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In this paper, the control of an electronic throttle valve based on second-order sliding-mode concepts is presented. The so-called twisting algorithm is chosen as the control law. It is shown that the tracking performance for discontinuous reference signals is significantly improved by introducing nonlinear damping by appropriately specifying the sliding surface. The control concept requires the measured plate angle as well as its time derivative, which is computed with the help of a robust exact differentiator. The effectiveness of the proposed concept, consisting of a twisting algorithm for control and supertwisting algorithm for differentiation, is demonstrated by experimental results.

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This paper demonstrates the functionality and ease of use of a recently implemented robust exact differentiator block for numerical simulations performed within the Matlab/Simulink software environment. It is demonstrated that the differentiator block may be used for various applications and may be easily integrated within existing Simulink models. The underpinning discrete time differentiation algorithm is briefly outlined and its parameters up to differentiator order 10 are presented. An extended version of the toolbox supports the so-called automatic code generation feature of Matlab/Simulink. This functionality allows compilable code to be produced for many available hardware platforms. Three applications are presented in the paper, where two require the production of executable code. The simulation based application presents a differentiator based edge detection algorithm for image processing purposes which utilises the simulink block directly.

Higher order sliding mode differentiators have received a great deal of attention in the literature. For the case of reconstructing the first derivative, theoretical convergence conditions for the differentiator are available from which differentiator parameters may be selected. For the case of higher order derivatives, some parameter settings have been suggested for differentiators of certain order but there is no tuning algorithm available to determine convergent parameters for differentiators of arbitrary order. Whilst recognising the strong theoretical properties of sliding mode differentiators, practitioners report difficulties in achieving wide envelope performance from a single set of differentiator parameters. This paper proposes a constructive design paradigm to generate differentiator parameters which is seen to provide a natural framework to facilitate simple on-line adaptation of the chosen gains. Simulation experiments as well as experimental results are presented to demonstrate the proposed approach.