Stabilization of an Inertia wheel Inverted Pendulum using Model Based Predictive Control

Model Predictive Control (MPC) refers to a specific procedure in controller design, explicitly using the plant model to predict the future output, the control law is computed by solving an optimization problem and receding horizon control is used for control implementation. This paper studies the problem of stabilization of a non-minimum phase inertia wheel inverted pendulum (IWP) having one actuator and two degrees of freedom using Model based predictive Control strategy. Two different schemes of MPC are proposed, to begin with MPC based on Generalized Predictive Control (GPC) is used and then GPC is extended to MPC based on Laguerre functions to reduce the number of terms used to solve the optimization problem. It is shown using simulations that both the control schemes stabilize the IWP system around an unstable equilibrium point and effectively maintain this state. In the basic MPC approach approximation of control signal required a large number of parameters i.e. a high control horizon resulting in increased computational load. Furthermore, the MPC based on Laguerre functions is able to achieve stabilization by using a fraction of terms as compared to GPC. Parametric uncertainties are considered to demonstrate the robustness of MPC control based on Laguerre Functions.