Experiment

3.1 Improvement of IDM

Figure 3.1 and Figure 3.2 illustrate the previous and advanced structure of IDM. The disadvantage of previous one is that the counter-mass will vibrate up and down which may change the normal force of the slider when the piezoelectric element deforms rapidly. The behavior affects the contact friction between the slider and the guide surface and enormously increases the complexity of the system because frictional force is one of the important points. The vibration also causes inaccuracy in measuring. Now, a new concept of IDM is constructed to solve the problem. In the advanced structure of IDM, piezoelectric elements are fixed from end to end of the slider and the counter-mass. Oiless bearings are placed across the intermediate mechanism to prevent the piezoelectric element from vibration and reduce the friction between piezoelectric elements and the intermediate mechanism during deformation. Besides, the guide is used to yield IDM to walk step by step straightly.

As shown in Figure 3.3, P-840.10 preloaded LVPZT translators, used in IDM for experiment, are high resolution linear actuators for static and dynamic applications. They provide sub-millisecond response and sub-nanometer resolution. These translators are equipped with highly reliable multilayer PZT ceramic stacks protected by a non-magnetic stainless steel case with internal spring preload that makes them ideal for dynamic applications. The standard translator tip and base have tapped holes. Technical

notes are listed in Table 3.1.

3.2 Experimental Setup

Figure 3.4 and Figure 3.5 depict the overall structure and configuration with actual instrument for measuring the displacement of the piezoelectric actuator respectively. The photographs of the system and IDM are also presented in Figure 3.6 and Figure 3.7. In the experiment, the HP10705A interferometer with 10nm (0.4µin) resolution and 3MHz maximum data update rate measures the actual output displacement of IDM. The sampling time of the data is controlled by DSP module and then sent to HP10885A. The HP10885A Axis board’s primary function is to convert reference and measurement signals from an HP 5517C laser head and measurement receiver to a 32-bit digital position word. The unit of measurement associated with the position word is a fraction of the wavelength of the laser light being used. A conversion is required if the position must be known in some other units (mm, inch, etc.).

After conversion, the raw data is read by DSP module directly. The main functions of the DSP module are:

(1) to send signals to HP10885A to control the sequence of data sample and hold (8 bits digital output);

(2) to do data reading (32 bits digital input);

(3) to produce driving voltage waveforms needed in the experiment (8 bits DA) and send to IDM.

We achieve this goal by utilizing code composer studio (CCS) software

to integrate these tasks into a program which can be loaded to the DSP controller. Because of low driving voltage waveforms from DSP module (8 bits DA), a voltage amplifier is needed to amplify the analog signal from 0~2V to 0~100V to drive the piezoelectric actuator.

3.3 DSP Program Flowchart

The 2407A DSP controllers shown in figure 3.8 are designed to meet the needs of control-based applications. By integrating the high performance of a DSP core and the on-chip peripherals of a microcontroller into a single-chip solution, the 240xA series yields a device that is an affordable alternative to traditional microcontroller units (MCUs) and expensive multichip designs. At 40 million instructions per second (MIPS), the 2407A DSP controllers offer significant performance over traditional 16-bit microcontrollers and microprocessors. The 16-bit, low power, fixed-point DSP core of the 2407A device provides analog designers a digital solution that does not sacrifice the precision and performance of their systems. See details in Figure 3.9 and Figure 3.10.

Code composer studio (CCS) is a fully software integrated development environment (IDE) for building and debugging programs for the DSK (DSP Starter Kit), i.e. the DSP board. CCS integrates all host and target tools in a unified environment to simplify DSP system configuration and application design. This easy to use development environment allows DSP designers of all experience levels full access to all phases of the code development process.

The software is used for three phases in the overall DSP system design

process:

(1)Coding and building: writing code using the editor, creating a

‘project’, and compiling and linking.

(2)Debugging: syntax checking, probe points, break points (3)Analysis: statistics, benchmarking, real-time debugging

Figure 3.11 describes the complete flowchart of the DSP program. The processes are as follows:

(1) Start: The program starts.

(2) CPU will be initialized first. Then we set and enable time interrupt to define the sampling time.

(3) A while loop for DA control waveforms applying to the piezoelectric actuator is executed. The program waits for the time interrupt every 50 us (sampling rate = 20kHz).

(4) The program gets into time interrupt, the DSP module starts to read data by 32bits digital input.

(5) MSB Check: Because we do not know if an error occurs, the received data has to be checked first if an error occurs. The method provided from operating manual is to examine the most significant bit (MSB). If the MSB is one (true), it implies the data is correct. Otherwise, there exists an error. We should adjust all the experiments of the laser interferometer and see if the light status is ready especially the indicator of the receiver. Then restart the program again to step (1).

