Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain

118

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

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

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

118

“…On the other hand, system with Assumption also covers a class of nonlinear systems with unknown control coefficients , for example, the system

{\overset{x}{true}}_{1} = θ_{1} x_{2}, {\overset{x}{true}}_{2} = θ_{2} u, y = x_{1}

can be transformed into

ż_{1} = z_{2}, ż_{2} = u, y = θ_{1} θ_{2} z_{1}

z_{1} = \frac{x_{1}}{θ_{1} θ_{2}}

and

z_{2} = \frac{x_{2}}{θ_{2}}

. In the case of output feedback control for feedforward nonlinear time‐delay systems, the existing results allow usually the growth rate only including either an unknown constant or input functions c ( u ) and

\overset{c}{true} (u (t - τ))

, for example, . In the absence of time delay, Yu et al considers the case of θ c ( u ), which introduces two dynamic gains and cannot be applicable to time‐delay case.…”

Section: Problem Formulation and Key Lemmasmentioning

confidence: 99%

Global adaptive regulation of feedforward nonlinear time‐delay systems by output feedback

Jia

Cui

et al. 2016

SUMMARYThe problem of global adaptive state regulation is investigated via output feedback for uncertain feedforward nonlinear time-delay systems. Compared with existing results, our control schemes can be applicable to more general nonlinear time-delay systems because of combining the low-gain scaling approach with the backstepping method. In particular, we allow that there exist uncertain output function and uncertain growth rate imposed on nonlinear terms. Also, one considers a class of nonlinear systems with main-axis delay. By the Lyapunov-Krasovskii theorem, delay-independent controllers are proposed by constructing novel lowgain observers driven by system input, to regulate the states of original system while all the closed-loop signals are globally bounded. Furthermore, two examples are given to illustrate the usefulness of our results.

“…In this paper, we solve an output feedback control problem of more generalized upper triangular nonlinear systems with uncertain time‐varying delays in both states and input. Our output feedback control problem treated in this paper is a generalized version of those in . The key features are as follows: Delays in the input and the states are uncertain and time varying. Delays in nonlinearities are with integral forms. Nonlinearities are extended by including more power of u as well as unknown parameters. …”

Section: Introductionmentioning

confidence: 99%

Output feedback regulation of upper triangular nonlinear systems with uncertain time‐varying delays in states and input

Koo

Choi

2017

Self Cite

Summary In this paper, an output feedback controller is studied to regulate a class of upper triangular nonlinear systems with uncertain time‐varying delays. The key features of our considered system are that there are uncertain time‐varying delays in both states and input and the high‐order nonlinearity is in a more relaxed form over the previous results. Theoretical analysis and numerical example are presented to show the benefits of our controller. Copyright © 2017 John Wiley & Sons, Ltd.