A novel disturbance observer-based backstepping controller with command filtered compensation for a MIMO system

Rashad, Ramy; Aboudonia, Ahmed; El-Badawy, Ayman

doi:10.1016/j.jfranklin.2016.07.017

Cited by 36 publications

(25 citation statements)

References 17 publications

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“…Consider the following system:

\begin{matrix} alignleft \\ align-1 {\dot{x}}_{1} & align-2 = 0.4 x_{2} + \frac{x_{2}^{3}}{2} + d_{1}, \\ align-1 {\dot{x}}_{2} & align-2 = x_{2}^{2} u + \tanh (u) + d_{2}, \\ align-1 y & align-2 = x_{1}, \end{matrix}

where d 1 and d 2 are mismatched and matched disturbances, respectively. Note that is in pure‐feedback form and nonaffine‐in‐control, so that the algorithms in the works of Yang and Zheng, Fang et al, and Rashad et al cannot be implemented directly.…”

Section: Simulationmentioning

confidence: 99%

“…In the work of Rashad et al, an observer‐based backstepping controller with command filtered compensation is developed for the following disturbed affined nonlinear systems in the strict‐feedback form:

\begin{matrix} right {\dot{x}}_{i} & left = f_{i} ({\bar{x}}_{i}) + g_{i} ({\bar{x}}_{i}) x_{i + 1} + d_{i}, & right \\ right {\dot{x}}_{n} & left = f_{n} ({\bar{x}}_{n}) + g_{n} ({\bar{x}}_{n}) u + d_{n}, \end{matrix}

where

{\overset{x}{true}}_{i} = {false[x_{1}, …, x_{i} false]}^{T}

, d i and d n are mismatched and matched disturbances, f i and g i are nonlinear smooth vector fields, i =1,…, n −1. Following the controller design procedure in the work of Rashad et al,

scriptG false(x, z false)

can be derived in two steps.…”

Section: Simulationmentioning

confidence: 99%

“…According to Rashad et al, the feedback gains should be assigned such that the matrices

J_{1} = ([], \begin{matrix} center center \\ array 0 & array 1 \\ array - k_{11} & array - k_{12} \end{matrix}), J_{2} = ([], \begin{matrix} center center \\ array 0 & array 1 \\ array - k_{21} & array - k_{22} \end{matrix})

are Hurwitz, and λ min ( J 1 )> λ min ( J 2 ), where λ min ( J i ) represents the minimum eigenvalue of the matrix J i . The observer gains μ 1 and μ 2 should be assigned large values for fast convergence of estimate error.…”

Section: Simulationmentioning

confidence: 99%

“…However, this will introduce high‐frequency noise in the control signal. The detailed parameter tuning guidelines can be referred to in the work of Rashad et al We set k 11 =3, k 12 =4, k 21 =5, k 22 =6, μ 1 =15, μ 2 =6, γ =50.…”

Section: Simulationmentioning

confidence: 99%

“…The design procedure proposed in this paper does not rely on the structure of the existing disturbance‐rejection algorithms. Thus, various types of disturbance‐attenuation techniques, such as the algorithms in the works of Yang and Zheng, Fang et al, and Rashad et al, can be combined with the proposed method according to the performance requirements of the practical engineering. In addition, although the tracking performance is guaranteed by Tikhonov's theorem, the singular perturbation parameter, which dominates the effectiveness of the timescale decomposition, is independent from the original system.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A novel redesign framework to extend the application scope of a class of disturbance‐rejection algorithms

Hao

Pei

2019

Intl J Robust & Nonlinear

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Summary In this paper, a novel redesign method is developed for a class of disturbance‐rejection algorithms so that they can be applied to pure‐feedback nonaffine‐in‐control nonlinear systems with matched and mismatched disturbances. First, a series of augmented dynamical equations, which evolve faster than the original system, are constructed to establish a boundary‐layer subsystem to derive the virtual and actual inputs for the nominal system. Then, the composite interconnected system is studied in the standard singular perturbed form. In the slow timescale, the reduced slow subsystem (RSS) is transformed into the chain of integrators form in the error coordinate, for which the existing antidisturbance methods can be employed. The tracking performance of the closed‐loop system is approximated by RSS under singular perturbation theory. The proposed redesign method is adopted to three existing disturbance‐rejection algorithms for a pure‐feedback nonaffine‐in‐control numerical example in the presence of matched and mismatched disturbances. The effectiveness is demonstrated by simulation experimental results.

