Design of H-infinity Controller for A Linear Spring Connected Double Inverted Pendulum

A modified double inverted pendulum – modified by connecting the mass carrying the pendulum with another mass through a spring makes the general inverted pendulum become a more interesting problem. The system is defined as a linear spring connected double inverted pendulum as proposed by Hou et al. [1],[2]. The system is highly nonlinear and unstable. However, the system can be simplified to a linear control problem through the linearization of a pre-specified equilibrium point such as the upright position of the double pendulum. Therefore, the linearized system allows the designer to apply various techniques of control methods to stabilize the system such as classical PID controller, LQR, etc. Practically, the system is unavoidably affected by an exogenous disturbance. The robust control technique is an appropriate method to deal with this situation. Also, if the energy of the disturbance is bounded, therefore, one can apply the popular robust H infinity control to solve this problem. Then, the H infinity controller is applied to an example of the linear spring connected double pendulum compared with LQR method through simulation.