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Hybrid PID control for transient performance improvement of motion systems with friction

Abstract : We present a novel reset control approach to improve transient performance of a PID-controlled motion system subject to friction. In particular, a reset integrator is applied to circumvent the depletion and refilling process of a linear integrator when the system overshoots the setpoint, thereby significantly reducing settling times. Moreover, robustness for unknown static friction levels is obtained. A hybrid closed-loop system formulation is derived, and stability follows from a discontinuous Lyapunov-like function and a meagre-limsup invariance argument. The working principle of the controller is illustrated by means of a numerical example. I. INTRODUCTION In this paper, we present a reset control approach to improve transient performance of a PID-controlled mechanical motion system subject to friction. Especially in high-precision positioning systems, friction is a performance limiting factor. The presence of Coulomb friction may induce non-zero steady-state positioning errors, and the presence of the velocity-weakening (Stribeck) effect may induce so-called hunting limit cycles [1], [2], which compromises position accuracy as well. In the past decades, many different control approaches have been developed to either compensate for friction, or to achieve high-precision positioning despite the presence of frictional effects. Friction compensation techniques make use of a parametric friction model in the control loop (see, e.g., [1], [3]-[5]) or in a calibration procedure (see, e.g., [6]). Obtaining an accurate friction model is in general a difficult task, since it is challenging to exactly capture the physics associated with friction into a model with limited complexity, suitable for online implementation. Moreover, model mismatches and a changing friction characteristic may lead to over-or undercompensation of friction [3]. Non-model-based control techniques do not aim at friction compensation, but change the effect of friction on the closed-loop system to obtain the desired performance. Examples are impulsive control [7] or dithering-based controllers [8]. A drawback of these control schemes is that the use of impulsive control forces may result in excitation of unmodeled, high-frequency system dynamics. Although several successful applications of the above control approaches have been presented in the literature, linear (loop-shaped) controllers are still applied in the vast majority of industrial motion systems, due to the intuitive design and tuning tools for such controllers, and knowledge and experience of control practitioners. In particular, the classical PID controller is most commonly used for frictional systems, since the integrator action is capable of compensating for unknown static friction by integrating the position error. However, also PID control is prone to performance limitations. In the presence of Coulomb friction, a limitation is the slow convergence and the resulting long settling times [9]. Namely, an integrator action is required to escape a stick phase by building up the control force to overcome the (possibly unknown) static friction. However, if the position overshoots the setpoint, the integrator buffer needs to deplete and refill in order to change sign to overcome the static friction again. This process takes increasingly more time with a decreasing position error, resulting in long settling times. In [10], a controller has been proposed to improve transient performance (besides compensating robustly for the Stribeck effect) by employing a switched PID controller, which resets the integrator state in such a way that a large part of the depletion/refilling process is circumvented. The switching mechanism relies on online identification of the static friction, which requires exact detection of stick-slip transitions. In practice, however, velocity measurement noise and discrete sampling may lead to the inability of detecting zero velocity and thus prevent such exact identification of the static friction, which may lead in turn to small steady-state limit cycling around the setpoint. In this work, we present a novel reset integrator control scheme that does not suffer from the robustness issues described above, while still significantly improving transient performance. Reset integrators have been used to enhance transient performance of linear motion systems, see, e.g., [11]-[16] but, to the best of the authors' knowledge, not of systems with friction (which are inherently nonlinear). The main contributions of this paper are twofold. First, we design a novel reset PID controller for systems with friction that both improves transient performance with respect to a classical PID controller, and induces robust stability with respect to uncertainties in the static friction. Second, we analyse stability of the resulting hybrid closed-loop system exploiting a meagre-limsup invariance argument [17, §8.4].
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R. Beerens, Andrea Bisoffi, Luca Zaccarian, W.P.M.H. P M H Heemels, H. Nijmeijer, et al.. Hybrid PID control for transient performance improvement of motion systems with friction. American Control Conference (ACC 2018), Jun 2018, Milwaukee (WI), United States. pp.539-544, ⟨10.23919/ACC.2018.8431613⟩. ⟨hal-01970887⟩

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