Design of hybrid resetting pid and lag controllers with application to motion control

Abstract

In this paper, new designs for hybrid PID and lag controllers with state resetting are presented. Lyapunov stable designs are shown for first and second order plants, which in case of integral reset for first order plants reduces to that of a Clegg integrator but differs from the First Order Reset Elements (FORE)'s commonly used in the literature for nonintegral lag controllers. Furthermore, the proposed PID and lag designs utilize different resetting conditions especially for second order plants, which is an important class of systems for motion control. Different solutions to retain a linear integrator's steady-state disturbance rejection capability are presented. Simulations and experiments for motion control of a typical servo motor driven positioning stage show the performance benefits of these hybrid controllers and verify the analysis.

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

“…By building upon a well-known control strategy embraced by the industry, we aim at reducing the threshold for control engineers to use a nonlinear control technique in an industrial environment. Inspired by the Clegg integrator (Clegg, 1958) and the First Order Reset Element (Horowitz & Rosenbaum, 1975), reset controllers have been used to increase performance in (linear) motion control applications (see, e.g., Aangenent, Witvoet, Heemels, van de Molengraft, & Steinbuch, 2010;Deenen, Heertjes, Heemels, & Nijmeijer, 2017;El Rifai & El Rifai, 2009;van Loon, Hunnekens, Heemels, van de Wouw, & Nijmeijer, 2016;Zaccarian, 2011 andvan Loon, Gruntjens, Heertjes, van de Wouw, &Nešić, Zaccarian, & Teel, 2008 for corresponding analysis tools), or disturbance attenuation (see Zhao & Wang, 2016). To the best of the authors' knowledge, however, reset integrators have not yet been applied to improve settling performance of nonlinear systems with friction.…”

Generalized Clegg integrator for integral feedback control systems

“…3 Another modified reset law cleared an integral state variable whenever the integrator’s input and output had opposite signs. 5 In contrast to the previous reset control whose reset instants depended on the feedback signal, the reset law proposed by Guo et al 6 prespecified reset times. Despite these fruitful results, one missing element is a concrete formulation connecting the CI with the LI.…”