Synthesis of low‐complexity mechanical networks with constrained element values

Summary This paper investigates the synthesis problem of one‐port mechanical networks consisting of one damper, one inerter, and a finite number of springs, where the damping coefficient and inertance are some values in given intervals. Due to the construction limitation, the element values of dampers and inerters are usually required to be constrained in certain ranges instead of any positive values. A necessary and sufficient condition is derived for any positive‐real admittance to be realizable as such class of networks, which is in terms of the coefficients of the admittance and the upper and lower bounds of element value constraints. Moreover, the corresponding synthesis procedure is presented based on the derivation process and realizations of three‐port spring networks. Finally, numerical examples are given for illustration. The results of this paper can be utilized in the design of inerter‐based mechanical control systems. This paper solves the realization problem of any positive‐real admittance as a one‐port mechanical network containing one damper, one inerter, and a finite number of springs, where the damping coefficient and inertance are constrained to be some values in given intervals. A necessary and sufficient condition for the realizability is presented in Theorem 2, and the corresponding realization procedure is presented in Procedure 1. In addition, numerical examples are presented to illustrate the results.