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Zhuk said that Rybak and a friend then left the square, tracking away from its Lenin statue, and headed towards the city's Palace of Culture.
The control filter in the IMC controller was a digital FIR device designed to minimize the expectation of the mean square tracking error.
It is proved that the design scheme ensures that all the error variables are bounded in probability while the mean square tracking error becomes semiglobally uniformly ultimately bounded SGUUB) in an arbitrarily small area around the origin.
Stability analysis based on Lyapunov functions proves that all the error variables are bounded in probability; simultaneously, the mean square tracking error enters in finite-time in an arbitrarily selected small region around the origin wherein it remains thereafter.
Experiments on the constructed parallel kinematic machine show that the proposed two-loop controller can successfully eliminate the effects of the variant friction force and achieve high positioning accuracy with a mean square tracking error within 0.02 mm, which is superior to that of the H∞ controller (0.15 0.28 mm), the PD controller (0.11 0.22 mm) and the PD controller with DOB (0.09 0.19 mm).
Finally, three given tasks, i.e., rhombic path, straight-line path and square path tracking tasks, are fulfilled by three-link, four-link and five-link planar robot arms, respectively.
It is shown that the closed-loop system is stable and the mean-square tracking errors can be made arbitrarily small by choosing design parameters.
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The servo system has both a millimeter operating range and a root mean square (RMS) tracking error of about 80 nm for a circular trajectory.
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CEO of Professional Science Editing for Scientists @ prosciediting.com