Modelling and Offset-free Predictive Control of the Parallel-Type Double Inverted Pendulum

This paper presents a nonlinear model of the parallel-type double inverted pendulum system with an elastic spring that produces opposing torques on the pendulums. The effects of solid and viscous frictional forces are considered in the developed model. The stabilising control of the nonlinear system is investigated by designing an offset-free model predictive control (OfMPC) scheme based on the linearised model. The use of OfMPC makes it possible to optimize the system performance while also ensuring that the physical limits of the system are not exceeded. Numerical simulation is used to show the effectiveness and prospective benefits of using the proposed controller over the conventional method.