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This paper presents LQR sliding surface-based Sliding Mode Controller (LQR–SMC) for balancing control of a Rotary Double Inverted Pendulum (RDIP) system. It is a challenging research topic in control engineering due to its nonlinearity and instability. The RDIP system uses only a motor to control two serially connected pendulums to stand at the upright position. The sliding surface is designed based on the LQR optimal gain. Nonsingular gain matrix is obtained by using the left inverse of the input matrix in the state space form of the system dynamics. The Lyapunov stability theory is used to determine the stability of the controller. To evaluate the performance of LQR–SMC, some performance indices, including the Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE), and the Integrated Square Error (ISE), are used. System stability can be maintained by LQR–SMC under external disturbances as well as model and parameter uncertainties.

Control of rotary double inverted pendulum system using LQR sliding surface based sliding mode controller