Explicit expression-based practical model predictive control implementation for large-scale structures with multi-input delays

Abstract

In this paper, two practical model predictive control (MPC) implementation algorithms with multi-input delay (NFMPCMID1 and NFMPCMID2) are developed in discrete-time formulation for vibration control of large-scale structures. By introducing a particular augmented state vector, the controlled dynamic equation with multi-input delay is transformed into the standard form without any explicit time delay. Because of no approximation for multi-input delay involved, the system performance and stability are easily guaranteed. In order to solve the computation efficiency and memory requirement for large-scale structure, a novel explicit expression form of Newmark-β method is derived, from which the future states can be easily predicted without computing matrix exponential and its integration. By applying this explicit expression form into MPC, the control input of NFMPCMID1 method can be computed by some matrix–matrix multiplications, and also the control input of NFMPCMID2 method can be computed just by two off-line transient analyses and one on-line transient analysis at every sampling instant on the structure. For no computation of matrix exponential and its integration in NFMPCMID1 and NFMPCMID2 methods, the off-line computation efficiency is greatly improved, and the memory requirement is greatly reduced, especially for the NFMPCMID2 method. In additional, due to the small amount of on-line computation, the on-line computation efficiency is also guaranteed. At last, the stability, feasibility and efficiency of the proposed methods are verified by several typical numerical examples.