Non-Identifier-Based Adaptive Speed Control for a Two-Mass Flexible Servo System: Consideration of Stability and Steady State Accuracy

Abstract

High-gain-control belongs to the class of non-identifier-based control concepts which goes without an identification algorithm to control plants with unknown parameter values. Although the simplicity of this strategy is a striking advantage, a nondecreasing gain function is used. This restricts the applicability especially in the context of tracking problems or disturbances. For this reason, Funnel-control was introduced which is a proportional controller with a time-varying gain function. The gain is not monotone and can increase and decrease as well. Due to the proportional behavior, the steady state error cannot be expected to vanish. Theoretically, the error can be forced being arbitrarily small. But due to sensor noise, a large control error must be accepted in general. To obtain steady state accuracy as well as reduced mechanical vibrations, the Funnel-controller is amended by an additional integral control action and by a dynamic feedback. Proofs are given that these extensions are introduced in such a way that the closed loop stability is not endangered.