Series-parallel mechanical circuit synthesis of a positive-real third-order admittance using at most six passive elements for inerter-based control

Synthesis of mechanical networks: the inerter

This paper is concerned with the problem of synthesis of (passive) mechanical one-port networks. One of the main contributions of this paper is the introduction of a device, which will be called the inerter, which is the true network dual of the spring. This contrasts with the mass element which, by definition, always has one terminal connected to ground. The inerter allows electrical circuits ...

Passive Admittance Matrix Modeling for Guitar Synthesis

In physics-based sound synthesis, it is generally possible to incorporate a mechanical or acoustical immittance (admittance or impedance) in the form of a digital filter. Examples include modeling of the termination of a string or a tube. However, when digital filters are fitted to measured immittance data, care has to be taken that the resulting filter corresponds to a passive mechanical or ac...

Minimal series-parallel network realizations of bicubic impedances

An important open problem in the synthesis of passive controllers is to obtain a passive network which realizes an arbitrary given impedance function and contains the least possible number of elements. This problem has its origins in electric circuit theory, and is directly applicable to the costeffective design of mechanical systems containing the inerter. Despite a rich history, the problem c...

COSPECTRALITY MEASURES OF GRAPHS WITH AT MOST SIX VERTICES

Cospectrality of two graphs measures the differences between the ordered spectrum of these graphs in various ways. Actually, the origin of this concept came back to Richard Brualdi's problems that are proposed in cite{braldi}: Let $G_n$ and $G'_n$ be two nonisomorphic simple graphs on $n$ vertices with spectra$$lambda_1 geq lambda_2 geq cdots geq lambda_n ;;;text{and};;; lambda'_1 geq lambda'_2...

Simulation of the Admittance Control Based Haptic Interface Device