Reset PID Design for Motion Systems With Stribeck Friction

Abstract

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.

Friction force estimation in pneumatic cylinders by full automation of experimental procedures

“…The friction models for sliding mechanical elements in the literature can be divided into two as classical (standard) or complex (dynamic) friction models (Odabaş and Morgül, 2020). Friction models such as Coulomb (Guo et al, 2013), Coulomb-viscous (Yerlikaya and Balkan, 2018), and Stribeck (Beerens et al, 2022) are the standard models, whereas LuGre (Mashayekhi et al, 2022), modified LuGre (Saha et al, 2016), and Dahl (Piatkowski, 2014) are the dynamic friction models. Further detail about friction models was given by Keck et al (2017) and Liang et al (2012).…”