In this article, an optimized PID controller for a fuel cell is introduced. It should be noted that we did not compute the PID controller's coefficients based on trialand-error method; instead, imperialist competitive algorithms have been considered. At first, the problem will be formulated as an optimization problem and solved by the mentioned algorithm, and optimized results will be obtained for PID coefficients. Then one of the important kinds of fuel cells, called proton exchange membrane fuel cell, is introduced. In order to control the voltage of this fuel cell during the changes in the charges, an optimal controller is introduced, based on the imperialist competitive algorithm. In order to apply this algorithm, the problem is written as an optimization problem which includes objectives and constraints. To achieve the most desirable controller, this algorithm is used for problem solving. Simulations confirm the better performance of proposed PID controller.

Today, the issue of energy is very important for this purpose utilizing energy losses is very important. One of these ways is the use of heat dissipation in thermal systems. many attempts are doing to develop cogeneration systems taking into account cost, safety and environmental issues that gas turbine system of such a system can be noted. One important application of gas turbine cycle because of cycle high temperatures is to use them for hybrid cycle. For this purpose, the solid oxide fuel cell can be used that is very suitable for boiler input due to the high air temperature. In this regard, two different scenarios have been considered. In the first scenario, only the gas turbines cycle is used where the first law efficiency, second law efficiency and exergy destruction of the total cycle are 42.02 %, 50.28 % and 38960 KW, respectively. In this case, the most exergy destruction is related to combustion chamber. In the second scenario, fuel cell gas turbine cycle will be used, where the first law efficiency, second law efficiency and exergy destruction of the total cycle are 46 %, 56.84 % and 810 740 KW, respectively. In this case, the most exergy destruction is related to combustion chamber.