Figure 4.1: Experimental set-up.
An experimental set-up has been developed for measuring the electrical resistance of the SMA and the displacement of the SMA actuated systems. For linear and non-linear sys- tems, same experimental set-up has been used. The experimental set-up, as shown in Fig. 4.1, comprises of a data acquisition system (DAQ)-DS1006©dSPACE, a DC programmable power supply (6642A from Agilent), a laser displacement sensor (opto NCDT-1402-100 from Micro- Epsilon), a voltage divider circuit and a PC having SIMULINK©MathWorks installed. De- tailed description of each of these equipments are provided below.
(a) dSPACE DS1006: dSPACE (DS1006), shown in Fig. 4.2a, is a real time controller, having an extension box, referred as DS1006 controller board. The dSPACE hardware may be connected to the desktop-PC through bus interface or via Ethernet. The I/O board of DS1006 contains 20 analog input ports (the yellow box shown in Fig. 4.2a), out of which three ports have been used in the experiment to acquire the analog voltage signals from different sensors. Among these ports, one is occupied by the displacement sensor and the rest are connected to the voltage divider circuit, discussed later. Out of the 8 analog output ports (the blue box shown in Fig. 4.2a) on the controller board, one is used to send the voltage signal to be applied across the SMA wire. The complete working principle of dSPACE is presented in Fig. 4.2b. To make use of the dSPACE, a Simulink model has to be developed, which is connected to the dSPACE hardware through I/O interfaces, provided by dSPACE’s RTI (Real-Time Interface). The Real-Time Workshop, generates the C code automatically from the model. The cross compiler compiles the C code and links the object files and libraries into an executable application for real-time processor. The generated real-time application is downloaded to the dPSACE hardware using Control Desk. The processed signals are acquired accordingly using the I/O board for real time application.
(b) Programmable Power Amplifier: The programmable power supply (PPS), 6642A from Agilent, shown in Fig. 4.3a, is used to amplify the analog output signal from DS1006, before it is applied across the SMA. It is called PPS because, in this power supply, the output voltage and current can be adjusted by the user, by using the knobs or buttons, provided at the front panel of the power supply. Depending on the applica- tion and system requirements, voltage and current can be set to any values in between the minimum and maximum rated value. The PPS can be used in two different modes namely, voltage control mode and current control mode.
(a)
(b)
Figure 4.2: (a) dSPACE with DS1006 processor and I/O board and (b) schematic of the working principle of dSPACE.
• Voltage Control Mode : In the voltage control mode, the power supply main- tains a constant output voltage as current can vary from 0 to maximum rated current (10 A). In this mode, the power supply provides an output voltage proportional to input voltage.
• Current Control Mode : The working principle of the current control mode is opposite in comparison to that of the voltage control mode. In this mode, the power supply delivers an output current, which is proportional to an input voltage.
In this work, the voltage control mode has been used for all the experiments. The power supply has an input voltage range of 0 to -5 V and output range of 0 to 20 V or 0 to 10 A, respectively; offering a gain of ‘4’ during voltage control mode and ‘2’ for current control mode. The analog signal coming from the I/O board of dSPACE (DS1006) is applied to the input port of power amplifier, as shown by the green box in Fig. 4.3b . The power amplifier amplifies the signal 4 times and is sent through the output port, presented in the same figure, by the yellow box. The amplified voltage signal from the output port is applied across the SMA, so as to induce resistive heating of the wire and raise the temperature of the same.
(a)
(b)
Figure 4.3: (a) Front and (b) back panel of the DC programmable power supply.
(c) Laser Displacement Sensor: A laser displacement sensor, opto NCDT-1402 - 100, Micro-Epsilon, Germany, as depicted in Fig. 4.4, is used to measure the displacement
of the SMA actuated system. The sensor has a measuring range of 0 to 100 mm, with a resolution of 10µm and provides an analog output voltage of 1 to 5 V. The analog output voltage (Vout) of the displacement sensor is acquired using one of the analog input ports of DS1006. From the output voltage, the displacement of the system is calculated as,
δm = 25(Vout−V0) mm (4.1)
Here,V0is the analog voltage signal obtained from the displacement sensor correspond- ing to its initial position with respect to the object.
Figure 4.4: Laser displacement sensor (opto NCDT-1402-100).
(d) Voltage Divider Circuit: To measure the electrical resistance of the SMA wire during phase transformation, a simple voltage divider circuit is designed and fabricated. The schematic of the circuit is shown in Fig. 4.5. Here the SMA wire, whose electrical resistance has to be measured, is serially connected with a known resistance (R0). In this work, R0 = 5 Ω is taken. The total voltage drop (VT) across the SMA wire and the known resistance R0, and the voltage drop (VSM A) only across the SMA (RSM A), are acquired using two analog input ports of DS1006. From these two voltages, the
electrical resistance of the SMA wire (RSM A) is calculated following,
RSM A =
VSM A
VT −VSM A
R0. (4.2)
R
SMAR
0V
SMAV
0V
TFigure 4.5: Schematic of the voltage divider circuit.
At each time step, the measured electrical resistance is used in the developed EKF model to have the posteriori estimate of the stress and temperature of SMA wire.
4.2.1 Experimental Procedure
The schematic of the complete experimental procedure is depicted in Fig. 4.6. Here, SMA actuated linear spring is considered, for explaining the experimental procedure. The voltage profile required for SMA actuation is implemented in the Simulink. This voltage signal is then converted to analog form using dSPACE - DS1006 and is sent through the analog output port of the I/O board of DS1006. The output signal from dSPACE is applied to the input port of the PPS (shown by black wire (1)), amplifying the signal 4 times. The amplified voltage signal (VT) is acquired through the output pin of the PPS (green and red wire) and is applied across both the SMA wire and resistance, (R0). The electrical resistance of SMA is measured using the voltage divider circuit following Eqn. (4.2), where the required voltages i.e. VT and
Figure 4.6: (a) Schematic of experimental set-up.
VSM Aare acquired through two analog input ports of the I/O board of DS 1006. The output of the displacement sensorVoutis acquired through the I/O board, from which the displacement is calculated following Eqn. (4.1). The voltage applied across the SMA wire (VSM A) and the measured electrical resistance of SMA (RSM A) are used in the estimator for estimating the stress and temperature of the SMA wire. From the estimated stress, displacement of the system is calculated and is compared with the experimental response; so as to verify the accuracy of the EKF estimation.