Background Conventional airship mathematical modeling usually involves six coupled degrees of freedom and two inputs, namely tail and thrust. The current study focuses on aerodynamic modeling. The aerodynamic model is developed in 3D-space based on plane semi-empirical model of a symmetric airship. The model depends on the main geometrical parameters of the airship. The study introduces an optimal shape design of the airship. The objective function is established to reduce drag and the effect of side flow and increases both lift force and pitching moment. Three types of airship shape construction are investigated, namely NPL, GNVR, and Wang. Results MATLAB genetic algorithm toolbox is used to obtain the optimal shape. The population size is 50 and the number of generations is also 50 for NPL, GNVR and Wang shapes at each corresponding angle of attack $$(\alpha =\left[ -20^\circ ,20^\circ \right] )$$ ( α = - 20 ∘ , 20 ∘ ) and side-slip angle $$(\beta =\left[ -20^\circ ,20^\circ \right] )$$ ( β = - 20 ∘ , 20 ∘ ) . The shapes are compared to select the best fit within the operating range. To get the optimal shape, weighted averaging is performed on the optimal solution. Conclusion The GNVR geometric construction technique is the best method to generate the optimum shape of the airship in the presence of side-slip angle effect with the utilized objective function that reduces drag and side flow and increases lift and pitching moment.

Background: A non-linear mathematical model of underactuated airship is derived in this paper based on Euler-Newton approach. The model is linearized with small disturbance theory, producing a linear time varying (LTV)model. The LTV model is utilized to design a linear quadratic tracking (LQT) controller. Two scenarios of LQT are presented in this work according to assumed costates transformations to compute the LQT control law. Results: The LTV model is verified by comparing its output response with the result of the nonlinear model for a given input signal. It shows an acceptable error margin. The verified LTV model is used in designing the LQT controller. The controller is designed to minimize the error between the output and required states response with acceptable control signals using a weighted cost function. Two LQT controllers are presented in this work based on two different transformations used in solving the differential Riccati equation (DRE). These controllers are tested by a sample trajectory to deduce the characteristics of each assumption. Finally, a hybrid LQT controller is used and tested on circular, helical, and bowed trajectories. Conclusion: The first assumption of costates transformation has a good tracking performance, but it is sensitive to the change of trajectory profile. Whereas, the second one overcomes this problem due to considering the trajectory dynamics. Therefore, the first assumption is performed across the whole trajectory tracking except for parts of trajectory profile changes where the second assumption is applied.