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.

This paper presents an offset-free nonlinear model predictive controller (NMPC) for linear motor drive system which have been proposed to address the challenges of their rotary counterparts in precision linear motion control. The main challenges associated with the linear motors is that they are more sensitive to disturbances and parameter variations. The frictional force which affects the drive system is nonlinear and discontinuous. Since it is not possible to generate a discontinuous motor force to achieve desired tracking control, a continuous friction model is used to approximate the actual discontinuous friction model. Extant studies [1], [2] proposed predictive control of linear motors but focused on positioning in the meter range. Here, we propose an offset-free NMPC for micro-positioning applications in which the unmodelled nonlinear functions and the external disturbances are modelled as the integrating disturbance state that is estimated using an extended Kalman filter while the inherent robustness of NMPC is relied on to handle the parametric uncertainties. Numerical simulations are used to show the effectiveness of NMPC in controlling the linear drive system for precise motion tracking in the micrometer range.