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The solution to the problem on building mathematical models of technical objects through the approximation of various experimental dependences is offered in the paper. This approach is especially true for modeling aircraft because the aerodynamic coefficients of their models can be obtained either by full-scale study or by computer simulation only. Currently, the experimental simulation is performed either through the regression analysis (RGA) methods, or through spline approximation. However, the RGA has a significant disadvantage, namely a poor approximability of piecewise and multiextremal dependencies. The RGA gives a rough approximation of the experimental data for similar curves. Spline approximation is free from this disadvantage. However, a high degree of discretization, a strict binding to the number of spline points, and a large number of equations, make this approach inconvenient for application when a compact model building and an analytic transformation are required. A problem solution combining the advantages of both approaches and clearing up the troubles is offered in the paper. The proposed approach is based on the regression construction of the mathematical models of the dependence fragments, the multiplicative excision of these fragments in the local functional form, and on the additive combining of these local functions into a single analytic expression. The effect is achieved by using special “selection” functions multiplicatively limiting a nonzero definition domain for each of the approximating functions. The method is named “cut-glue” by the physical analogy of the approximation techniques. The order and structure of the approximating function for each segment can be arbitrary. A significant advantage of the “cut-glue” approximation is in a single analytic expression of the whole piecewise function instead of a cumbersome system of equations. The analytical and numerical studies of the properties and operational experience of the proposed method are resulted.

In this paper we consider one of the problems in the development of control system for the feeder for MAAT transportation system. This problem is connected with estimation of inboard energy requirements. Traditionally such estimation is made on the basis of static relations. They allow assessing the power required to move a solid body with a constant air speed. However a contribution from aerodynamic forces and moments can vary depending on a regime of motion (value of linear and angular accelerations, angle of attack, etc). Because of that fact, this work investigates the estimation of the total required inboard energy and contribution of aerodynamic forces and moments to it in specified feeder motion regimes. The method of assessment is based on the feeder model, which is built on the equations of the rigid body. This paper contains general structure of feeder mathematical model, which includes equations of statics, dynamics and control mechanisms. The example of the exact feeder shape gives the application of this models with the details in terms of aerodynamic characteristics, inertial mass parameters and locations of control mechanisms. Feeder model is complemented by the external environment model, including the wind flow model. Development of the latter models is investigated in the talk ???Probabilistic Approaches to Estimation of Flight Environment for Feeder of Multibody Transport Airship System???, presented on this conference. Three main feeder motion regimes were chosen for the estimation of the required power. These three regimes are hovering in one point, motion along a straight line and motion along a specified circle. Steady motion is considered along with transient regimes, when the feeder is moving to the specified trajectories. The results allow assessing the required power for steady and transient regimes for each considered trajectory, different values of air speed, different locations of centre of gravity and different angles of attack. Additionally, study of Kalman controllability and Lyapunov stability was made for the special feeder motion regimes. The conclusions about the optimal feeder shape are given based on this work

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