Pole-clustering design with sliding-mode methods for multi-degree-of-freedom systems

This paper proposes a sliding-mode controller design with adaptable pole-clustering capability for linear multiple-input multiple-output systems, in which the influences of parameter uncertainties and external disturbances on the system performance can be arbitrarily lessened to cluster all closed-loop poles within the desired regions in a complex plane. Due to parameter uncertainties or variations in a physical system, the closed-loop poles through linear state feedback might be perturbed away from the required ones and could not be constrained within the specified regions in a complex plane. In established sliding-mode control, system responses during sliding motions are completely invariant to system perturbations satisfying the so-called matching condition. However, this invariance property usually accompanies undesirable chatter phenomenon. In this paper, the proposed sliding-mode controller is designed to decrease the effects of system perturbations to an extent that is acceptable according to performance specifications, instead of being completely insensitive. One advantage of this design over the conventional one is the reduction of chatter level. To be precise, chatter alleviation can be achieved while the sliding mode is guaranteed during an entire response in this design. To verify the scheme, we performed experiments on its implementation in a two-degree-of-freedom magnetic levitation system. The results show that the proposed scheme not only satisfies the requirements for performance robustness but also achieves chatter alleviation.