Synthesis of a New Robust Exponential Sliding Mode Differentiator with its Observer Applications

Deepika, Deepika; Narayan, Shiv; Kaur, Sandeep

doi:10.1002/asjc.1943

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…Super‐twisting differentiator (STD)is another SMB differentiator, 12 which is designed according to the ST algorithm as follows:

\{\begin{array}{l} {\overset{z}{true}}_{0} false(t false) = prefix- λ_{0} L^{\frac{1}{2}} ⌈ σ_{0} false(t false) ⌋^{\frac{1}{2}} + z_{1} false(t false) \\ {\overset{z}{true}}_{1} false(t false) \in prefix- λ_{1} L sgn false(σ_{0} false(t false) false), \end{array}

where, as before,

σ_{0} (t) = z_{0} (t) - f (t)

λ_{0}

and

λ_{1}

denote differentiation gains which may be designed based on numerical simulations, 12 and L is the Lipschitz constant of

{\dot{f}}_{0} (t)

, that is,

| {\ddot{f}}_{0} (t) | < L

.Recent studies mainly dealt with the analysis of the convergence and accuracy of SMB differentiators. For instance, the best‐possible numeric differentiation accuracy of the STD has been studied in Reference 48, a mere example of the filtering differentiator subject to white noise is provided in Reference 49, and a modified STD with exponential convergence rate has been proposed in Reference 50. Moreover, a family of smooth explicit Lyapunov functions has been proposed for the STD which allows to study the convergence and robustness of the differentiator with respect to initial condition 51 …”

Section: A Summary Of the Continuous‐time Differentiatorsmentioning

confidence: 99%

Time‐discretizations of differentiators: Design of implicit algorithms and comparative analysis

Mojallizadeh

Brogliato

Acary

2021

Intl J Robust & Nonlinear

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A complete review of the known differentiators and their time‐discretizations have been addressed in this study. To resolve the drawbacks of the explicit (forward Euler) discretization, which is commonly utilized in sliding‐mode‐based differentiators, implicit time discretization methods are proposed to handle the set‐valued functions. The proposed schemes are supported by some analytical results to show their crucial properties, for example, finite‐time convergence, exactness, invariant sliding‐surface, chattering elimination, insensitivity to the gains during the sliding‐phase, and the well‐posedness. The causal implementation of the proposed implicit schemes has been addressed clearly and supported by flowcharts. Semi‐implicit schemes are also presented to provide a compromise between the performance and the ease of implementation. Finally, an exhaustive comparison is made using numerical experiments among 25 different state‐of‐the‐art differentiators to evaluate the behaviors of the differentiators facing the noise and initial error. Realistic conditions are considered in the simulations to provide useful information based on practical conditions. General conclusions are that implicit discretizations can supersede explicit and semi‐implicit ones.

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“…Super‐twisting differentiator (STD)is another SMB differentiator, 12 which is designed according to the ST algorithm as follows:

\{\begin{array}{l} {\overset{z}{true}}_{0} false(t false) = prefix- λ_{0} L^{\frac{1}{2}} ⌈ σ_{0} false(t false) ⌋^{\frac{1}{2}} + z_{1} false(t false) \\ {\overset{z}{true}}_{1} false(t false) \in prefix- λ_{1} L sgn false(σ_{0} false(t false) false), \end{array}

where, as before,

σ_{0} (t) = z_{0} (t) - f (t)

λ_{0}

and

λ_{1}

denote differentiation gains which may be designed based on numerical simulations, 12 and L is the Lipschitz constant of

{\dot{f}}_{0} (t)

, that is,

| {\ddot{f}}_{0} (t) | < L

Section: A Summary Of the Continuous‐time Differentiatorsmentioning

confidence: 99%

Time‐discretizations of differentiators: Design of implicit algorithms and comparative analysis

