Robust structured controllers for piezoelectric microactuators

Abstract

This paper introduces a new control scheme which incorporates the concept of shaping filter together with the use of the ν-gap metric and the robust design of a structured controller. The main motivation in doing this is related to the development of efficient control laws for small size actuators. Designing a structured controller is known to be computationally intractable via the traditional H∞ method. This is mainly due to the non-convexity of the resulting control problem which is of fixed order or structure type. To solve this kind of control problem easily and directly, without using any complicated mathematical manipulations and without using too many "user defined" parameters, we utilize the heuristic Kalman algorithm (HKA) for the resolution of the underlying constrained non-convex optimization problem. The experimental results validate the proposed technique and demonstrate its convenience for the development of fast and precise positioning systems.

Keywords: Heuristic Kalman algorithm; Non-convex optimization problems; Piezoelectric actuators; Shaping filter; Structured controller; Uncertain systems; control.