The simplest aeroautoelastic model with three degrees of freedom was used to examine the influence of the integrating, differentiating and proportional inertia-free link on the aeroelastic characteristics of the system. The parameters found and the corresponding roots of the characteristic equation were compared with numerical results obtained using the method of evaluating the effect of design parameters of an automatic control system on the stability of an elastic aircraft in the flow. Findings of the research show that for the stable operation of the automatic control system, it is necessary to use the speed of the first mass as an input signal. In this case, the constraints for the studied parameters of the dynamical system were determined. The study of the dependence of the natural frequencies of the dynamic system on the value of the parameters showed that the characteristic equation has three pairs of complex conjugate roots. Changing the gain leads to a monotonous increase in the modules of the real and imaginary parts of the first natural frequency. For the second and third natural frequencies, the negative real part of the root has a minimum at which the best control mode is implemented. According to the results of calculations in the considered example, it is recommended to set a large gain of the integral link and a small gain of the differential link.