Mojallizadeh

Brogliato

Acary

2021

Intl J Robust & Nonlinear

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show abstract

“…Remark 2. In most of the existing SMOs and differentiator designs such as in previous studies [9][10][11][12][13][14][15][16][17], the discontinuous function such as sign(.) has been employed.…”

Section: Problem Statementmentioning

confidence: 99%

“…Then, Basin et al [14] have provided the results of nonrecursive fixed time HOSMD by introducing the discontinuous term with more than one degree in every differential equation of estimator. Stimulated by a new power rate reaching exponential law [15], a faster nonhomogeneous exponential sliding mode differentiator has been proposed in Deepika et al [16] An experimental application of all the aforementioned differentiators has been well presented in Ahmed et al [17] for reconstruction of states of Van der Pol oscillator.…”

Section: Introductionmentioning

confidence: 99%

Frameworks for double hyperbolic function‐based robust sliding mode differentiator and observer for nonlinear dynamics

Deepika

2020

Asian Journal of Control

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This paper puts forward contemporary designs of sliding mode differentiator and state observer for evaluation of unknown nonlinear signal derivatives and unknown internal system states, respectively, by the virtue of tangential and inverse sinusoidal hyperbolic functions. The utility of the proposed frameworks is that it bestows smooth and robust estimation without inciting unacceptable oscillations (chattering), unlike high gain discontinuous function-based preliminary observers/differentiators. Moreover, the employed double hyperbolic functions would drive the various deviations in estimations of signals or states to a very close neighborhood of origin in finite time which is substantiated via Lyapunov's energy function. To demonstrate the efficiency of the introduced techniques, two examples for estimating the derivatives of a nonlinear signal and internal states of motor are also illustrated with time varying uncertainties. At last, the attained simulation outcomes of the proposed differentiator are further compared with formerly formulated designs such as higher-order sliding mode differentiator (HOSMD) and uniformly convergent differentiator (UCD).

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“…The response speed of the system can be improved; meanwhile, the chattering of the system will be definitely suppressed [18][19][20]. Actually, disturbances exist in the sliding mode control (SMC) [21][22][23][24]. These articles have introduced a comparatively complete theory, but some of them are not combined with the micro-grid system, and some of them do not make allowances for the system speed response and jitter suppression in terms of control effects.…”

Section: Introductionmentioning

confidence: 99%

Research on photovoltaic energy storage micro‐grid systems based on improved sliding mode control

Zhang

2022

IET Renewable Power Gen

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In islanded microgrid systems, PV power generation efficiency and energy loss of storage battery are the current research trends. Due to the intermittent and fluctuating characteristics of PV power generation, various loads connected to the DC microgrid system would also bring DC bus voltage low-frequency fluctuations and other problems. In order to solve the above problems, an maximum power point tracking (MPPT) tracking strategy (sliding mode control based on squirrel search algorithm) is proposed in this study; meanwhile, a sliding mode control strategy based on an improved reaching law is designed. The components of the PV energy storage system and the control method are mainly focused on, and the PV energy storage system is optimized by improving the sliding mode control. The proposed control algorithm is verified and analyzed by MATLAB/Simulink simulation platform. Compared with the double integral sliding mode control algorithm MPPT tracking case, sliding mode control based on squirrel search algorithm shows excellent performance (short response time, good tracking maximum power point effect etc.). In addition, the sliding mode control based on the proposed reaching law reduces the system jitter, and effectively reduces jitter and vibration of the PV energy storage battery.

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Synthesis of a New Robust Exponential Sliding Mode Differentiator with its Observer Applications

Cited by 4 publications

References 24 publications

Time‐discretizations of differentiators: Design of implicit algorithms and comparative analysis

Time‐discretizations of differentiators: Design of implicit algorithms and comparative analysis

Frameworks for double hyperbolic function‐based robust sliding mode differentiator and observer for nonlinear dynamics

Research on photovoltaic energy storage micro‐grid systems based on improved sliding mode control

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