Reducing the Stabilizing Control Order for a Double Inverted Pendulum

The problem of stabilization of an unstable plant by a reduced-order single-channel controller is considered. The possibility of compensating small deviations of a double inverted pendulum on a cart by acting on the cart is studied. An algebraic method for finding the extreme locations of the poles through the construction of root simplexes is proposed. Using this, the Hurwitz stability boundaries for various reduced-order controllers are calculated. It is shown that robust stabilization of the pendulum system in the class of reduced-order controllers is impossible.. Keywords: automatic control system, reduced-order controller, double inverted pendulum, Hurwitz stability, multiple poles.