Sliding mode output‐feedback causal output tracking for a class of discrete‐time nonlinear systems

Self Cite

In this article, the problem of nonlinear sliding mode (SM) regulation is addressed for nonlinear systems in general and regular form that are subject to unmodelled disturbances. In particular, the error feedback SM regulator problem is defined, taking the concepts related to the zero output tracking submanifold as a starting point. Applying the internal model concept to the time‐invariant SM equation, the solvability conditions to the problem are derived. A nonlinear extended observer is proposed, and using the observer states, a sliding manifold is formulated. A SM control algorithm is proposed to ensure the designed manifold to be attractive, achieving robustness with respect to allowed uncertainties resulting in the tracking error to be uniformly ultimately bounded. The effectiveness of the proposed method is demonstrated by the application of the regulator to a third order nonlinear non‐minimum phase system.

“…Under the matching condition (3), the term d 0 (23) in (21) with b s = k 1 b 1 + b 2 is equal equivalently to zero, particularly…”

Section: Sm Regulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Error feedback sliding mode regulator

Campo

Loukianov

Avila

et al. 2023

Self Cite

“…A discrete controller can be obtained by discretizing a continuous controller 1 or by a theoretical design based on a discretized model of the system. 2,3 However, there are many kinds of native discrete systems (such as supply chain systems and batch control systems) whose dynamics are with respect to iteration, 4,5 and the period between iterations is not necessarily the same. Therefore, conventional active disturbance rejection control (ADRC) and its discretization are not applicable.…”

Section: Introductionmentioning

confidence: 99%

Active disturbance rejection control for discrete systems with zero dynamics

Wang

Pan

Sira‐Ramírez

et al. 2021

In this paper, a discrete active disturbance rejection control (DADRC) scheme is proposed to manipulate linear input-output systems with zero dynamics. The DADRC is formulated according to the relative degree of the system output and is designed to track a reference and cancel both internal uncertainties and external disturbances. A parameter tuning method is also presented based on a part of the model information. The robustness and effectiveness of the designed scheme are demonstrated via numerical simulations.

“…The Pendubot is a two‐link planar robot with a single actuator at the base joint of the first link, and the joint between two links is unactuated and allowed to swing freely 1,2 . It, together with other mechanical systems such as the inverted pendulum on a cart 3 and the Acrobot, 4 is used for control and robot education and for research as one of typical examples of underactuated mechanical systems 5,6 …”

Section: Introductionmentioning

confidence: 99%

Anti‐Swing control of the Pendubot using damper and spring with positive or negative stiffness

Xin

Makino

Izumi

et al. 2021

In this article, we study the anti‐swing control of the Pendubot which is a 2‐link planar robot with a single actuator driving the first joint, whose control objective is to stabilize the Pendubot to the downward equilibrium point (DEP) with the two links in the downward position for all its initial states with the exception of a set of Lebesgue measure zero. To achieve this control objective, with respect to the angle of the first joint, we present a proportional‐derivative (PD) controller using a damper and a linear spring with positive stiffness, and a sinusoidal‐derivative (SD) controller using a damper and a nonlinear spring (force being sinusoidal function of the displacement) allowing even negative stiffness. We prove that the control objective is achieved if some conditions on the stiffness of linear or nonlinear spring are satisfied. We present analytical solutions to the optimal design of the derivative gain and the stiffness which minimizes the real parts of the dominant poles of the linearized model of the corresponding closed‐loop systems around the DEP for all Pendubots in terms of their five physical parameters without any constraint. Our discussion shows that the SD controller is superior to the PD controller. We provide simulation results for a Pendubot to show that the presented SD controller can stabilize the Pendubot to the DEP faster than the presented PD controller.