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Technical Brief

# Development of a Cross-Coupled Robust Controller for a Multi-Axis Micromachining System

[+] Author and Article Information
Mumtazcan Karagoz

Department of Mechanical Engineering,
Bilkent University,
Ankara 06800, Turkey
e-mail: mumtazcan.karagoz@bilkent.edu.tr

Melih Cakmakci

Mem. ASME
Department of Mechanical Engineering,
Bilkent University,
Ankara 06800, Turkey
e-mail: melihc@bilkent.edu.tr

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received September 4, 2017; final manuscript received May 24, 2018; published online July 2, 2018. Assoc. Editor: Yang Shi.

J. Dyn. Sys., Meas., Control 140(12), 124501 (Jul 02, 2018) (8 pages) Paper No: DS-17-1442; doi: 10.1115/1.4040443 History: Received September 04, 2017; Revised May 24, 2018

## Abstract

In the current era of miniaturization for complex, ubiquitous, and energy efficient systems, micromanufacturing had become one of the most popular fields for engineering development. This paper introduces a modular robust cross-coupled controller design structure applied to a three axis micromachining system that can be extended to more axis systems and configurations. In order to develop a robust controller that can withstand the disturbances due to tool–workpiece interactions, a dynamic model of the whole system is needed. Developing control-oriented models for micromachining systems can be challenging. Using the sum of sines identification input, essential nonlinearities including the effects of assembly and slider orientation are included. Verification data show that these transfer function models represent the physical system satisfactorily while avoiding an over-fit. Using the transfer functions from the identified model, a controller structure with robust axis controllers with cross-coupled control (CCC) are developed and fine-tuned with simulations. Machining experiments are also done in order to compare the performance of the proportional-integral-derivative control design, an adaptive robust controller (ARC, both from earlier work in the literature) and the new $H∞$ robust controller. According to results of experiments, the new robust controller showed the best tracking and contouring performance with improved surface quality due to reduced oscillations.

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## Figures

Fig. 1

Micromachining using a three axis orthogonal positioning system

Fig. 2

Contour error versus tracking error

Fig. 3

(a) Identification and (b) verification Inputs

Fig. 4

Response in time domain: (a) identification and (b) verification

Fig. 5

Block diagram of the controller structure used with the micromachining system

Fig. 6

(a) Desired square profile, (b) Z-axis, (c) X-axis, and (d) Y-axis motion profiles

Fig. 7

Optical microscope images cut samples: (a) PID-CC controller and (b) H-CC controller

## Errata

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