Belinskaya

For four-dimensional model describing the helicopter motion along a given horizontal line the problem of automated synthesis of programmed motion is solved. This solution provides a helicopter motion from a given state of rest in the given state of rest. Time to perform the maneuver is not set. The considered helicopter model is a control dynamic system, which is not a flat system. For such systems general approaches to the terminal problem solution are presently unknown. To solve the terminal problem two approaches are applied. The first approach is based on the use of finite symmetry, which converts the initial conditions of the problem in the final conditions. The use of such symmetry can reduce the number of final conditions. The second approach is based on the use of covers and consists in the construction of a special mapping, which for two given dynamic systems surjectively maps the set of solutions of the first system in the set of solutions of the second system. The programmed motion in this case can be found as the solution of two related specifically posed Cauchy problems for these dynamic systems. The resulting programmed control is a piecewise continuous function of time.

 The authors consider an aircraft with four propellers (four-propeller rotorcraft). The propellers are attached to two bars rigidly fastened in the middle. The propellers on different bars are rotated in opposite directions. Changes of tractive forces of the propellers allows to control motion of the rotorcraft. The mathematical model of such an aircraft represents a dynamical system with a 12-dimensional state and 4-dimensional control. Dynamic feedback linearizing this system is constructed in the article. The feedback is used to track given reference trajectories with stability at the stages of take-off and landing. Acceptability of the found control is verified. Results of numerical simulation demonstrate efficiency of the proposed approach.