| Title |
Sliding Surface Part Transformed Integral SMCs with Output Prediction Performance for Uncertain MIMO Linear Plants |
| DOI |
https://doi.org/10.5573/ieie.2026.63.6.105 |
| Keywords |
Variable structure system; Sliding mode control; Boundary layer function; Sliding surface part transformation VSS |
| Abstract |
This note presents sliding mode controls(SMCs) for discontinuous and continuous sliding surface part transformation by using the partly transformed integral sliding surface without the reaching phase to determine the output prediction performance for MIMO uncertain linear plants. The research extends the concept proposed in [72] for second order plants to the MIMO version and is an alternative approach to that described in [70] and [71], yet has the same performance. Theoretically discontinuous and practically continuous sliding surface partly transformed variable structure systems(VSSs) are proposed. A partially transformed MIMO version integral sliding surface without the reaching phase is suggested to derive its ideal sliding dynamics from a given initial condition to the origin. By using the solution for the ideal sliding dynamics, the real 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, the modified boundary layer function is used to make continuous approximation of the discontinuous VSS. 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 an inherent property of the VSS is much improved in terms of the practical aspects. A design example and simulation study enables the usefulness of the proposed discontinuous and continuous sliding surface partly transformed VSS controllers to be verified. |