In this paper, we introduce a design framework for variable gain integral controllers with the aim to improve transient performance of linear motion systems. In particular, we focus on the well-known tradeoff introduced by integral action, which removes steady-state errors caused by constant external disturbances, but may deteriorate transient performance in terms of increased overshoot. We propose a class of variable gain integral controllers (VGICs), which limits the amount of integral action if the error exceeds a certain threshold, in order to balance this tradeoff in a more desirable manner. The resulting nonlinear controller consists of a loop-shaped linear controller with a variable gain element. The utilization of linear controllers as a basis for the control design appeals to the intuition of motion control engineers therewith enhancing the applicability. For the add-on part of the nonlinear variable gain part of the controller, we propose an optimization strategy, which enables performanceoptimal tuning of the variable gain based on measurement data. The effectiveness of VGIC is demonstrated in practice on a high-precision industrial scanning motion system.
In this paper, one-dimensional self-alignment of a rigid object via stick-slip vibrations is studied. The object is situated on a table, which has a prescribed periodic motion. Friction is exploited as the mechanism to move the object in a desired direction and to stop and self-align the mass at a desired end position with the smallest possible positioning error. In the modeling and analysis of the system, theory of discontinuous dynamical systems is used. Analytic solutions can be derived for a model based on Coulomb friction and an intuitively chosen table acceleration profile, which allows for a classification of different possible types of motion. Local stability and convergence is proven for the solutions of the system, if a constant Coulomb friction coefficient is used. Next, near the desired end position, the Coulomb friction coefficient is increased (e.g. by changing the roughness of the table surface) in order to stop the object. In the transition region from low friction to high friction coefficient, it is shown that, under certain conditions, accumulation of the object to a unique end position occurs. This behavior can be studied analytically and a mapping is given for subsequent stick positions.
In this paper, we introduce the split-path nonlinear integrator (SPANI) as a novel nonlinear filter designed to improve the transient performance of linear systems in terms of overshoot. In particular, this nonlinear controller targets the well-known trade-off induced by integral action, which removes steady-state errors due to constant external disturbances, but deteriorates transient performance in terms of increased overshoot. The rationale behind the proposed SPANI filter is to ensure that the integral action has, at all times, the same sign as the closed-loop error signal, which, as we will show, enables a reduction in overshoot (i.e., improves transient performance). The resulting closed-loop dynamics can be described by a continuous-time switched dynamical system, for which we will provide sufficient conditions for stability. Furthermore, we illustrate the effectiveness, the design and the tuning of the proposed controller in simulation examples.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.