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“…Consider the following system:

\begin{matrix} alignleft \\ align-1 {\dot{x}}_{1} & align-2 = 0.4 x_{2} + \frac{x_{2}^{3}}{2} + d_{1}, \\ align-1 {\dot{x}}_{2} & align-2 = x_{2}^{2} u + \tanh (u) + d_{2}, \\ align-1 y & align-2 = x_{1}, \end{matrix}

Section: Simulationmentioning

confidence: 99%

\begin{matrix} right {\dot{x}}_{i} & left = f_{i} ({\bar{x}}_{i}) + g_{i} ({\bar{x}}_{i}) x_{i + 1} + d_{i}, & right \\ right {\dot{x}}_{n} & left = f_{n} ({\bar{x}}_{n}) + g_{n} ({\bar{x}}_{n}) u + d_{n}, \end{matrix}

where

{\overset{x}{true}}_{i} = {false[x_{1}, …, x_{i} false]}^{T}

, d i and d n are mismatched and matched disturbances, f i and g i are nonlinear smooth vector fields, i =1,…, n −1. Following the controller design procedure in the work of Rashad et al,

scriptG false(x, z false)

can be derived in two steps.…”

Section: Simulationmentioning

confidence: 99%

“…According to Rashad et al, the feedback gains should be assigned such that the matrices

J_{1} = ([], \begin{matrix} center center \\ array 0 & array 1 \\ array - k_{11} & array - k_{12} \end{matrix}), J_{2} = ([], \begin{matrix} center center \\ array 0 & array 1 \\ array - k_{21} & array - k_{22} \end{matrix})

Section: Simulationmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A novel redesign framework to extend the application scope of a class of disturbance‐rejection algorithms

Hao

Pei

2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

Command filter‐based adaptive neural event‐triggered control of MIMO pure‐feedback systems with full‐state time‐varying constraints

Zhu

Huang

Ding

et al. 2022

Adaptive Control & Signal

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Summary This article is concerned with the issue of adaptive event‐triggered control for a class of pure‐feedback multi‐input multi‐output (MIMO) nonlinear systems with full‐state time‐varying constraints. By using the hyperbolic tangent as nonlinear mapping technique, the uncertain constrained MIMO non‐affine system is changed into a novel unconstrained MIMO system. Dynamic surface control (DSC) strategy is used to solve the issue of “explosion of complexity.” Command filter is adopted to overcome the insufficient of the DSC method by the error compensation mechanism. Adaptive event‐triggered control scheme is developed for the transformed non‐affine system based on relative threshold mechanism. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. All the signals in the controlled system are proved to be semi‐globally uniformly ultimately bounded by adding to compensation signals into the whole Lyapunov function. Two simulation examples demonstrate the capability of the proposed control strategy.

show abstract

Finite‐time command filter‐based adaptive tracking control for nonstrict feedback nonlinear systems with full‐state restrictions and unmodeled dynamics

Zhu

Huang

Ding

et al. 2023

Asian Journal of Control

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The finite-time command filter tracking control for a class of nonstrictly feedback nonlinear systems with unmodeled dynamics and full-state constraints is investigated in this paper. The hyperbolic tangent function is used as a nonlinear mapping technique to solve the obstacle of the full-state constraints. A new adaptive finite time control method is proposed through command filtering reverse engineering, and the shortcomings of the dynamic surface control (DSC) method are overcome by the error compensation mechanism. Dynamic signal is designed to handle dynamical uncertain terms. Normalization signal is designed to handle input unmodeled dynamics. Unknown nonlinear functions are approximated by radial basis function neural networks. Based on the Lyapunov stability theory, it is proved that all signals in the closed-loop system are semi-globally consistent and finally bounded and the output tracking error converges in finite time. Two numerical examples are utilized to verify the effectiveness of the proposed control approach.

show abstract

A novel disturbance observer-based backstepping controller with command filtered compensation for a MIMO system

Cited by 36 publications

References 17 publications

A novel redesign framework to extend the application scope of a class of disturbance‐rejection algorithms

A novel redesign framework to extend the application scope of a class of disturbance‐rejection algorithms

Command filter‐based adaptive neural event‐triggered control of MIMO pure‐feedback systems with full‐state time‐varying constraints

Finite‐time command filter‐based adaptive tracking control for nonstrict feedback nonlinear systems with full‐state restrictions and unmodeled dynamics

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