A Fuzzy Adaptive PID Controller Design for Fuel Cell Power Plant
Abstract
:1. Introduction
2. SOFC Model Description
2.1. Operation Principle of SOFC
- Reaction on the anode:
- Reaction on the cathode:
- Overall reaction:
2.2. Model Description
2.3. Problem Description
- Nonlinearity of the System: owning to Nerst’s equation in (4), the SOFC system is characterized as nonlinearity [26], and this deteriorates the control performance of the controller when the working conditions drift off from the ideal working conditions.
- Fuel Flow is Restricted: fuel flow must be restricted between 0 and 2 mol/s, which may cause actuator saturation and the dynamic property may be deteriorated.
- Hysteresis of the System: the rated voltage and the current load change rapidly, while the effect of the fuel flow on the output voltage is comparatively slow.
3. System Identification and Controller Tuning
3.1. System Identification
3.2. Controller Tuning
4. Fuzzy Control Design
4.1. Fuzzy PI Controller
4.1.1. Fuzzification
4.1.2. Fuzzy Logic Judgment
4.1.3. Defuzzification
4.2. The Realization of Anti-Windup
4.3. Differential Forward Algorithm
5. Simulation
5.1. Simulation of Step Response
5.2. Simulation of Disturbance Response
5.3. Discussion
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Parameter | Representation | Value | Parameter | Representation | Value |
---|---|---|---|---|---|
Reaction constant | 0.993 × 10−3 mol/(s A) | Activation energy | 120 kJ/mol | ||
Valve molar constant for hydrogen | 0.843 mol/(s atm) | Pre exponential factor | 101.2 kA/cm2 | ||
Valve molar constant for steam | 0.281 mol/(s atm) | Ohmic resistance constant | 0.2 Ω | ||
Valve molar constant for oxygen | 2.52 mol/(s atm) | Ohmic resistance constant | −2870 K | ||
Response time for hydrogen flow | 26.1 s | Constant temperature | 973 K | ||
Response time for steam flow | 78.3 s | Efficiency | 0.8 | ||
Response time for oxygen flow | 2.91 s | Thickness | 10−3 m | ||
Fuel processor response time | 5 s | Thermal conductivity | 2 W/(m K) | ||
Faraday’s constant | 96,486 C/mol | Relaxation time | 200 s | ||
Gas constant | 8.31 J/(mol K) | Density | 6600 kg/m3 | ||
Ideal standard potential | 1.1 V | Heat capacity | 400 J/(kg K) | ||
Number of cells in stack | 384 | Initial temperature | 1273 K |
Group | Kp | Ki | Kd | Overshoot (%) | Settling Time (s) |
---|---|---|---|---|---|
1 | 0.0722 | 0.0072 | 0.1358 | 6.63 | 26.5 |
2 | 0.1152 | 0.0145 | 0.2182 | 7.62 | 19.51 |
3 | 0.2354 | 0.0339 | 0.3628 | 9.55 | 13.64 |
4 | 0.3022 | 0.0459 | 0.4434 | 9.85 | 8.81 |
5 | 0.5259 | 0.0824 | 0.6488 | 10.72 | 5.54 |
6 | 0.6666 | 0.1152 | 0.7475 | 11.71 | 4.82 |
Kp1/Ki1 | ec | NB | NM | NS | ZO | PS | PM | PB |
---|---|---|---|---|---|---|---|---|
e | ||||||||
NB | PB/NB | PB/NB | PM/NM | PM/NM | PS/NS | ZO/ZO | ZO/ZO | |
NM | PB/NB | PB/NB | PM/NM | PS/NS | PS/NS | ZO/ZO | NS/ZO | |
NS | PM/NB | PM/NM | PM/NS | PS/NS | ZO/ZO | NS/PS | NS/PS | |
ZO | PM/NM | PM/NM | PS/NS | ZO/ZO | NS/PS | NM/PM | NM/PM | |
PS | PS/NM | PS/NS | ZO/ZO | NS/PS | NS/PS | NM/PM | NM/PB | |
PM | PS/ZO | ZO/ZO | NS/PS | NM/PS | NM/PM | NM/PB | NB/PB | |
PB | ZO/ZO | ZO/ZO | NM/PS | NM/PM | NM/PM | NB/PB | NB/PB |
Conventional PID | Fuzzy PID | ||||||
---|---|---|---|---|---|---|---|
Number | Overshoot (%) | Settling Time (s) | Saturation Time (s) | Number | Overshoot (%) | Settling Time (s) | Saturation Time (s) |
1 | 0.56 | 30.85 | 1.58 | 1 | 0 | 9.28 | 0.53 |
2 | 0.66 | 34.72 | 3.10 | 2 | 0 | 10.41 | 2.29 |
3 | 0.83 | 42.91 | 7.62 | 3 | 0 | 12.23 | 6.71 |
4 | 1.68 | 78.53 | 38.55 | 4 | 0 | 22.21 | 20.04 |
5 | −2.09 | 62.78 | 9.63 | 5 | 0 | 18.52 | 8.62 |
6 | −2.26 | 57.91 | 6.72 | 6 | 0 | 20.56 | 4.68 |
Conventional PID | Fuzzy PID | ||||||
---|---|---|---|---|---|---|---|
Number | Overshoot (%) | Settling Time (s) | Saturation Time (s) | Number | Overshoot (%) | Settling Time (s) | Saturation Time (s) |
1 | 0.33 | 23.28 | 1.51 | 1 | 0 | 12.14 | 1.13 |
2 | 0.43 | 26.02 | 2.61 | 2 | 0 | 12.71 | 2.98 |
3 | 0.59 | 30.29 | 5.23 | 3 | 0 | 13.07 | 5.09 |
4 | 0.82 | 34.31 | 12.94 | 4 | 0 | 15.13 | 9.87 |
5 | −0.79 | 37.63 | 5.03 | 5 | 0 | 13.67 | 5.47 |
6 | −1.11 | 39.42 | 5.65 | 6 | 0 | 14.45 | 5.32 |
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Qin, Y.; Sun, L.; Hua, Q.; Liu, P. A Fuzzy Adaptive PID Controller Design for Fuel Cell Power Plant. Sustainability 2018, 10, 2438. https://doi.org/10.3390/su10072438
Qin Y, Sun L, Hua Q, Liu P. A Fuzzy Adaptive PID Controller Design for Fuel Cell Power Plant. Sustainability. 2018; 10(7):2438. https://doi.org/10.3390/su10072438
Chicago/Turabian StyleQin, Yuxiao, Li Sun, Qingsong Hua, and Ping Liu. 2018. "A Fuzzy Adaptive PID Controller Design for Fuel Cell Power Plant" Sustainability 10, no. 7: 2438. https://doi.org/10.3390/su10072438