Hybrid integrator design for enhanced tracking in motion control

Deenen, D.A.; Heertjes, Marcel; Heemels, W.P.M.H.; Nijmeijer, Henk

doi:10.23919/acc.2017.7963385

Cited by 34 publications

(27 citation statements)

References 19 publications

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“…It can be concluded that continuous switching between gain and integrator mode is required to access the full (phase) potential of the HIGS. In terms of sensitivity peaking, Figure 16 shows the magnitude of the frequency response data of  e ( ) in (6) and  e ( ) in (17). Observe that the design with the HIGS meets the sensitivity requirements but with a significant improvement in low-frequency (below 200 Hz) disturbance suppression as compared with the BLS.…”

Section: Figure 12mentioning

confidence: 99%

“…with state x h ∈ R; input e ∈ R with corresponding time derivativėe ∈ R; control output u ∈ R; parameters h ∈ [0, ∞) and k h ∈ (0, ∞] representing the integrator frequency and gain value, respectively; and with  1 and  2 denoting the regions where the different subsystems are active. 17 To have well-posed dynamics, the input signal e is assumed to be continuous and piecewise differentiable. Moreover, the initial condition is assumed to be zero, ie, x h (0) = 0.…”

Section: Hybrid Integrator-gain Systemmentioning

confidence: 99%

“…See the work of Deenen et al 17 for a more detailed sketch of the proof, which is based on the circle criterion and which follows similar steps as outlined in the work of van Loon et al 18 The execution, however, differs, because  in (7) is structurally different from the reset element used in the work of the aforementioned author. 18…”

Section: The Sensitivity Function  E ( ) Is Hurwitz (All Poles Are Lmentioning

confidence: 99%

“…16 To exploit the hinted phase advantages of the Clegg integrator regarding closed-loop sensitivity peaking, but at the same time not compromise the time-domain performance properties that deteriorate by state resets, the hybrid integrator-gain system (HIGS) has recently been developed. 17 The HIGS is characterized by its ability to continuously switch between an integrator mode and a gain mode. The mode-switching functionality and resulting continuous (nonsmooth) behavior give access to, on the one hand, improved low-frequency disturbance rejection properties, while, on the other hand, avoiding high-frequency amplification and undesired overshoot and settling effects.…”

Section: Introductionmentioning

confidence: 99%

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Robust control and data‐driven tuning of a hybrid integrator‐gain system with applications to wafer scanners

Heertjes

Perdiguero

Deenen

2018

Adaptive Control & Signal

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A hybrid integrator-gain system is discussed that aims for improved low-frequency disturbance rejection, while, at the same time, does not deteriorate overshoot and settling times when compared with a linear integrator. The hybrid integrator has similar phase advantages as the well-known Clegg integrator but without inducing the discontinuous behavior resulting from resetting system state values. Optimal tuning of the controller parameters of the hybrid integrator is strongly influenced by machine-specific properties and therefore favors a data-driven optimization approach. However, as a time-domain optimization algorithm can easily lead to nonrobust solutions in the sense of large peaking of the closed-loop frequency response functions, frequency-domain robustness constraints will be imposed. By means of an adaptive weighting filter design, the parameter updates are penalized upon violation of said robustness constraints. Posed in an unconstrained problem formulation, this is subsequently solved by applying a Gauss-Newton-based parameter update scheme.Closed-loop stability of the linear time-invariant plant and controller in feedback connection with a hybrid integrator-gain system element follows from a circle-criterion-like analysis, which is based on evaluating (measured) frequency response data. Measurement results obtained from an industrial wafer scanner demonstrate the effectiveness of the approach.

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Section: Figure 12mentioning

confidence: 99%

Section: Hybrid Integrator-gain Systemmentioning

confidence: 99%

Section: The Sensitivity Function  E ( ) Is Hurwitz (All Poles Are Lmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust control and data‐driven tuning of a hybrid integrator‐gain system with applications to wafer scanners

Heertjes

Perdiguero

Deenen

2018

Adaptive Control & Signal

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“…Comprehensive overviews of these methods can be found in the monograph [12] and the recent survey paper [70]. Several additional relevant and successful industrial applications of reset control can be found in the literature (see, e.g., [27,52,65,34,84] and references therein). These applications are mostly focused on performance improvement with linear plants.…”

Section: Introductionmentioning

confidence: 99%

To stick or to slip: A reset PID control perspective on positioning systems with friction

Bisoffi

Beerens

Heemels

et al. 2020

Annual Reviews in Control

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We overview a recent research activity where suitable reset actions induce stability and performance of PID-controlled positioning systems suffering from nonlinear frictional effects. With a Coulomb-only effect, PID feedback produces a set of equilibria whose asymptotic (but not exponential) stability can be certified by using a discontinuous Lyapunov-like function. With velocity weakening effects (the so-called Stribeck friction), the set of equilibria becomes unstable with PID feedback and the so-called "hunting phenomenon" (persistent oscillations) is experienced. Resetting laws can be used in both scenarios. With Coulomb friction only, the discontinuous Lyapunov-like function immediately suggests a reset action providing extreme performance improvement, preserving stability and inducing desirable exponential convergence of a relevant subset of the solutions. With Stribeck, a more sophisticated set of logic-based reset rules recovers global asymptotic stability of the set of equilibria, providing an effective solution to the hunting instability. We clarify here the main steps of the Lyapunov-based proofs associated to our reset-enhanced PID controllers. These proofs involve building semiglobal hybrid representations of the solutions in the form of hybrid automata whose logical variables enable transforming the aforementioned discontinuous function into smooth or at least Lipschitz ones. Our theoretical results are illustrated by extensive simulations and experimental validation on an industrial nano-positioning system.

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Reset integral control for improved settling of PID-based motion systems with friction

et al. 2019

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Hybrid integrator design for enhanced tracking in motion control

Cited by 34 publications

References 19 publications

Robust control and data‐driven tuning of a hybrid integrator‐gain system with applications to wafer scanners

Robust control and data‐driven tuning of a hybrid integrator‐gain system with applications to wafer scanners

To stick or to slip: A reset PID control perspective on positioning systems with friction

Reset integral control for improved settling of PID-based motion systems with friction

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