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In previous investigations, the nonlinear hypothesis use the linear bounded maps. Nonlinear hypothesis are described as the combination of the first order terms, and after of the mentioned combination, one bounded map is applied to alter the result. This document proposes two nonlinear hypothesis which use different structures instead of using the linear bounded maps. They are termed as novel nonlinear hypothesis and second order nonlinear hypothesis and their goal is to improve the second order processes modeling. The proposed nonlinear hypothesis are described as the combination of the first order and second order terms. Since the delta parallel robot is a second order process, it is an excellent platform to prove the effectiveness of the two proposed hypothesis. INDEX TERMS Novel nonlinear hypothesis, second order nonlinear hypothesis, nonlinear hypothesis, delta parallel robot.

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The perturbations are the unwanted and unknown inlets in nonlinear plants which can affect the outlets. In this article, an estimator is studied for the variables and perturbations estimation in nonlinear plants. The saturation map is used in our estimator instead of the signum map to decrease the chattering, and we ensure the estimator convergence by the Lyapunov analysis. The conditions required by our estimator gains are found to reach the variables error convergence, and these gains are used for the perturbations estimation. An algorithm is proposed to choose the gains for achieving a satisfactory performance in our estimator. The studied estimator is applied for the variables and perturbations estimation in the gas turbine and gasification plants.