Mathematical investigation of the stability condition and steady state position of a pneumatic artificial muscle - Mass system

In this paper dynamics of an artificial muscle (PAM) - mass system is investigated. During shortening or lengthening of the PAM the position of the mass connected with PAM is varying. The aim of the paper is to consider the positioning of mass. The force produced by PAM is experimentally investigated and mathematically described. In the paper the influence of the pressure in the PAM on the stability of positioning of the mass is investigated. The steady state solution is given in the form of Lambert W-function. In the paper analytical procedure for solving differential equation of motion of PAM - mass system is introduced. The solution of the nonlinear differential equation is assumed to be periodic with time variable amplitude and phase. In the paper a numerical example is considered. The analytically obtained approximate solution is compared with numerical one. It is concluded that solutions are in good agreement. One of the most important result of investigation is that, based on the analytical results, we are possible to predict the steady state position of the mass. Besides, if the position is known the prediction of PAM's pressure is plausible.