For a simple unstable linear aeroelastic system of two degrees of freedom, the effects of an linear integrating, differentiating and proportional link on the equilibrium position stability are investigated. The instability of the system under consideration is indicated by means of the negative Glauert criterion. In the course of this study, two automatic control systems were considered which use motion velocity and acceleration as input signals to bring the system to a steady state. We also obtained the boundaries of the stability region, conditions imposed on the gain of the integrating, differentiating and proportional inertia-free link of the PID regulator in accordance to the parameters of the initial system. The parameters found by the method of the Routh-Hurwitz criterion followed by a matrix minor analysis are compared with numerical simulation results. The results obtained can be used in education courses on the stability theory and aeroservoelasticity.