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Research Papers

# Apply Robust Proportional Integral Derivative Controller to a Fuel Cell Gas Turbine

[+] Author and Article Information
Tooran Emami

New London, CT 06320
e-mail: Tooran.Emami@uscga.edu

Alex Tsai

New London, CT 06320
e-mail: Alex.Tsai@uscga.edu

David Tucker

United States Department of Energy,
National Energy Technology Laboratory,
Morgantown, WV 26507
e-mail: david.tucker@netl.doe.gov

Manuscript received May 12, 2017; final manuscript received October 17, 2017; published online March 13, 2018. Assoc. Editor: Robert J. Braun. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Electrochem. En. Conv. Stor. 15(2), 021006 (Mar 13, 2018) (11 pages) Paper No: JEECS-17-1048; doi: 10.1115/1.4038635 History: Received May 12, 2017; Revised October 17, 2017

## Abstract

The performance of a 300 kW solid oxide fuel cell gas turbine (SOFC-GT) pilot power plant simulator is evaluated by applying a set of robust proportional-integral-derivative (PID) controllers that satisfy time delay and gain uncertainties of the SOFC-GT system. The actuators are a fuel valve (FV) that models the fuel cell (FC) thermal exhaust, and a cold-air (CA) valve which bypasses airflow rate from the FC cathode. The robust PID controller results for the upper and lower boundary of uncertain gains are presented first, followed by a design for the upper and lower boundary of uncertain time delays process for both, FV and CA bypass valves. The final design incorporates the combined uncertain gain and the time delay modeling for the upper and lower boundary of both actuators. This multiple-input multiple-output technique is beneficial to plants having a wide range of operation and a strong parameter interaction. The practical implementation of the PID controllers and the set point responses are presented through simulation in the matlab/simulink environment.

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## References

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## Figures

Fig. 1

NETL HyPer test facility

Fig. 2

Computer-aided design rendering of HyPer hardware facility

Fig. 3

Fig. 4

The block diagram of controlled multiple-input multiple-output systems

Fig. 5

Step response for the upper bound gains uncertainties in Eq. (25) for turbine speed and FC mass flow rate with the PID controllers Eqs. (23) and (24)

Fig. 6

Step response for the lower bound gain uncertainties in Eq. (25) for speed and FC mass flow rate with the PID controllers Eqs. (23) and (24)

Fig. 7

The results of step responses for upper bound phase uncertainties in Eq. (26) for turbine speed and FC mass flow rate with PID controllers in Eqs. (23) and (24)

Fig. 8

The results of step responses for lower bound phase uncertainties in Eq. (26) for speed and FC mass flow rate with PID controllers in Eqs. (23) and (24)

Fig. 9

Simulation for the gain and phase uncertainties in Eq. (27) for turbine speed and FC mass flow rate with PID controllers in Eqs. (23) and (24)

Fig. 10

Simulation for the gain and phase uncertainties in Eq. (28) for turbine speed and FC mass flow rate with PID controllers in Eqs. (23) and (24)

## Errata

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