(6) Sign Check: The meaning of the second MSB indicates the sign of the position value; therefore it is sometimes called the sign bit. The sign bit zero (false) means positive and one (true) means negative position. Negative position needs to be calculated by 2’s complement. The position register is

saved to the buffer.

(7) End: The program ends.

(8) Measurement: After the program ends, the position register saved in the buffer can be transferred to the real world displacement. The following equation describes how position is calculated from the value in the position register:

number on

Compensati register N

Position

Position

λ

where:

λ

N = 64 when linear optics are being used

N = 128 when plane mirror optics are being used N = 256 when high resolution optics are being used

9997288 1 0

refraction . of

index s ' number Air

on

Compensati

Then the experimental results will be plotted into a time-position graph step by step continuously. These files can help us to compare the results of different driving waveforms.

3.4 Experimental Results

Figure 3.12 to Figure 3.15 shows the displacement of the counter-mass with 100V, 95% duty triangle input waveforms but different frequencies.

During the rapid phase of the input waveform, the position of the counter-mass suddenly drops to a bottom because the piezoelectric actuator contracts. The slider makes a big displacement at this point according to the

principle of the stick-slip device and the counter-mass follows the step, too.

The vibration of the slider caused by preload spring will continue little time when the slow phase of the input waveform is applying to the piezoelectric actuator. Thus, the position of the counter-mass linked to the slider will follow the reaction. At lower frequency, the position of the counter-mass becomes steady with the slow phase of the input waveform. As the frequency of input waveform increases, the effect takes place obviously. Steady rise of the position no longer exists.

The positioning of the mechanism we emphasize is on the slider. Take a look at Figure 3.16 to 3.19. These figures illustrate the displacement of the slider with 100V, 95% duty triangle input waveforms but different frequencies. The slider steps a little displacement at first resulting from the slow extension of the piezoelectric actuator. With the turning point of the input waveform, the piezoelectric actuator tends to return to the original length. Due to the rapid phase process, the piezoelectric actuator contracts so fast that the inertial force greatly exceeds the friction force and the slider starts to move. The internal spring preload of the piezoelectric actuator will make a mechanical vibration during the fast contraction, thus the slider accompanies the effect to converge to a steady state finally. One step is finished. By the operating cycle, IDM can walk step by step periodically.

Some problems about the frequency of the input waveform exist. If the frequency becomes higher, the convergence of every one step becomes worse because of the mechanical vibration of IDM. This brings about the difficulty of precise positioning. Therefore we should avoid using unreasonable frequency exceeding 500Hz.

100Hz, 95% duty triangle driving waveform is chosen as the standard of

positioning in the experiment due to the better stepping. Figure 3.20 and Figure 3.21 depicts the mean value of step of the slider and the counter-mass respectively. Each step is about 1um.

The forward movement of IDM with different input voltages is shown in Figure 3.22. It is easy to see that the step size increases as the input voltage increases since higher input voltage causes stronger inertial force to make a step. Conversely, IDM can also do the backward movement as introduced in section 2.4 while we change the duty of the triangle waveform. The measurement of the backward movement is shown in Figure 3.23.

3.5 Observation of Forward and Backward Movement

Figure 3.24 and Figure 3.25 plots the displacement of the slider with input frequency 100Hz but different amplitudes and duties. The step size increases obviously as the input voltage increases. It also depends on the duty of the input waveform. An extreme duty is selected to make a larger displacement due to the sudden inertial force is larger to overcome the friction force.

The forward movement of IDM is similar to the backward movement but little difference in step size. With same condition but converse duty, the step of the backward movement is larger than that of the forward movement. One possibility is to assume the friction between the bottom of IDM and the surface of the guide in forward and backward is quite different since the inaccurate manufacture of IDM. Another possibility may be the sudden stop of the principles of IDM illustrated in Figure 2.4. The difference between forward and backward movement results from the sudden stop of the

counter-mass which contributes to the displacement in the same direction or not.

3.6 Discovery of IDM

From several experiments, we found that the standard sine waveform during certain frequencies may let IDM move. It is surprised to break the normal convention of applying the asymmetric waveforms to drive IDM. We just need general sine waveform with certain frequency (about 1300Hz to 1600Hz) and lower voltage to drive IDM. The phenomenon may help us to do longer traveling. Figure 3.26 is a good example of movement by 50V, 1400Hz sine waveform input. Figure 3.27 depicts the velocity of the slider with various sine waveforms. IDM do not move anymore out of the range of the frequency.

With sine waveform input voltage higher than 60V in the range of frequency, the displacement of IDM quickly moves beyond the sensing range of the laser interferometer. We can not handle the displacement of IDM anymore by interferometer measuring system. The scene of walking even can be seen with a naked eye. Therefore, larger displacement positioning (mm, cm, etc.) is not the question as long as the characteristic is known well.