Impedance and actuation models

We first perform Laplace transform for the time variable of p x,z,t) (noting the independence of p from the y coordinate) in (4.9) and convert the PDE into the Laplace domain  

By assuming symmetric charge distribution about x = 0, we obtain the solution to (4.12) as 

If we ignore the surface resistance of IPMC, the boundary condition for (j) can be easily set as 

we obtain the impedance for the special case that neglects surface and through-polymer resistance (i.,e, with the Dynamics of Ion Movement block in Fig. 4.3 only)  

As illustrated in Fig. 4.4, a cascade structure is taken for the actuation model. Here H s) represents the transfer function from the actuation voltage y(s) to the tip displacement w L, s) under the actuation-induced stress, 

---

Experiments have been conducted to validate the impedance and actuation models for IPMCs. The experimental setup is illustrated in Fig. 4.5. A cantilevered IPMC beam was placed in a small water tank and its tip displacement was measured with a laser displacement sensor (OADM 20I6441/S14F, Baumer Electric). The IPMC was subject to a voltage input generated from a dSPACE system (DS1104, dSPACE Inc.), and its current was measured for the validation of the impedance model. 

---