Oscillations and transfer properties of relay servo systems—the locus of a perturbed relay system approach

Boiko, Igor

doi:10.1016/j.automatica.2004.11.002

Cited by 103 publications

(89 citation statements)

References 19 publications

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“…Given the definition of S in (26), the effect of the application of (25) to the uncertain system (10b)-(10c) would be the same of applying (36) to system (34), with wnc defined in (37). This proves that the proposed control law (25) drives σ to the origin in minimum time, for the worst-case realization of the disturbance terms.…”

Section: Minimum-time Convergencementioning

confidence: 79%

“…Yet, it is an interesting topic that the reader may deepen making reference to [6], [34]- [37]. Indeed, in systems with chains of integrators and certain dynamics of lag type in series, chattering may exist or not depending on the type of the discontinuous control law (ideal relay or relay with hysteresis) and the effect of parasitic dynamics.…”

Section: A Definition Of the Augmented Systemmentioning

confidence: 99%

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Sliding Mode Control of Constrained Nonlinear Systems

Incremona

Rubagotti

Ferrara

2017

IEEE Trans. Automat. Contr.

169

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Abstract-This technical note introduces the design of sliding mode control algorithms for nonlinear systems in the presence of hard inequality constraints on both control and state variables. Relying on general results on minimum-time higher-order sliding mode for unconstrained systems, a general order control law is formulated to robustly steer the state to the origin, while satisfying all the imposed constraints. Results on minimum-time convergence to the sliding manifold, as well as on the maximization of the domain of attraction, are analytically proved for the first-order and second-order sliding mode cases. A general result is presented regarding the domain of attraction in the general order case, while numerical results on the estimation of the domain of attraction and on minimum-time convergence are discussed for the third-order case, following a procedure applicable to a sliding mode of any order.

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Section: Minimum-time Convergencementioning

confidence: 79%

Section: A Definition Of the Augmented Systemmentioning

confidence: 99%

Sliding Mode Control of Constrained Nonlinear Systems

Incremona

Rubagotti

Ferrara

2017

IEEE Trans. Automat. Contr.

169

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“…This problem is sometimes referred to in the literature as the "transfer properties" analysis of the relay control system (see [5,3]). The "equivalent gain k DF n (see Fig.2)…”

Section: Figure 2 Df-analysis In the Complex Planementioning

confidence: 99%

“…An alternative approach, theoretically exact as it includes the higher harmonics up to a desired order, is going to be described. The "Locus of a Perturbed Relay System" (LPRS) J(ω) associated to the plant transfer function P (s) takes the form (see [5,3])…”

Section: Figure 2 Df-analysis In the Complex Planementioning

confidence: 99%

“…Recently suggested, the "Locus of a Perturbed Relay System" approach (in short LPRS, see [5,3]) offers a simple alternative way to compute the exact frequency value of the self excited oscillation (the same computed by means of the Tsypkin method) while giving additional informations abour the equivalent gain which are not offered by the Tzypkin locus.…”

Section: Introductionmentioning

confidence: 99%

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Analysis and shaping of the self-sustained oscillations in relay controlled fractional-order systems

Caponetto

Maione

Pisano

et al. 2013

fcaa

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This work deals with Single-Input-Single-Output (SISO) fractional order systems with a discontinuous relay control element in the feedback loop. Stable self-sustained oscillations often occur in the closed loop relay system, and this work takes advantage of Describing Function (DF) analysis and of another more accurate approach, called Locus of a Perturbed Relay System (LPRS) method, for analyzing in the frequency domain the characteristics of the limit cycle oscillations. The use of fractional lead compensator is also suggested for the purpose of shaping the characteristics of the limit cycle. The proposed analysis and design procedures will be supported by thoroughly discussed simulation examples.MSC 2010 : Primary 34A08; Secondary 34C25, 93C80, 34A36

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Generating oscillations in inertia wheel pendulum via two‐relay controller

Aguilar

Boiko

Freidovich

2011

Intl J Robust & Nonlinear

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SUMMARYThe problem of generating oscillations of the inertia wheel pendulum is considered. We combine exact feedback linearization with two-relay controller, tuned using frequency-domain tools, such as computing the locus of a perturbed relay system. Explicit expressions for the parameters of the controller in terms of the desired frequency and amplitude are derived. Sufficient conditions for orbital asymptotic stability of the closed-loop system are obtained with the help of the Poincaré map. Performance is validated via experiments. The approach can be easily applied for a minimum phase system, provided the behavior of the states of the zero dynamics is of no concern.

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Oscillations and transfer properties of relay servo systems—the locus of a perturbed relay system approach

Cited by 103 publications

References 19 publications

Sliding Mode Control of Constrained Nonlinear Systems

Sliding Mode Control of Constrained Nonlinear Systems

Analysis and shaping of the self-sustained oscillations in relay controlled fractional-order systems

Generating oscillations in inertia wheel pendulum via two‐relay controller

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