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

Abstract. This paper presents two approaches to analytical design of nonlinear control systems using transformation of plant equations into quasilinear forms or into

The design problem of control systems for nonlinear plants with differentiated nonlinearity is considered. The urgency of this problem is caused by the big difficulties of practical design of nonlinear control systems with the help of the majority of known methods. In many cases, even provision by these methods of just stability of equilibrium point of a designing system represents a big challenge. Distinctive feature of the method of nonlinear control systems design considered below is the use of the nonlinear plants models represented in a quasilinear form. This form of the nonlinear differential equations exists, if nonlinearities in their right parts are differentiated across all arguments. The quasilinear model of the controlled plant allows reducing the design problem to the solution of an algebraic equations system, which has the unique solution if the plant is controlled according to the controllability condition provided in the article. This condition is similar to the controllability condition of the Kalman’s criterion. Procedure of the nonlinear control systems design on a basis of the plant’s quasilinear models is very simple. Practically, it is close to the known polynomial method of the linear control systems design. The equations of the nonlinear systems designed with application of the plant’s quasilinear models also can be represented in the quasilinear form. The basic result of this article is the proof of the theorem and the corollary from it about conditions of the asymptotical stability at whole of the equilibrium point of the nonlinear control systems designed on a basis of the plant’s quasilinear models. For the proof of the theorem and consequence, the properties of simple matrixes and known theorems of stability of the indignant systems of the differential equations are used. A way of the stability research of the equilibrium point of the quasilinear control systems based on the proved theorem is illustrated by numerical examples. Computer simulation of these systems verifies correctness of the hypoyhesis of the proved theorem. Obtained results allow applying the method of nonlinear systems design on a basis of the quasilinear models for creation of various control systems for plants in power, aviation, space, robotechnical and other industries.

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