Robust multivariable control of a binary distillation column

Coppus, G. W. M.; Shah, S.L.; Wood, R. K.

doi:10.1049/ip-d.1983.0037

Cited by 26 publications

(8 citation statements)

References 8 publications

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“…By continuity, (u )" P and so u 3 \ ( P). This contradicts (8). Therefore, we may assume that (u LI ) is unbounded.…”

Section: Proof Of ¹Heorem 33 (A) By Hypothesis There Existsmentioning

confidence: 77%

“…These investigations extend the well-known principle that closing the loop around an exponentially stable, linear, "nite-dimensional, continuous-time, single-input, single-output plant , with transfer function G , compensated by an integral controller with gain k, will result in a stable closed-loop system which achieves asymptotic tracking of arbitrary constant reference signals, provided that the modulus "k" of the integrator gain k is su$ciently small and kG (0)'0 (see References [5}7]). Therefore, if a plant is exponentially stable and if the sign of G (0) is known (this information can be obtained from plant step response data), then the problem of tracking by low-gain integral control reduces to that of tuning the gain parameter k. Such a controller design approach (&tuning regulator theory' [5]) has been successfully applied in process control, see, for example, References [8,9]. Furthermore, the problem of tuning the integrator gain adaptively has been addressed in various papers for "nite-dimensional [1, 10}12] and in"nite-dimensional systems [2,3,13], with input nonlinearities considered in References [2,3,11] and both input and output nonlinearities treated in Reference [1].…”

Section: Introductionmentioning

confidence: 98%

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Discrete‐time low‐gain control of linear systems with input/output nonlinearities

Fliegner

Logemann

Ryan

2001

Intl J Robust & Nonlinear

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SUMMARYDiscrete-time low-gain control strategies are presented for tracking of constant reference signals for "nite-dimensional, discrete-time, power-stable, single-input, single-output, linear systems subject to a globally Lipschitz, non-decreasing input nonlinearity and a locally Lipschitz, non-decreasing, a$nely sectorbounded output nonlinearity (the conditions on the output nonlinearities may be relaxed if the input nonlinearity is bounded). Both non-adaptive and adaptive gain sequences are considered. In particular, it is shown that applying error feedback using a discrete-time &integral' controller ensures asymptotic tracking of constant reference signals, provided that (a) the steady-state gain of the linear part of the plant is positive, (b) the positive gain sequence is ultimately su$ciently small and (c) the reference value is feasible in a very natural sense. The classes of input and output nonlinearities under consideration contain standard nonlinearities important in control engineering such as saturation and deadzone. The discrete-time results are applied in the development of sampled-data low-gain control strategies for "nite-dimensional, continuoustime, exponentially stable, linear systems with input and output nonlinearities.

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“…By continuity, (u )" P and so u 3 \ ( P). This contradicts (8). Therefore, we may assume that (u LI ) is unbounded.…”

Section: Proof Of ¹Heorem 33 (A) By Hypothesis There Existsmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 98%

Discrete‐time low‐gain control of linear systems with input/output nonlinearities

Fliegner

Logemann

Ryan

2001

Intl J Robust & Nonlinear

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“…Using equations (13), (14), (15), (18), and (20) we obtain the following quadratic programming problem…”

Section: Perez and Behdinan 21 Demonstrate That The Psomentioning

confidence: 99%

“…[15][16][17] If this is not the case, the singularity of the matrix F(0) can be referred to as a control singularity at transient state (v ! 0) 11 and most design control methods fail.…”

Section: Proposed Robust Fractional Order Controllermentioning

confidence: 99%

Robust fractional order controller based on improved particle swarm optimization algorithm for the wind turbine equipped with a doubly fed asynchronous machine

Sedraoui

Boudjehem

2012

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this paper, an improvement of the particle swarm optimization algorithm is proposed. The aim of this algorithm is to determine the optimal parameters of a robust fractional order controller which guarantees stability and robustness of required nominal performances. Controllers with fractional order are first obtained by a previous transformation of the multi-objective optimization problem into an equivalent single-optimization problem, and then solved by the proposed improved particle swarm optimization algorithm. In order to examine the stability and performance robustness, this controller is applied on an ill-conditioned wind turbine equipped with a doubly fed asynchronous machine, where the system dynamics is modeled by an unstructured output multiplicative uncertainty model. The simulation results show the effectiveness of the proposed synthesis method, where the control is compared (for the same design frequency-domain specifications) for both the robust fractional order controller such as that designed through the standard particle swarm optimization algorithm and that obtained by resolving the multi-objective optimization problem.

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“…Under the above assumptions on ϕ, and ψ, the problem of tracking feasible constant reference signals r by low-gain integral control reduces to that of appropriately choosing the gain function k. In a purely linear and finite-dimensional context, such a controller design approach ("tuning regulator theory"; see [5,17,21]) is well known and has been successfully applied in process control (see, for example, [3,18]). …”

Section: Introductionmentioning

confidence: 99%

Low-Gain Integral Control of Well-Posed Linear Infinite-Dimensional Systems with Input and Output Nonlinearities

Fliegner

Logemann

Ryan

2001

Journal of Mathematical Analysis and Applications

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Time-varying low-gain integral control strategies are presented for asymptotic tracking of constant reference signals in the context of exponentially stable, wellposed, linear, infinite-dimensional, single-input-single-output, systems-subject to globally Lipschitz, nondecreasing input and output nonlinearities. It is shown that applying error feedback using an integral controller ensures that the tracking error is small in a certain sense, provided that (a) the steady-state gain of the linear part of the system is positive, (b) the reference value r is feasible in an entirely natural sense, and (c) the positive gain function t → k t is ultimately sufficiently small and not of class L 1 . Under a weak restriction on the initial data it is shown that (a), (b), and (c) ensure asymptotic tracking. If, additionally, the impulse response of the linear part of the system is a finite signed Borel measure, the global Lipschitz assumption on the output nonlinearity may be considerably relaxed.

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Robust multivariable control of a binary distillation column

Cited by 26 publications

References 8 publications

Discrete‐time low‐gain control of linear systems with input/output nonlinearities

Discrete‐time low‐gain control of linear systems with input/output nonlinearities

Robust fractional order controller based on improved particle swarm optimization algorithm for the wind turbine equipped with a doubly fed asynchronous machine

Low-Gain Integral Control of Well-Posed Linear Infinite-Dimensional Systems with Input and Output Nonlinearities

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