Split-path nonlinear integral control for transient performance improvement

Loon, S.J.L.M. van; Hunnekens, Bram; Heemels, W.P.M.H.; Wouw, Nathan van de; Nijmeijer, Henk

doi:10.1016/j.automatica.2016.01.005

Cited by 16 publications

(22 citation statements)

References 15 publications

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“…However, in many (industrial) applications a static input-output relation does not exist because plant performance is generally related to generic, time-varying steady-state plant behavior. This time-varying plant behavior emerges, for example, in reference tracking or disturbance attenuation problems, which are encountered, for example, in industrial motion systems, such as, pick-and-place systems (van Loon, Hunnekens, Heemels, van de Wouw, & Nijmeijer, 2016), electron microscopes, and wafer scanning systems (Heertjes & Nijmeijer, 2012;Heertjes, Schuurbiers, & Nijmeijer, 2009). Indeed, optimal steadystate plant performance and the corresponding optimal tuning are heavily dependent on the (time-varying) disturbance situation and reference trajectory at hand.…”

Section: Introductionmentioning

confidence: 99%

Extremum-seeking control for optimization of time-varying steady-state responses of nonlinear systems

2020

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Section: Introductionmentioning

confidence: 99%

Extremum-seeking control for optimization of time-varying steady-state responses of nonlinear systems

2020

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“…Radial unboundedness must be checked only in the σ, v and φ components because b, q and τ are bounded in C ∪ D ⊂ Ξ. To this end, nonnegativity of the last two terms in (51) and positive definiteness of…”

Section: A Lipschitz Lyapunov Function For the Simulation Modelmentioning

confidence: 99%

“…Specific examples are the hybrid integrator-gain system [21], [48], improving tracking performance and limiting overshoot. Overshoot reduction of linear systems using hybrid control is also presented, e.g., in [12], [51]. Analysis and design tools for reset controllers are presented in [34], [50] and in the recent overviews [9], [38].…”

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confidence: 99%

Reset PID Design for Motion Systems With Stribeck Friction

Beerens

Bisoffi

Zaccarian

et al. 2022

IEEE Trans. Contr. Syst. Technol.

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We present a reset control approach to achieve setpoint regulation of a motion system with a proportionalintegral-derivative (PID) based controller, subject to Coulomb friction and a velocity-weakening (Stribeck) contribution. While classical PID control results in persistent oscillations (hunting), the proposed reset mechanism induces asymptotic stability of the setpoint, and significant overshoot reduction. Moreover, robustness to an unknown static friction level and an unknown Stribeck contribution is guaranteed. The closed-loop dynamics are formulated in a hybrid systems framework, using a novel hybrid description of the static friction element, and asymptotic stability of the setpoint is proven accordingly. The working principle of the controller is demonstrated experimentally on a motion stage of an electron microscope, showing superior performance over classical PID control. I. INTRODUCTIONFriction is a performance-limiting factor in many highprecision motion systems for which many control techniques exist in the literature. A branch of control solutions relies on developing as-accurate-as-possible friction models, used for online compensation in a control loop, see, e.g., [7], [22], [31], [32]. These model-based friction compensation methods are typically prone to model mismatches due to, e.g., unreliable friction measurements, or time-varying or uncertain friction characteristics. Model-based techniques, therefore, may suffer from over-or undercompensation of friction, thereby resulting in loss of stability of the setpoint [39], and thus limiting the achievable positioning accuracy. Adaptive control methods (see, e.g., [5], [17]) provide some robustness to timevarying friction characteristics, but model mismatches (and the associated performance limitations) still remain. Non-modelbased control schemes have also been proposed, examples of which are impulsive control (see, e.g., [36], [47]), ditheringbased techniques (see, e.g., [29]), sliding-mode control (see, e.g., [10]), or switched control [35]. Apart from properly smoothened and paramterized sliding-mode control solutions (see, e.g., [3]), these non-model-based controllers may employ high-frequency control signals, risking excitation of highfrequency dynamics, in addition to raising tuning challenges.

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“…14 Another recent example also inducing discontinuous output signals is given by the split-path nonlinear integrator. 15 Contrarily, an example that avoids the resets and generates a continuous output signal instead is given by the variable-gain integrator controller. 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.…”

Section: Introductionmentioning

confidence: 99%

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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Split-path nonlinear integral control for transient performance improvement

Cited by 16 publications

References 15 publications

Extremum-seeking control for optimization of time-varying steady-state responses of nonlinear systems

Extremum-seeking control for optimization of time-varying steady-state responses of nonlinear systems

Reset PID Design for Motion Systems With Stribeck Friction

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

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