An approach to the LQG/LTR design problem with specifications for finite-dimensional SISO control systems

TL;DR

This paper presents a practical approach for designing LQG/LTR controllers for SISO systems that incorporates specific frequency domain specifications using weighting augmentation, demonstrated through a geared DC motor example.

Contribution

It introduces a weighting augmentation method to embed frequency specifications into the LTR framework for LQG controller design, aiding practitioners.

Findings

Effective incorporation of frequency specifications into LQG/LTR design.

Successful application to torque control of a geared DC motor.

Enhanced control performance with robustness considerations.

Abstract

This is an expository paper which discusses an approach to the LQG/LTR design problem for finite-dimensional SISO control systems. The approach is based on the utilisation of weighting augmentation for incorporating design specifications into the framework of the LTR technique for LQG compensator design. The LQG compensator is to simultaneously meet given analytical low- and high-frequency design specifications expressed in terms of desirable sensitivity and controller noise sensitivity functions. The paper is aimed at nonspecialists and, in particular, practitioners in finite-dimensional LQG theory interested in the design of feedback compensators for closed-loop performance and robustness shaping of SISO control systems in realistic situations. The proposed approach is illustrated by a detailed numerical example: the torque control of a geared DC motor with an elastically mounted output shaft.