Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems

Kamalapurkar, Rushikesh; Fischer, N.; Obuz, Serhat; Dixon, Warren E.

doi:10.1109/tac.2015.2451472

Cited by 97 publications

(56 citation statements)

References 54 publications

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“…21,[27][28][29]47 Actually, for general mechanical systems, the function f(x) usually represents structural behaviors, such as motion flow in hydraulic actuation systems and mechanism nonlinearity in manipulators etc and can be modeled and/or identified offline to a satisfactory level. That is to say, for most mechanical systems, we can always capture some model information, and the inherent model/identification error can be lumped to the additive disturbance term.…”

Section: Remarkmentioning

confidence: 99%

“…Similar assumptions can also be found in previous studies. [27][28][29] 3 | OUTPUT FEEDBACK CONTROLLER DESIGN…”

Section: Remarkmentioning

confidence: 99%

“…The stability analysis using LK functionals was provided to prove that semiglobally uniformly ultimately bounded tracking performance can be achieved by the controller in Sharma et al 21 In view of the fact that the practical systems may be subject to time-varying delay in the control input, Fischer et al 27 and Obuz et al 28 extended the control method in Sharma et al 21 to solve this problem based on the assumption that the change rate of the input delay is bounded by a known bound. Moreover, time-varying input and state delay compensation for uncertain disturbed nonlinear systems was also realized in Kamalapurkar et al 29 However, all aforementioned controllers are developed under the assumption of accessibility of full state information for feedback. But for many practical engineering systems, only the system output is available due to some realistic restrictions such as cost and structure.…”

Section: Introductionmentioning

confidence: 99%

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

Deng

Yao

2017

Intl J Robust & Nonlinear

118

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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

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Section: Remarkmentioning

confidence: 99%

“…Similar assumptions can also be found in previous studies. [27][28][29] 3 | OUTPUT FEEDBACK CONTROLLER DESIGN…”

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Deng

Yao

2017

Intl J Robust & Nonlinear

118

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“…• It can be observed from (15) that, proposed stability approach is independent of the rate of change in h and thus can negotiate any arbitrarily time-varying delay within the stipulated maximum bound. On the contrary, [30]- [31] can negotiate only slowly varying time delay and also bound ofḧ is required. • Computation of switching gainĉ of AROLC using (9), unlike [29]- [33], does not require predefined bound of the uncertainties and helps to to attain the tracking objective.…”

Section: ) Stability Analysis Of Arolcmentioning

confidence: 99%

“…In this case, uncertainty in the inertia matrix was considered. The same approach was later extended for time varying input delay in [30] and also for state delay [31]. A filtered tracking error based control law is used in [32] to tackle the effect of known constant input time delay and used fuzzy logic systems of first type to approximate the unknown disturbances with predefined uncertainty bound.…”

Section: Introduction a Background And Motivationmentioning

confidence: 99%

Adaptive robust tracking control of a class of nonlinear systems with input delay

Roy

Kar

2016

Nonlinear Dyn

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In this paper, the tracking control problem of a class of uncertain Euler-Lagrange systems subjected to unknown input delay and bounded disturbances is addressed. To this front, a novel delay dependent control law, referred as Adaptive Robust Outer Loop Control (AROLC) is proposed. Compared to the conventional predictor based approaches, the proposed controller is capable of negotiating any input delay, within a stipulated range, without knowing the delay or its variation. The maximum allowable input delay is computed through Razumikhin-type stability analysis. AROLC also provides robustness against the disturbances due to input delay, parametric variations and unmodelled dynamics through switching control law. The novel adaptive law allows the switching gain to modify itself online in accordance with the tracking error without any prerequisite of the uncertainties. The uncertain system, employing AROLC, is shown to be Uniformly Ultimately Bounded (UUB). As a proof of concept, experimentation is carried out on a nonholonomic wheeled mobile robot with various time varying as well as fixed input delay, and better tracking accuracy of the proposed controller is noted compared to predictor based methodology.

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Improved sliding mode observer based repetitive control for linear systems with time‐varying input and state delays

Chuei,

Zheng,

Cao

et al. 2023

Adaptive Control & Signal

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SummaryControl systems are frequently subject to the negative effects of time delays and disturbances, which diminish the systems' tracking performance. In response to these challenges, this paper presents a novel approach, that is, the improved sliding mode observer based repetitive control (ISMO‐RC), to enhance the system's periodic signal tracking in the presence of the input and state time delays and the input disturbances. The design takes the advantages of RC and ISMO, in which RC effectively compensates periodic signals, while ISMO compensates both aperiodic disturbances and the time‐varying input and state delays. The stability of the whole system is guaranteed via the linear matrix inequality (LMI) and the Lyapunov–Krasovskii functional analysis. The proposed controller is evaluated through extensive simulations and experiments, which demonstrate its superiority over comparative control methods.

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Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems

Cited by 97 publications

References 54 publications

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

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

Adaptive robust tracking control of a class of nonlinear systems with input delay

Improved sliding mode observer based repetitive control for linear systems with time‐varying input and state delays

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