Nonlinear model predictive acceleration synchronization technique for rigid-model-based tracking control of multi-DOF flexible systems

Abstract

In this paper, the problem of stabilization and tracking control of uncertain flexible multivariable continuum mechanism systems with additional appendage considering boundedness of undesired vibrational effects are investigated. It is proposed that rather than controlling the entire dynamical system through installation of additional actuators on appendage, it is more desirable to stabilize the core system while considering undesired vibrational effect in the appendage as optimization cost. To this end, the nonlinear programming problem corresponding to a predictive control scheme is presented based on a cost defined according to magnitude of accelerations of undesired vibrations in the appendage. Stabilization of control algorithm is conducted based on demonstration of existence of feasible Lyapunov functions. Candidate Lyapunov functions are defined based on sliding functions analysis. The associated sliding functions are defined for core subsystems which correspond to degrees of freedom of dynamical system that are associated with reference signals. Undesired vibrations caused by other degrees of freedom corresponding to appendage are considered as segments of control cost in the optimization problem. To ensure the feasibility of control model in real-time applications, the control algorithm is obtained in discrete-time basis. Based on investigation of monotonically decreasing Lyapunov functions and expression of sliding functions as a combination of dynamical terms, reference inputs and control input terms, stabilizing constraints of closed-loop system are calculated. Similarly, based on combination of sliding surfaces with considered control and vibrational constraints, additional constraints for boundedness of vibrational terms in nonlinear programming problem are obtained. Numerical comparisons with a sliding control algorithm for core mechanical system and a reaching law method indicate improvements regarding reduction of undesired vibrational effects in appendage. Furthermore, regulation of appendage dynamics is conducted without installation of additional actuators, which reduces the implementation cost in comparison with a full-control scheme for core system and appendage.