor under the influence of diversified process disturbances. Simulation results reveal that the proposed model-based DAC scheme is superior to a model-based linearizing control strategy, a sliding mode controller, and an intelligent, model-free DAC scheme, especially when faced with significant plant=model mismatch and unanticipated uncertainties.

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“…Partial Differential Equations (PDE) are used to model systems whose state varies not just in time, but also depend on one or more independent variables. For example, PDEs are used to model systems that have deformable structures [1], thermo-fluidic interactions [2], and chemical processes [3], [4]. Furthermore, the states of these PDEs are often vector-valued, representing, e.g.…”

Section: Introductionmentioning

confidence: 99%

Computing Input-Ouput Properties of Coupled Linear PDE systems

Shivakumar

Peet

2019

2019 American Control Conference (ACC)

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In this paper, we propose an LMI-based approach to analyze input-output properties of coupled linear PDE systems. This work expands on a newly developed statespace theory for coupled PDEs and extends the positive-real and bounded-real lemmas to infinite dimensional systems. We show that conditions for passivity and bounded L2 gain can be expressed as linear operator inequalities on R × L2. A method to convert these operator inequalities to LMIs by using parameterization of the operator variables is proposed. This method does not rely on discretization and as such, the properties obtained are prima facie provable. We use numerical examples to demonstrate that the bounds obtained are not conservative in any significant sense and that the bounds are computable on desktop computers for systems consisting of up to 20 coupled PDEs.

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Control of coupled PDEs–ODEs using input–output linearization: Application to a cracking furnace

Cited by 18 publications

References 10 publications

Adaptive stabilization for a class of coupled PDE-ODE systems with multiple unknown parameters

Adaptive stabilization for a class of coupled PDE-ODE systems with multiple unknown parameters

A Direct Adaptive Control Strategy for Nonlinear Process Control Using a Shape-Tunable Nonlinear Controller

Computing Input-Ouput Properties of Coupled Linear PDE systems

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