| Title |
An Improved Continuous Transformed Integral Sliding Mode Control(ICTISMC) with Prescribed Control Performance for Regulation Controls of Uncertain General Linear Systems |
| DOI |
http://doi.org/10.5370/KIEE.2019.68.6.775 |
| Keywords |
variable structure system ; sliding mode control ; sliding surface transformation ; boundary layer method ; prescribed performance |
| Abstract |
In this paper, an improved continuous transformed integral sliding mode control(ICTISMC) with the prescribed control performance is designed for simple regulation controls of uncertain general linear systems, as an alternative approach of [51] with the same performance. An transformed integral sliding surface with an integral state having a special initial condition is adopted for removing the reaching phase and predetermining the ideal sliding trajectory from a given initial state to the origin in the state space. The ideal sliding dynamics of the transformed integral sliding surface is dynamically obtained and the solution of the ideal sliding dynamics can predetermine the ideal sliding trajectory(transformed integral sliding surface) from the given initial state to the origin. Provided that the value of the transformed integral sliding surface is bounded by certain value by means of the continuous input, the norm of the state error to the ideal sliding trajectory is analyzed and obtained in Theorem 1. A corresponding discontinuous control input with the exponential stability is proposed to generate the perfect sliding mode on the every point of the pre-selected transformed integral sliding surface. The existence condition of the sliding mode together with the closed loop stability is proved in Theorem 2 for the complete formulation. For practical applications, the discontinuity of the VSS control input is approximated to be continuous based on the modified fixed boundary layer method. The bounded stability by the continuous input is investigated in Theorem 3. With combining the results of Theorem 1 and Theorem 3, as the prescribed control performance, the pre specification on the error to the ideal sliding trajectory is possible by means of the fixed boundary layer continuous input with the transformed integral sliding surface. The suggested algorithm with the continuous input can provide the effective method to increase the control accuracy within the boundary layer by means of the increase of the gain. Through an illustrative design example and simulation study, the usefulness of the main results is verified. |