Polynomial-method-based SIMO controller design for a double inverted pendulum

In this paper, a state feedback controller is designed via polynomial method for a double inverted pendulum. The polynomial method is first extended into state space. Then based on the equations of motion, the linearized state space model of double inverted pendulum is derived near the upright balance position. The state feedback controller is designed via polynomial method where Ackermann's formula is used to determined the gain matrix. The polynomial-method-based controller design is validated through real experiments. It is shown that the existence of closed-loop zeros in the overall control system imposes limit on the selection of the time constant in polynomial method. In the end, the performance of the controller design is compared with the well-known linear quadratic regulator control. The two controllers share an identical state feedback control configuration, but their design procedures are different. It is found that the two different control methods have a similar performance. However compared with the trial-and-error-based linear quadratic regulator optimal control, polynomial method is much more straightforward in terms of its design procedure due to clear physical meanings of its control parameters.