Input Design for Guaranteed Fault Diagnosis in Inkjet Print-heads

Student: Dhruv Khandelwal

Supervisors: dr. prof. Siep Weiland

dr. Amol Khalate (Océ)

Overview

• Motivation

• System and Problem Description

• Proposed Strategy

• Preliminary result

• Planned Trajectory

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Motivation • Océ designs and manufactures printers for industrial applications

such as: • Large format prints such as architectural plots and advertisement

banners,

• Manuscript printing and publishing houses,

• Printing with non-conventional ink/substrate.

• Performance requirements from printers: o Speed

o Accuracy

o Reliability – To ensure that any occurrence of a fault does not affect the quality of the final product. This is true, for instance, if: • The ink or the print substrate is expensive,

• The print job requires a long time,

• There are strict accuracy requirements.

If a known fault has occurred in a given nozzle, the software can be adapted such that the print-quality is maintained.

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System and Problem Description

• Piezo actuation pulse:

4

System and Problem Description

• Piezo actuation pulse and acoustic residual signal measurement:

5

• Faults - During operation, a print-head may develop several kinds of faults. Some of the commonly seen faults are:

– Deviated nozzle

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• Faults - During operation, a print-head may develop several kinds of faults. Some of the commonly seen faults are:

– Deviated nozzle

– Blocked nozzle

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• Faults - During operation, a print-head may develop several kinds of faults. Some of the commonly seen faults are:

– Deviated nozzle

– Blocked nozzle

– Air bubble in the nozzle

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• System constraints - The particular nature of the system poses some constraints. These are:

– Incomplete input/output data – The print-head design does not permit for data to be collected during actuation of the nozzle.

– Real time constraints – Any diagnostic procedure must be repeated for each of the 256 nozzles of a print-head. A printer may contain 8-24 such print-heads. The detection of faults must be completed in between two passes of the carriage.

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Problem Statement: • Design an auxiliary piezo input that guarantees the detection of

faults inside an inkjet print-head nozzle. • Devise an algorithm for the quick diagnosis of faults.

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• System constraints - The particular nature of the system poses some constraints. These are:

– Incomplete input/output data – The print-head design does not permit for data to be collected during actuation of the nozzle.

– Real time constraints – Any diagnostic procedure must be repeated for each of the 256 nozzles of a print-head. A printer may contain 8-24 such print-heads. The detection of faults must be completed in between two passes of the carriage.

Proposed Strategy

• Input design for guaranteed fault detection – This problem is posed as finding an input that maximizes the norm of error produced between the outputs of the nominal system and the faulty systems.

o For the simplest case of one nominal and one faulty system (without considering any uncertainties), this can be written as:

,)(max arg*#10

1u

uGGu

u

U

where the norm ||. ||# used could be ℋ∞, ℋ2, Hankel norm or the gap metric.

),( 11 sG

),( 00 sG

+

-)(ku )(ke

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• Fault diagnosis – Given the LTI models 𝐺0, … , 𝐺𝑛, and the designed

optimal piezo input, the reachable sets of each of the sets can be computed. A fault can then be successfully diagnosed if the reachable set for the corresponding fault becomes completely disjoint from all other sets at any time instant 𝑘, in the horizon [0, 𝐿𝑦].

This method has a few advantages: o It is possible to compute the time required to guarantee the diagnosis

of a particular fault. o Almost all computation is done offline. Thus, this method should be

well suited for the real time constraints.

0G

1G

2G

1y

2y 1k

0G

1y

2y 2k

2G

1G0G

1y

2y 3k

2G

1G

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Preliminary Result

• We adopt the following framework to describe the system: the input is defined over a finite input horizon −𝐿𝑢, 0 and the output is defined over

a finite output horizon [0, 𝐿𝑦].

0kuLk yLk

k

)(ky

• Designed optimal input, in terms of the hankel norm, for the most simple scenario – one nominal and one faulty system, with no uncertainties:

-1.5 -1 -0.5 0 0.5 1 1.5

x 10-6

-0.2

-0.1

0

0.1

0.2

0.3

Time(s)

Outp

ut

Input

Nominal system response

Faulty system response

104

105

106

107

-70

-60

-50

-40

-30

-20

-10

0

|U(f

)| (

dB

)

FFT of the input

Frequency (Hz)

FFT of the input

Frequency response of the error system

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Planned Trajectory

Design optimal piezo input for the scenario:

1 nominal system and 1 faulty system with no

uncertainties.

Design optimal piezo input for the scenario: 1 nominal system and 1

faulty system with parametric uncertainty.

Design optimal piezo input for the scenario: 1

nominal system and multiple faulty systems

with uncertainties.

Design an algorithm to diagnose faults given a

piezo input (characterize reachable

sets).

Experimentally verify piezo input design and

fault diagnosis.

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THANK YOU.

Questions?

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