Implementation of H-Infinity Control Algorithms for Sensor-Constrained Mechatronic Systems Using Low-Cost Microcontrollers

Abstract

This paper introduces a novel method which is intended to assist in the design and implementation of optimal H-infinity ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> ) algorithms in low-cost mechatronic applications. The particular problem considered is position control in a situation where there are both sensor-related uncertainties (caused by low-resolution sensors) and limited computational resources. The first part of the method presented in this paper describes how to design the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> algorithm based on dynamic features of the sensor. The second part of the method involves finding a suitable numerical controller representation in order to reduce memory and CPU load. Evaluation of the method is based on empirical studies using three industrial sensors employed in a sub-acted robot. Results for a classic proportional integral derivative (PID) controller are included, in order to provide comparisons with the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> approach. In the empirical evaluation, the PID implementation shows marginal stability when the low-resolution sensor is employed; by contrast, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> implementation is found to remain stable in the same circumstances.