Second-order terminal sliding mode control of uncertain multivariable systems

Abstract

A second-order terminal sliding mode controller for uncertain multivariable systems is proposed in this paper. The controller adopts the hierarchical control structure. The paper derives the state transform matrices which are used to transform a multivariable linear system to the block controllable form consisting of two subsystems, an input-output subsystem and a stable internal dynamic subsystem. The proposed controller utilizes a non-singular terminal sliding mode manifold for the input-output subsystem to realize fast convergence and better tracking precision. Meanwhile, a chattering-free second-order terminal sliding mode control law is presented. The stability of uncertain multivariable systems can be realized using the proposed controller. A derivative estimator is utilized in the paper to estimate the derivatives of the sliding mode functions for the controller. The simulation results are presented to validate the design method.

Terminal sliding mode observer based parameter estimation method for permanent magnet synchronous motor control system

“…Differentiating V with respect to time, one obtains: For the latter case, that is, e 2 =0 but e 1 ≠0, the state variables of the system will not always stay on the points (e 2 =0, e 1 ≠0) and will continue to cross the axis e 2 =0 in the phase plane 0−e 1 e 2 [22,23].…”

“…(6) and using the equivalent control principle [24] : (23) where the definition of u eq is the same with that in Eqs. (17) and (21).…”

Hybrid Terminal Sliding-Mode Observer Design Method for a Permanent-Magnet Synchronous Motor Control System

“…Once s reaches zero, it will stay at zero, and from (12), i s andi s will converge to zero within finite time. The total time from s(0) = 0 toī s (t s ) = 0 can be calculated as follows [24], [25]:…”

Fuzzy moving fast terminal sliding mode control for robotic manipulators

“…Recently, a great deal of TSMC approaches were used in robotic manipulators [6][7][8][9][10][11] because of some superior properties such as better tracking precision, fast convergence, insensitivity to system uncertainty and external disturbance [10,12] . But, the TSMC approaches still have a singularity problem.…”