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Firstly, the dynamic model for APF is build in which both the system parameter variations and external disturbance are considered.
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Specifically, we prove (i) that the same conditions that guarantee the stability of the system also ensure that the controller attains a desired level of performance (quantified in terms of the admissible deviation of the HBR from the prescribed profile) and (ii) that the controller is robust to bounded perturbations both in the system parameters and the control input.
This method allows to identify both the system parameters and the friction force coefficients.
Next, three identification procedures, which allow estimating both the system parameters and the friction model coefficients, are introduced.
The adaptive control scheme is able to compensate for the uncertainties arising from both the system parameters and the actuator failures.
A step-by-step identification procedure is subsequently introduced allowing the estimation of both the system parameters and the friction model coefficients.
However, the behaviour of the beam is shown to change significantly depending on both the system parameters and type of constraint.
which depends on the system parameter.
The system parameter settings are shown in Table 3.
Increase in the values of one or both of the system parameters 'stiffens' the system and results in increase in the frequency parameter.
This adaptive law also provides both the estimates of the system parameters and external disturbances such that a prior knowledge of the spacecraft inertia or boundedness of disturbances is not required.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com