ITAE Optimal Sliding Modes for Third-Order Systems With Input Signal and State Constraints

Abstract

In this note, 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 switching plane passes through the system representative point (RP) 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 are selected to minimize the integral of the time multiplied by the absolute error (ITAE) without violating velocity, acceleration and input signal constraints. Furthermore, 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 control action and monotonic tracking error convergence to zero is ensured.Index Terms-Sliding-mode control, switching plane design, timevarying switching planes, variable structure systems.

Dead-beat and reaching-law-based sliding-mode control of perishable inventory systems

“…for any integer k ≥ 0 the inequality h(k) ≤ d max holds. Consequently, taking into account (24) and the theorem assumption (25) we have for k ≥ n p + 1…”

“…For this purpose, we propose discrete-time sliding-mode (SM) control, which is well known to be efficient and robust regulation technique [13][14][15][16][17][18][19]. Since a proper choice of the switching plane is the key part of the design of SM controllers [20][21][22][23][24][25], in this work, we determine the plane parameters for a dead-beat scheme. In this way we obtain fast response to the changes in demand and the minimum stock level.…”

Fuzzy swinging-up with sliding mode control for third order cart-inverted pendulum system

“…we substitute from (16) and (18) in (14) to obtain the cart position third-order differential equation. , cos…”

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.…”