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To improve the robustness of tracking differentiator,the nonlinear sliding mode tracking differentiator is analyzed in details in this paper.Then an improved second-order sliding mode tracking differentiator is presented using Lyapunov stability theory.Integrating the characteristics of linear and nonlinear tracking differentiators,the proposed tracking differentiator can track and differentiate any signal;meanwhile,its structure is simple and it is easy for application.Numerical simulations are carried out on this improved tracking differentiator and on a super-twisting tracking differentiator.Results show that the improved tracking differentiator can reduce the chartering of differential signal.
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This paper presents a comparison study of four advanced tracking differentiators, including global robustexact differentiator, hybrid continuous nonlineardifferentiator, robust exact uniformly convergent arbitrary order differentiator and Taylor expansion series based differentiator. The numerical simulations are performed by three typical signals with different type of noise to illustrate the performanceof tracking differentiation, sensibility to noise and robustness ability. The results show that, over all, these differentiators could track derivate signal of low frequencysignal well and Taylor expansion seriesbased differentiatoris more sensitive to noise than other three differentiators.
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A new robust technique control is developed in this paper for a nonlinear uncertain system. This technique is based on backstepping method integrating sliding mode differentiator used to estimate the derivative of tracking error. This technique has many objects especially minimizing sensors number and ameliorating control performance. The efficiency of this technique is illustrated by simulation results. The differentiator used is robust in presence of external disturbance.
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The perturbation induced by signal frequency is one of the main problems for tracking differentiator design, and classical linear differentiators are usually sensitive to signal frequency. An improved second-order sliding mode nonlinear tracking differentiator is proposed in this paper using Lyapunov stability theory, considering the robustness of sliding mode control theory. This tracking differentiator can track and differentiate any signal. At the same time it has a simple form and is easy to be applied. A numerical simulation is presented for the linear tracking differentiator and the nonlinear tracking differentiator with different input signals, and results verified the effectiveness of the second order sliding mode tracking differentiator. A method to eliminate perturbation caused by noise is presented at the end of this paper.
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This paper presents a high-order differentiator for delayed measurement signal. The proposed differentiator not only can correct the delay in signal, but aslo can estimate the undelayed derivatives. The differentiator consists of two-step algorithms with the delayed time instant. Conditions are given ensuring convergence of the estimation error for the given delay in the signals. The merits of method include its simple implementation and interesting application. Numerical simulations illustrate the effectiveness of the proposed differentiator.
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In this paper, describing function method is used to analyze the characteristics and parameters selection of differentiators. Nonlinear differentiator is an effective compensation to linear differentiator, and hybrid differentiator consisting of linear and nonlinear parts is the combination of both advantages of linear and nonlinear differentiators. The merits of the hybrid differentiator include its simplicity, rapid convergence at all times, and restraining noises effectively. The methods are confirmed by some examples.
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Summary A novel switching differentiator with a considerably simplified form is proposed. Under the assumption that the time‐derivative of a time‐varying signal has a Lipschitz constant, it is shown that estimation error is asymptotically convergent to zero. The estimated derivative shows neither chattering nor peaking phenomenon. A differentiator that estimates the first‐order derivative of a signal is first proposed, and, by connecting this differentiator in series, higher‐order derivatives also become available. Simulation results show that the proposed differentiator shows extreme performance improvements compared to the previously established widely used differentiators such as high‐gain observer or higher‐order sliding mode differentiator.
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