Table 7 Chronological summary of FTC

PFTC

Li [108]

1. Air or fuel flow rate;

2. Temperature.

Burner independent controller and fuel fault-tolerant controller.

N. P.

Ensure safe temperature;

High level of fuel utilization maintained.

Experimental model of 5kW SOFC system.

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AFTC

Sun [109, 110]

1. Air or fuel flow rate;

2. Temperature.

Observer based feedback controller.

N. P.

Improve system stability.

Experimental.

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Wu [111]

1. Power;

2. Air excess ratio;

2. Temperature.

Controller:

\(u={K}_{\mathrm{P}}\left(y-{y}_{\mathrm{ref}}\right)+{K}_{\mathrm{I}}\int \left(y-{y}_{\mathrm{ref}}\right)\mathrm{d}t+{K}_{\mathrm{D}}\frac{\mathrm{d}}{\mathrm{d}t}\left(y-{y}_{\mathrm{ref}}\right)\)

\(u\): manipulated variables;

y: controlled variables;

\({K}_{\mathrm{P}}\): proportional gains;

\({K}_{\mathrm{I}}\): integral gains;

\({K}_{\mathrm{D}}\): derivation gains;

\({y}_{\mathrm{ref}}\): reference value.

Achieve high efficiency and low unit cost.

Experimental.

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Wu [112]

1. Air or fuel flow rate.

Cost functions:

\({J}_{1q}\left(k\right)=\frac{1}{2}\sum_{p=0}^{{N}_{\mathrm{p}}}{({T}_{\mathrm{r}}\left(k+p\right)-{T}_{q}(k+p))}^{2}+\frac{1}{2}\sum_{p=0}^{{N}_{\mathrm{p}}}{({V}_{\mathrm{r}}\left(k+p\right)-{V}_{q}(k+p))}^{2}+\frac{{\lambda }_{1}}{2}\sum_{p=0}^{{N}_{\mathrm{p}}-1}{({W}_{\mathrm{f}q}\left(k+p\right)-{W}_{\mathrm{f}q}(k+p-1))}^{2}\)

\({J}_{2q}\left(k\right)=\frac{1}{2}\sum_{p=0}^{{N}_{\mathrm{p}}}{({T}_{\mathrm{r}}\left(k+p\right)-{T}_{q}(k+p))}^{2}+\frac{1}{2}\sum_{p=0}^{{N}_{\mathrm{p}}}{({V}_{\mathrm{r}}\left(k+p\right)-{V}_{q}(k+p))}^{2}+\frac{{\lambda }_{2}}{2}\sum_{p=0}^{{N}_{\mathrm{p}}-1}{({W}_{\mathrm{a}q}\left(k+p\right)-{W}_{\mathrm{a}q}(k+p-1))}^{2}\)

\({\lambda }_{1}\) and \({\lambda }_{2}\): control weighting factors;

\({V}_{\mathrm{r}}\) and \({T}_{\mathrm{r}}\): reference trajectories;

\({T}_{q}\) and \({V}_{q}\): predicted values;

\({N}_{\mathrm{p}}\): prediction horizon.

Improve system operation efficiency; Extended service life.

Experimental.

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Xue [113]

1. Air or fuel flow rate;

2. Power.

Fuzzy controller with four different input signals.

N. P.

Solve the problem of combustion chamber temperature fluctuation.

A kW scale SOFC power generation system with reforming unit.

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