Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

Abstract

SummaryThis paper addresses the output feedback tracking control of a class of multipleinput and multiple-output nonlinear systems subject to time-varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory-based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time-varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady-state tracking accuracy in spite of the presence of time-varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a LyapunovKrasovskii functional. A specific study on a 2-link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme. | INTRODUCTIONTime delay that includes state delay and input delay is a pervasive phenomenon encountered in many practical engineering applications such as robotic systems, electrical networks, and hydraulic actuation systems. The existence of time delay may result in unexpected degradation in control performance and even instability. 1 Hence, how to effectively attenuate the effect of time delay has always been the research hotspot during the latest several decades, with numerous control schemes proposed, such as previous studies 2-12 for input delay and other studies [13][14][15][16][17][18] for state delay. Especially in Sun et al 17 and Sun and Liu, 18 stabilization of high-order uncertain nonlinear systems with state delays were investigated by using adaptive approach. 19,20 This paper focuses on the problem of input delay, ie, the time delay that occurs between the control input and the plant. Specifically, predictor-based techniques such as Artstein model reduction 2 and finite spectrum assignment, 3 which originate from classic Smith predictor method, 4 are typically exploited to compensate for the input delay. The core design in these predictor-based approaches is to transform the delayed system to a delay free one by using finite integrals over past control values. 21 In addition, many predictive controllers have also been synthesized based on the fact that the input delayed systems can be modeled as

Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation

“…At present, there are a few results reported on uncertain nonlinear systems with input delay . Specifically, a predictor‐based controller, which contained a finite integral of past control value, was developed in References to for a class of uncertain nonlinear systems with matching condition. Then, truncated predictor control was investigated in References and , where the nonlinear function was assumed to be Lipschitz and the input delay should be small.…”

A new practical robust control of cable‐driven manipulators using time‐delay estimation

“…To utilize SM control and its variants in practical systems, some methods have been proposed and used to suppress the chattering, such as reaching laws, boundary layer, adaptive control, fuzzy logical, neural networks control, and high‐order SM (HOSM) control . The latter has enjoyed many interests thanks to its good comprehensive performance.…”

Global output feedback regulation of nonlinear time delay systems subject to sensor measurement faults

“…where j (j ∈ N 1∶n ) is the state variable of the compensator, q j satisfies the condition in Lemma 1, L 1 (t) is defined in (2). Then, we give the main result of this article, which can be summarized as the following theorem.…”

“…It is well known that time delays are frequently encountered in various engineering fields such as chemical processes, rolling mills, and so on, which may cause the instability or performance degradation of the systems. [1][2][3] Furthermore, almost all physical systems are nonlinear in nature, and nonlinear time delay systems have uncontrollable linearization around the origin, so their stability/stabilization has been considered as one of the most challenging subjects. [4][5][6] In recent years, many stability results have been obtained from various perspectives (see .…”