Table 8 Chronological summary of intelligent control

NNPC

Hajimolana [116]

1. Temperature

\(J\left(k,u\left(k\right)\right)=\sum_{L={M}_{1}}^{{M}_{2}}{({\alpha }_{\mathrm{r}}\left(k+L\right)-{\alpha }_{\mathrm{m}}(k+L))}^{2}+\gamma \sum_{L=1}^{{M}_{u}}{(u(k+L-1))}^{2}\)

\({\alpha }_{\mathrm{r}}\left(k+L\right)\): j-step predictions of the process output;

\({\alpha }_{\mathrm{m}}(k+L)\): reference course;

\(u(k)\): control input;

\({M}_{1}\) and \({M}_{2}\): costing scope;

\(\gamma\): weight of the control signal.

Effectively control the temperature of the cell-tube.

Dynamic model of tubular SOFC.

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NNPC

Hajimolana [117]

1. Temperature

NNPC device adopts seven layer network, the hidden layer adopts sigmoid transfer function, and the output layer adopts linear transfer function.

N. P.

Improve transient response capability.

Dynamic model of tubular SOFC.

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NNPID

Ji [114]

1. Air or fuel flow rate.

Controller:

\({u}_{\mathrm{c}}\left(k\right)=u\left(k-1\right)+{K}_{\mathrm{P}}\cdot {x}_{\mathrm{c}1}\left(k\right){+K}_{\mathrm{I}}\cdot {x}_{\mathrm{c}2}\left(k\right)+{K}_{\mathrm{D}}\cdot {x}_{\mathrm{c}3}\left(k\right)=u\left(k-1\right)+\sum_{l=1}^{3}{K}_{l}(k){x}_{\mathrm{c}l}(k)\)

\({K}_{l}(k)\): parameters of adaptive neural network based PID controller;

Improve operational reliability and safety.

Experimental.

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DHASL-MATD3

Li [118]

1. Air or fuel flow rate.

Target value:

\({y}_{t}^{1}=r\left({s}_{t},{a}_{t}\right)+\gamma \underset{i=\mathrm{1,2}}{\mathrm{min}} {Q}_{{\theta }_{i}^{^{\prime}}}({s}_{t+1},{\pi }_{{\phi }_{1}}({s}_{t+1}))\)

N. P.

Effectively control the output voltage of SOFC system.

Experimental.

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FOPID

Li [119]

1. Air or fuel flow rate.

Reward function:

\(r\left(t\right)=-\left[{\mu }_{1}{e}^{2}\left(t\right)+{\mu }_{2}\sum_{i=1}^{5}\left|{a}_{i}\left(t-1\right)\right|\right]+\chi\)

N. P.

Maintain fuel utilization.

Experimental.

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TGSL-TD3PG

Li [120]

1. Air or fuel flow rate.

Target function of the algorithm:

\(F\left(t\right)={\int }_{0}^{\infty }t{(e(t))}^{2}\mathrm{d}t\)

\(e(t)\): voltage error at time t.

Stable output voltage;

Stable fuel utilization.

Experimental.

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