Force Control of a Shape Memory Alloy Spring Actuator Based on Internal Electric Resistance Feedback and Artificial Neural Networks

Figures & data

Figure 1. Experimental setup.

Figure 2. Layout of the experimental setup.

Figure 3. Feedforward ANN to describe the relation between force and electric resistance.

Figure 4. Recurrent neural network to describe the relation between force and electric resistance.

Figure 5. Artificial neural networks trained to work as controller model.

Table 1. Values of the correction factor $\alpha$ according to the percent error between the measured force and the reference force

Percent Error	Correction Factor $\alpha$
error $>20\mathrm{\%}$	$0.02$
10%$<$ error $<20\mathrm{\%}$	$0.015$
5%$<$ error $<10\mathrm{\%}$	$0.01$
1%$<$ error $<5\mathrm{\%}$	$0.005$
error $<1\mathrm{\%}$	$0.002$

Figure 6. Block diagram of the simplified predictive controller.

Figure 7. Block diagram of the closed loop system control.

Figure 8. Example of a training experiment of the feedforward ANN that works as sensor with one hidden layer.

Figure 9. Example of a training experiments of the feedforward ANN that works as model to the controller with one hidden layer.

Table 2. MSE values of the test experiments for the trained neural networks

ANN	MSE
ANN used as sensor	$6.25$
ANN used as model	$1.21$

Figure 10. Force control in a SMA spring using the designed simplified predictive controller based on artificial neural network. Desired force, ANN estimated force and experimental force as function of time.

Figure 11. Force control in a SMA spring using the designed simplified predictive controller based on artificial neural network. Current passing through the spring as a function of time. Data are related to the specific experiment given in Figure 10

Figure 12. ANN force error and force sensor error as function of time.