다입출력 불확실 선형 플랜트를 위한 출력 예측 성능을 갖는 슬라이딩 면 변환 적분 슬라이딩 모드 제어

Abstract

In this note, the discontinuous and continuous sliding surface transformation SMCs by using the transformed integral sliding surface without the reaching phase and with the output prediction performance are presented for MIMO uncertain linear plants. Theoretically discontinuous and practically continuous sliding surface transformed VSSs are proposed. The transformed integral sliding surface with the no reaching phase is suggested and its ideal sliding dynamics from a given initial condition to the origin is obtained. By using the solution of the ideal sliding dynamics, the real robust output can be predetermined and predicted. The closed loop exponential stability together with the MIMO existence condition of the sliding mode on the predetermined sliding surface is investigated theoretically for the complete formulation of the MIMO VSS design for the output prediction performance. Another ideal sliding dynamics is given. For practical applications, a continuous approximation of the discontinuous VSS is made by means of the modified boundary layer function. In addition, the closed loop bounded stability together with the MIMO existence condition of the sliding mode by the continuous VSS is analyzed for the entire trajectory. The discontinuity of the control input as the inherent property of the VSS is much improved in view of the practical aspects. Through a design example and simulation studies, the usefulness of the proposed discontinuous and continuous sliding surface transformed VSS controllers is verified.