Pole-placement design with adjustable robustness using sliding-mode technique

A pole-placement design with adjustable performance robustness is proposed in this paper, in which the effect of parameter uncertainties and external disturbances on system performance can be arbitrarily attenuated to cluster all closed-loop eigenvalues within specified regions in the complex plane. Due to parameter uncertainties or variations in a real system, closed-loop eigenvalues through linear state feedback are perturbed away from desired ones, and would not be retained within specified regions in the complex plane. In conventional sliding-mode control, the system constrained in a sliding mode is completely insensitive to system perturbations satisfying the matching condition. However, this invariance property of a sliding mode almost always brings undersirable chatter phenomenon. In this paper, the proposed scheme using the sliding-mode technique is designed to attenuate the effect of uncertainties to an acceptable extent, instead of being completely insensitive. One advantage of this design over the conventional sliding-mode control is the reduction of chatter level, chatter alleviation. Moreover, the sliding mode in this design exists during an entire response, while in the conventional sliding-mode control there exists a reaching phase before the existence of a sliding mode and no invariance property is guaranteed during this phase.