Application of the state-dependent Riccati equation method in nonlinear control design for inverted pendulum systems

The purpose of this paper is to present the application of the nonlinear control design technique based on state-dependent Riccati equation (SDRE) on the generalized (n-link) inverted pendulum system. All relevant steps of the control design process, which include presenting the system structure, transformation of the system description into a specific equivalent form, and deriving the discrete-time SDRE formulation, are described in detail. The results of the proposed control design technique are demonstrated on a simulation model of the rotary single inverted pendulum system using appropriate blocks and applications from the Simulink block library developed by the authors of the paper. The advantages of a SDRE-based control algorithm over standard linear quadratic optimal control are shown by comparing both methods in simulation experiments which involve stabilization of the pendulum in the unstable upright equilibrium.