Control system with two stages using adaptive controller for a serial rotary-type double inverted pendulum

Inverted pendulums are very often used to verify many control theories, because they are typical unstable systems and also are interesting objects. However, few innovative methods with respect to the adaptive control of inverted pendulum (IP) are reported. This paper presents a stabilization method by using the adaptive control for a serial rotary-type double inverted pendulum (SRDIP) whose whole basic parameters are unknown. The control system of a SRDIP is achieved by separating the control mode to two stages. The first stage is an adaptive control mode of the single IP placing the second IP in downward directions and another stage is a LQ control mode of the SRDIP. The control system prepares two kinds of adaptive controllers, which are a variable structure system (VSS) robust adaptive control and a self-tuning control (STC). The rotational angle of the first IP is stabilized by the VSS adaptive control, and the stability of the rotary arm is also achieved by constructing the STC that guarantees the boundary reference angle of the first IP. It is then difficult to construct the STC by only adjustable parameters of the VSS adaptive control system. Whole basic parameters of a SRDIP are estimated by adopting the recursive least squares (RLS) estimation method in order to accomplish both of the STC system and the LQ design of a SRDIP. The RLS algorithm is performed by superposing an available perturbation signal to the adaptive manipulated variable on a limited short interval. The STC system updates a LQ controller based on the QR methods devised for the real time operation. Before completing the first stage, a LQ controller for the SRDIP is obtained through a state space description from the estimated basic parameters. The control law is changed to a LQ control for the SRDIP from an adaptive control mode in the second stage. Finally, it is verified by simulation studies and practical experiments that the proposed system is useful as a control strategy of the SRDIP with an unknown parameter. © 2010 The Institute of Electrical Engineers of Japan.