Constant reference tracking for fast linear constrained systems

Abstract

This paper addresses the constant reference tracking problem of linear constrained systems with fast dynamics. Constraints satisfaction and tracking goals are guaranteed by introducing an augmented servo architecture resulting in an analytical closed-form solution. The proposed architecture has been combined with explicit model predictive control (eMPC) method to achieve optimal tracking, constraints satisfaction and piecewise closed form solution simultaneously. The proposed architecture is intuitive and gives a direct insight into the physical system and closed loop feedback properties, and therefore makes it easy to tune and select design parameters in practice. Furthermore, the piecewise closed form solution leads to a computationally efficient controller which enables it to be applicable for fast dynamic systems. The constant reference signal assumption reduces the complexity of the explicit MPC solution considerably. However, it is shown that the present method can be easily applied to applications with finite predefined set-points. Furthermore, in order to cope with non-predefined set-point applications, a convex combination based interpolation is suggested and guaranteed to be feasible under some mild assumptions.