MATRICES OF ERROR COEFFICIENTS OF UAVS’ CONTROL SYSTEMS WITH PID-REGULATORS

Abstract

Multirotor unmanned aerial vehicles (UAVs) are currently widely used in various military and civilian areas, including rescue work, traffic monitoring, identifying fires in forests, monitoring the technical condition of buildings, roads and railways,  agricultural work and geological research, and many others.

A large number of works are devoted to the development of control systems of UAVs. However, in these works, the main emphasis is put on ensuring  the systems’ stability based on modern methods of feedback control theory, including adaptive and optimal control, fuzzy logic control, robust control, etc. At the same time, relatively little attention is paid to various aspects of the study of dynamic accuracy of UAV control systems under various external controlling and disturbing influences, which are both deterministic and random. Particularly important in this case are the issues of studying the accuracy of UAVs with possible partial losses of motor efficiency. The fact is that the indicated loss of efficiency leads to the fact that independent, in the ideal case, control channels of roll, pitch, yaw angles, as well as the flight altitude control channel become interconnected. Therefore, in this case, the analysis of dynamic accuracy of the UAV control systems should be carried out based on the methods of the theory of multivariable feedback control.

Analytical formulas for matrices of error coefficients of multirotor UAVs with PID regulators are derived in the paper. The obtained expressions allow investigating the accuracy of the UAVs’ control systems with partial loss of the motor efficiency, subjected to deterministic external reference signals given in the form of power polynomials. A numerical example of calculation of matrices of error coefficients for quadcopters is presented.