Tuning of a PID controlled gyro by using the bifurcation theory

This paper concerns the control design of a PID controlled gimbals suspension gyro, whose parameters are determined by using bifurcation theory. The non-linear mathematical model of the gyro is deduced by using the nutation theory of gyroscopes. Considering a PID controller with constrained integral action, it is shown that depending on different values of the maximum allowed integral action a Poincaré–Andronov–Hopf bifurcation may appear. The analysis of the stability or instability of this bifurcation, from the first Lyapunov value, gives a procedure to adjust the parameters of the PID controller. The developed control methodology is evaluated through numerical simulations.