This week I focused on solidifying the relationships between the equations in my table of equations. I found another article by the authors I have been referencing throughout this entire process (http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=7864464). This article provided much more insight into the relationship between power, temperature, and output force. The article states that the temperature biases the force-strain profile in a linear manner; therefore, this is where the constant c (c = 2.31 mN/C degrees) comes from. It is the slope of the Force versus temperature graph. Thus, this constant allows for conversion of change in temperature to change in force.
Next, since temperature cannot be directly measured from the actuator, a relationship must be found between force and power. Temperature may be determined by power input (which can be directly controlled). Thus, there is a linear relationship between force and power.
In this equation Cth, lambda, and P(t) are known. T ambient is known. However T(t) is unknown, as is dT(t)/dt. Therefore, problems I have been running into include determining these values.
Another aspect that I have not yet dealt with is the issue of open loop versus closed loop force control. The article quantifies open loop force control with the following formula, in which s is time. I am trying to figure out whether this equation is relevant to developing a procedure and equation for creating the actuators.