Second-order reset elements for stage control design

Hazeleger, Leroy; Heertjes, Marcel; Nijmeijer, Henk

doi:10.1109/acc.2016.7525315

Cited by 44 publications

(43 citation statements)

References 18 publications

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“…where, ω r is the corner frequency of the filter; β r is the damping coefficient [11] where both states are reset to zero when the reset condition is met. This can be considered as traditional reset control system.…”

Section: Reset Elementsmentioning

confidence: 99%

“Constant in Gain Lead in Phase” Element– Application in Precision Motion Control

Saikumar

Sinha

HosseinNia

2019

IEEE/ASME Trans. Mechatron.

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This work presents a novel 'Constant in gain Lead in phase' (CgLp) element using nonlinear reset technique. PID is the industrial workhorse even to this day in high-tech precision positioning applications. However, Bode's gain phase relationship and waterbed effect fundamentally limit performance of PID and other linear controllers. This paper presents CgLp as a controlled nonlinear element which can be introduced within the framework of PID allowing for wide applicability and overcoming linear control limitations. Design of CgLp with generalized first order reset element (GFORE) and generalized second order reset element (GSORE) (introduced in this work) is presented using describing function analysis. A more detailed analysis of reset elements in frequency domain compared to existing literature is first carried out for this purpose. Finally, CgLp is integrated with PID and tested on one of the DOFs of a planar precision positioning stage. Performance improvement is shown in terms of tracking, steady-state precision and bandwidth.

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Section: Reset Elementsmentioning

confidence: 99%

“Constant in Gain Lead in Phase” Element– Application in Precision Motion Control

Saikumar

Sinha

HosseinNia

2019

IEEE/ASME Trans. Mechatron.

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“…Clegg showed that his integrator benefits from a phase lead with respect to its linear counterpart. This category of controllers, thereafter called reset controllers, has been further developed and more sophisticated elements such as first-order reset element (FORE) in [4,5], generalised FORE (GFORE) in [6] and second-order reset element (SORE) in [7]. These reset elements were used in different capacities such as phase lag reduction, decreasing sensitivity peak, narrowband and broadband phase compensation, control of positioning systems with friction see [8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Fractional-order single state reset element

2021

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This paper proposes a fractional-order reset element whose architecture allows for the suppression of nonlinear effects for a range of frequencies. Suppressing the nonlinear effects of a reset element for the desired frequency range while maintaining it for the rest is beneficial, especially when it is used in the framework of a “Constant in gain, Lead in phase” (CgLp) filter. CgLp is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation—the waterbed effect. The ideal behaviour of such a filter in the frequency domain is unity gain while providing a phase lead for a broad range of frequencies. However, CgLp’s ideal behaviour is based on the describing function, which is a first-order approximation that neglects the effects of the higher-order harmonics in the output of the filter. Although CgLp is fundamentally a nonlinear filter, its nonlinearity is not required for all frequencies. Thus, it is shown in this paper that using the proposed reset element architecture, CgLp gets closer to its ideal behaviour for a range of frequencies, and its performance will be improved accordingly.

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“…The Clegg Integrator (CI) is an integrator which resets its state to zero when its input signal crosses zero. Extensions of the CI, which provide additional design freedom and flexibility, include First Order Reset Elements (FORE) [10], [17], Generalized First Order Reset Element (GFORE) [16], Second Order Reset Elements (SORE) [11], and Generalized Second Order Reset Element (GSORE) [16]. Several reset techniques, such as those based on reset bands [18], [19], fixed reset instants, partial reset (resetting to a non-zero value or resetting a selection of the controller states) [20], and the PI+CI approach [20] have also been studied to improve the performances of these controllers.…”

Section: Introductionmentioning

confidence: 99%

A Frequency-Domain Stability Method for Reset Systems

Dastjerdi

Astolfi

HosseinNia

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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Nowadays, the demand for an alternative to linear PID controllers has increased because of the rising expectations of the high-precision industry. The potential of reset controllers to solve this important challenge has been extensively demonstrated in the literature. However, similarly to other non-linear controllers, the stability analysis for these controllers is complex and relies on parametric models of the systems which may hinder the applicability of these controllers in industry. The well-known H β method tries to solve this significant issue. However, assessing the H β condition in the frequency-domain is complex, especially for high dimensional plants. In addition, it cannot be used to assess UBIBS stability of reset control systems in the case of reseting to non-zero values. These problems have been solved in this paper for the first order reset elements, and an easy-to-use frequency approach for assessing stability of reset control systems is proposed. The effectiveness of the proposed approach is demonstrated through a practical example.

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Second-order reset elements for stage control design

Cited by 44 publications

References 18 publications

“Constant in Gain Lead in Phase” Element– Application in Precision Motion Control

“Constant in Gain Lead in Phase” Element– Application in Precision Motion Control

Fractional-order single state reset element

A Frequency-Domain Stability Method for Reset Systems

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