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Chattering is further reduced by a saturation function.
The specific dechlorination rate was not related to PCB 61 concentration by a saturation function as reported previously but was related to the aqueous PCB concentration by a linear function from the lowest to the highest PCB concentration tested.
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In this paper, this problem is removed by using a saturation function with a high slope, as an approximation of the signum function.
In the absence of post-processing of the data by passing through a saturation function, the mean square error of prediction of the linear regression models become significantly worse.
The proposed sliding mode control strategy eliminated the chattering phenomenon by replacing the sign function with a saturation function, and by replacing the constant coefficients in the reaching law with adaptive ones.
Furthermore by adding an integrator and incorporating a saturation function in the control law, the chattering phenomenon caused by the sign function is avoided.
To express the compensation by neutral substitutions, we arbitrarily used a saturation function β v/(γ + v) where β and γ are parameters.
Therefore, this analysis does not include a saturation function for the omega-3 FA benefit.
This method extends the conventional quadratic programming control allocation by penalizing the previous step before sampling intervals at a lower cost, and also the actuator magnitude and rate limitation are considered simultaneously by an auxiliary saturation function.
To improve the chattering induced by the traditional sliding mode control and guarantee the reachability of the system, a specific saturation function with dynamic boundary layer is proposed to replace the sign function in the preceding control law.
Meanwhile, a new saturation function is introduced to solve the singular problems of the controller.
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