Sliding‐mode control of the third‐order system subject to velocity, acceleration and input signal constraints

Abstract

In this paper the design of a time-varying switching plane for the sliding-mode control of the third-order system subject to velocity, acceleration and input signal constraints is considered. Initially, the plane passes through the system representative point in the error state space and then it moves with a constant velocity to the origin of the space. Having reached the origin the plane stops moving and remains fixed. The plane parameters (determining angles of inclination and the velocity of its motion) are selected to ensure the minimum integral absolute error (IAE) without violating velocity, acceleration and input signal constraints. The following cases of the switching plane parameters selection are considered. Firstly, the IAE is minimized subject to each of the three constraints separately. Then, every pair of the constraints is considered, and finally all three constraints are taken into account simultaneously. In all the cases the switching plane is chosen in such a way that the reaching phase is eliminated, insensitivity of the system with reference to the external disturbances and the model uncertainty is guaranteed from the very beginning of the proposed control action and fast, monotonic error convergence to zero is achieved.

An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems

“…Example 1 In this section, in order to verify the performance of the proposed FTSM control method, the following uncertain nonlinear third-order system is considered [50]:…”

“…Assumption 3 [50] There exists a constantμ which for every pair (x, t) satisfies the condition |d(x, t)| ≤ μ.…”

Linear quadratic optimal sliding mode flow control for connection‐oriented communication networks

“…Now, we substituteK 1 given by (32) into the expression on the right-hand side of (18) and compare with its left-hand side, which allows to represent elementsk i3 (i = 1, 2, 3) in terms ofk 11 . We proceed in this way until a general pattern is determined, i.e.…”

“…Since a proper choice of the switching plane is the key part of the design of sliding mode controllers, several authors considered this issue for continuous time systems [26][27][28][29][30][31][32]. However, fewer results on the sliding plane selection for discrete time systems have been reported yet [22,33,34].…”

The problem of state constraints in designing the discrete time sliding mode controller

“…The issue of limiting state variables is an important problem in the sliding mode control due to its frequent occurrence in practice [33][34][35][36][37][38][39][40]. Usually, during the sliding mode controller design, the problem of constraining the state variables is omitted in favor of limiting the control signal.…”