A novel distributed model predictive control method based on a substructuring technique for smart tensegrity structure vibrations

Abstract

This paper considers distributed model predictive control (DMPC) for the vibrations of smart tensegrity structures with input saturation. A distributed control strategy is necessary to enable the autonomy in the individual subsystems, reduce the computational burden of centralized control, and enhance the fault tolerance of control systems. In this work, the dynamic model for smart tensegrity structures equipped with active piezoelectric actuators is generated first by the finite element method. Then, based on the substructuring technique, the entire tensegrity structure system is decomposed into a series of multilevel subsystems. For each subsystem, the continuous-time predictive model equations are discretized by the explicit form of the Newmark-β algorithm. Finally, based on the parametric variational principle, the DMPC problem with input saturation is transformed into a series of linear complementarity problems. The proposed method provides a simple, unified and flexible multilevel distributed control framework for solving the vibration control problems of smart tensegrity structure systems. Numerical experiments illustrate that the proposed DMPC method is effective and exhibits performance comparable to that of a typical centralized model predictive control (CMPC) method. In addition, the constraints of the control input saturation for the proposed DMPC method can be satisfied.