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This dissertation presents a methodology for designing membership functions for fuzzy controllers, and application of this methodology to feedwater heater level control. This method, namely the simulated annealing, assumes that the rule base is determined by an expert who is knowledgeable about the process to be controlled. Although this method is applicable to any type of fuzzy controller, max-min center-average fuzzy controllers with triangular and trapezoidal membership functions were used due to the popularity of this combination. This method essentially performs a random search for the parameters of the membership functions that yield the minimum squared error between the plant outputs and their set points for a given test signal as a disturbance. A major dimensionality reduction is accomplished through the identification of some requirements on membership functions. A significant improvement is made in handling membership function constraints that allows the use of every generated solution in the search process. The proposed methodology was applied to a challenging control problem in thermal power plants. This is concerned with the control of individual liquid levels in cascade-arranged feedwater heaters that are currently controlled by individual pneumatic proportional-only controllers. The first three feedwater heaters of a typical fossil plant are analyzed for this purpose. The control system simulation was performed using a model of the feedwater heaters. This model was validated using data from a fossil power plant. The feedwater heater level control problem is very important for avoiding flashing/flooding problems that may cause turbine damage, and for maintaining proper temperatures across the heaters that improves the thermal efficiency of the cycle. The feedwater heater system is nonlinear and highly inter-connected since the drain flow from each heater is cascaded back to the previous heater and the feedwater exiting a heater enters the next heater in the train. The current control systems (individual pneumatic proportional-only drain valves) are not robustly stable. An optimal fuzzy control system was developed for controlling the levels in this system for a typical load following transient. The optimal fuzzy controller was found to improve rise time and settling time, and decrease the level overshoot. Optimal membership functions for the fuzzy controller for various optimization parameters such as initial solutions, initial temperatures, and temperature profiles were evaluated. The selection of these optimization parameters is essential for the success of the algorithm. The final cost and the total number of trials for each case were used to evaluate an appropriate combination of the parameters.