Low-gain integral control of continuous-time linear systems subject to input and output nonlinearities

Fliegner, T.; Logemann, Hartmut; Ryan, E. P.

doi:10.1016/s0005-1098(02)00238-8

Cited by 38 publications

(36 citation statements)

References 8 publications

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“…However, even for linear systems, closed-loop system stability with an integral control action is only guaranteed with sufficiently small integral gain and under necessary and sufficient conditions on the plant [5], [6]. Particularly, an analytic calculation of the maximum integral gain for guaranteeing closed-loop system stability of finite-dimensional linear systems can be found in [7].…”

mentioning

confidence: 99%

Bounded Integral Control of Input-to-State Practically Stable Nonlinear Systems to Guarantee Closed-Loop Stability

Konstantopoulos

Zhong

Ren

et al. 2016

IEEE Trans. Automat. Contr.

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Abstract-A fundamental problem in control systems theory is that stability is not always guaranteed for a closed-loop system even if the plant is open-loop stable. With the only knowledge of the input-to-state (practical) stability (ISpS) of the plant, in this note, a bounded integral controller (BIC) is proposed which generates a bounded control output independently from the plant parameters and states and guarantees closed-loop system stability in the sense of boundedness. When a given bound is required for the control output, an analytic selection of the BIC parameters is proposed and its performance is investigated using Lyapunov methods, extending the result for locally ISpS plant systems. Additionally, it is shown that the BIC can replace the traditional integral controller (IC) and guarantee asymptotic stability of the desired equilibrium point under certain conditions, with a guaranteed bound for the solution of the closed-loop system. Simulation results of a dc/dc buck-boost power converter system are provided to compare the BIC with the IC operation.

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mentioning

confidence: 99%

Bounded Integral Control of Input-to-State Practically Stable Nonlinear Systems to Guarantee Closed-Loop Stability

Konstantopoulos

Zhong

Ren

et al. 2016

IEEE Trans. Automat. Contr.

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“…Let f3M: a point 31 is said to be a critical point ( and f ( ) is said to be a critical value) of f if f \( )"0.S We denote, by C( f ), the set of critical values of f. The following two lemmas will be used later. The "rst result appeared originally in Reference [3], while a proof of the second lemma may be found in Reference [1].…”

Section: The Class N Of Input/output Nonlinearitiesmentioning

confidence: 99%

“…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]. The purpose of this paper is twofold:…”

Section: Introductionmentioning

confidence: 99%

“…Whilst the structure of the discrete-time analysis in Section 3 below parallels that of the continuous-time analysis in Reference [1], there are several points where these analyses di!er in an essential manner; moreover, the discrete-time low-gain results should be regarded primarily as the main tool in the subsequent derivation, in Section 4, of sampled-data low-gain integral control strategies for a class of continuous-time nonlinear systems which is the main aim of the paper.…”

Section: Introductionmentioning

confidence: 99%

“…In the sampled-data context (ii), our aim is to establish the e$cacy of the control structure in Figure 2, wherein S and H denote standard sampling and hold operations, respectively, and LG represents the (discrete-time) low-gain &integral' controller given by (1), where the gain sequence (k L )L1 > is either prescribed or updated adaptively and the nonlinearities in the input and output channel, and , have the same properties as above.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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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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Low-gain integral control of continuous-time linear systems subject to input and output nonlinearities

Cited by 38 publications

References 8 publications

Bounded Integral Control of Input-to-State Practically Stable Nonlinear Systems to Guarantee Closed-Loop Stability

Bounded Integral Control of Input-to-State Practically Stable Nonlinear Systems to Guarantee Closed-Loop Stability

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

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

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