Design of feedforward and feedback controllers by signal processing and convex optimization techniques.

摘要

We present three topics demonstrating the advantages of incorporating signal processing and convex optimization techniques into the design of high performance controllers for, but not limited to, nanofabrication systems.; In “Robust Multi-objective Control by Q-Parameter Design,” we propose a new algorithm called “D-Q iteration” to perform μ-synthesis of robust multi-objective controllers. The traditional D-K iteration for μ-synthesis has several limitations, including sensitivity to the quality of D-step curve fitting, and the hardness of incorporating time domain specifications. We replace the K-step in DKIT with a Q-parameter design step in DQIT with following advantages.; If we approximate H_∞ control by a finite-dimensional Q-design problem at sampled frequencies, there is no need to fit parametric D-scales. Hence, the difficulties of D-step curve fitting are avoided. A numerical example shows significant improvement over DKIT is possible.; Motivated by that many control specifications are convex and readily formulated as Q-design problems, we show an approach to improve standard multi-objective control, where a nominal performance objective is minimized, subject to an unstructured robust stability constraint. If we replace the unstructured RS constraint with its D-scaled version, the nominal performance can be further improved. We also show how to embed nominal Q-design specifications into DQIT. It enables the synthesis of robust performance H_∞ controllers satisfying multiple (including time domain) nominal specifications.; In “Frequency-shaping Feedforward Filter Design,” we improve tracking performances of feedback control systems by adding a feedforward filter that also takes account of the actuator effort. Motivated by the mixed-sensitivity H_∞ feedback control, we propose a design procedure that first computes filter magnitudes at sampled frequencies, and then generates phases by complex cepstrum. It is tested on a nano-positioning system.; In “Adaptive Vibration Control for Nanofabrication Systems,” we investigate how to alleviate vibration problems in nanofabrication systems by using adaptive signal processing techniques. We analyze a simplified dynamical model to capture physical insights into both ground-induced and stage-induced vibration problems. We discuss the effects of physical dynamics on the solution of converged adaptive filters, and hence on the selection of sensors, sampling rates, and adaptation algorithms. Several cases are simulated and discussed to demonstrate its potential.