Search results for "Cubic function"
showing 4 items of 4 documents
On stability and robustness of Virtual Torsion Sensor (VTS) for flexible joint robots
2016
The so called ‘Virtual Torsion Sensor’ (VTS) has been introduced in pervious works for flexible joint robots without sensing of the joint output states, i.e. link position and velocity. Since VTS is incorporated into the feedback control loop, so as to improve the links' positioning accuracy, the related stability is crucial for the overall control design and robust operation of VTS. In this paper, we analyze the stability of including VTS into the feedback loop while assuming the predicted joint torsion is gained by the proportional term of the underlying motor position feedback control. We start our consideration by an ideal case of the linear joint stiffness, first assuming the measured …
Biorthogonal Multiwavelets Originated from Hermite Splines
2015
This chapter presents multiwavelet transforms that manipulate discrete-time signals. The transforms are implemented in two phases: 1. Pre (post)-processing, which transforms a scalar signal into a vector signal (and back). 2. Wavelet transforms of the vector signal. Both phases are performed in a lifting way. The cubic interpolating Hermite splines are used as a predicting aggregate in the vector wavelet transform. Pre(post)-processing algorithms which do not degrade the approximation accuracy of the vector wavelet transforms are presented. A scheme of vector wavelet transforms and three pre(post)-processing algorithms are described. As a result, we get fast biorthogonal algorithms to trans…
Spectrum of composition operators on S(R) with polynomial symbols
2020
Abstract We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum reduces to {0}, while the spectrum of any non mean ergodic composition operator with a polynomial always contains the closed unit disc except perhaps the origin. We obtain a complete description of the spectrum of the composition operator with a quadratic polynomial or a cubic polynomial with positive leading coefficient.
Programmable VLSI cubic-like function implementation
2006
An analogue VLSI implementation of a cubic-like function is presented, whose design is focused to reduce the circuit complexity. Simulations show that the V–I characteristic of the circuit resembles a cubic function, which can be easily adjusted by changing the bias parameters.