An IPMC (ionic polymer-metal composite) is a Nafion sheet plated with gold on both sides. An IPMC bends when an electric field is applied across its thickness. IPMCs have been used as robotic actuators in several applications and as active catheters in biomedical applications. With the aim of improving actuator settling times, a state-space model has been developed for a 20 mm 10 mm 0.2 mm polymer sample (Mallavarapu, 2001):
where u is the applied input voltage and y is the deflection at one of the material’s tips when the sample is tested in a cantilever arrangement.
a. Find the state-transition matrix for the system.
b. From Eq. (4.109) in the text, it follows that if a system has zero initial conditions, the system output for any input can be directly calculated from the state-space representation and the state-transition matrix using
Use this equation to find the zero initial condition unit step response of the IPMC material sample.
c. Use MATLAB to verify that your step response calculation in
Part b is correct.
