BEST System Identification Toolkit User s Manual

Transcription

1 CAEN ELS s.r.l. July 2017

2 Contents 1 Document Revisions 4 2 Introduction 5 3 Installation 6 4 Hardware overview 7 5 Software overview Configuration tab Sweep parameters Channel selection Amplitude and offset control BPM scaling Plots Interaction Import and export Raw data viewer Identification Examples A Amplitude and phase calculation 20 2

3 List of Figures 2.1 System Identification setup overview Desktop icon BEST Central Unit hardware Main window Configuration tab Amplitude and phase plot Drag-to-scale Raw data viewer Identification tab Ident (debug) tab Model-fitting example (1st order) Model-fitting example (higher order)

4 Chapter 1 Document Revisions Document Revision Date Comments July 2017 Initial release 4

5 Chapter 2 Introduction From the firmware version 1.2 upwards, BEST Central Unit can act as a function generator, providing a sinusoidal stimulus to the beamline. BEST System Identification Toolkit makes use of the function generator capability to measure the frequency response of the system. The measurements are displayed in the graphical user interface, can be exported in CSV file and can also be used in system identification with user-defined model. Figure 2.1: System Identification setup overview 5

6 Chapter 3 Installation The BEST System Identification Toolkit can be downloaded from CAENels BEST repository. Procedure: 1. Connect BEST Central Unit to the internet. 2. Open Terminal (Ctrl + Alt + T) 3. Update information about new packages: sudo apt-get update 4. Download and install System Identification Toolkit sudo apt-get install best-sys-id System identification Toolkit will be installed and a shortcut icon will be created on desktop, as shown on Figure 3.1. Figure 3.1: Desktop icon 6

7 Chapter 4 Hardware overview The Figure 4.1 shows a overview of BEST system when used in function generation mode. Figure 4.1: BEST Central Unit hardware 7

8 There is an Nios II CPU running on the FPGA board in the BEST Central Unit. In function-generation mode the Nios II controller CPU runs a function generation routine. The routine updates the accumulator with 50 khz rate with an user-settable increment. The accumulator is then used to calculate sine and cosine values. The sine and cosine values are forwarded to DMA, to be used as in-phase and quadrature signal. The sine value is also multiplied with amplitude and summed with offset, each independently settable per each channel, producing three setpoints. The three setpoints are then sent over UDP/IPv4 to PreDAC ( precision Digital-to-Analog Converter). PreDAC feeds the piezo drivers, which then drives the piezos on beamline optics, displacing the beam. The displacement of the beam is measured by a beamposition monitor (BPM), and the small currents produces by the BPM are measured with TetrAMM (4-channel ammeter). TetrAMM digitizes the data and sends the digital data over UDP/IPv4 to the FPGA in BEST Central Unit. The FPGA receives the data and calculates the beam position from the measured currents. The beam position is calculated as difference over sum, and it is normalized (i.e. it lies on the interval [-1, 1]). The measured currents, calculated beam position, function generator outputs, and in-phase and quadrature signals are captured with DMA and transmitted over PCI express to x86 computer memory, thus made available to applications. 8

9 Chapter 5 Software overview The Figure 5.1 shows the main window of BEST System Identification Toolkit. The interface consists of Configuration tab, Identification tab, Ident (debug info) tab, two plots for amplitude and phase, a list of all measured plots and controls for exporting and importing the measurements. Figure 5.1: Main window 9

10 5.1 Configuration tab Figure 5.2: Configuration tab Sweep parameters Configuration tab allows user configuration of the parameters of the frequency sweep. The function generator will perform a sweep with Length points, starting from Start freq and finishing at Stop freq. Sweep type can be either logarithmic or linear. The generation of frequency vector relies on numpy.linscale and numpy.logscale functions, with endpoint=true argument Channel selection The Output ch allows setting which position should be excited with a sine wave, all other channels will be set to Offset value. The Out PreDAC ch field indicates which PreDAC channel will be driven. Input ch fields selects which channel will be observed. The independent control of the two channels allow measuring both direct and parasitic response. These fields rely on configuration stored in /opt/caenels/best/config.ini which gets loaded to the FPGA at the startup by bestinitconf utility Amplitude and offset control Each of the three channels can have an amplitude and offset independently set by the user. Only one of the amplitudes in the function generator will be set different than zero, all the others channels will only output the offset value. Example: Let s say that amplitudes are set as [0.1, 0.2, 0.3], offsets are set as [3.0, 4.0, 5.0], channel 1 is connected to x position and channel 2 is connected to y position. 10

11 When performing the sweep with Output ch set to x, the PreDAC will on channel 1 output 0.1V sin(2 π f) + 3V, 4V on channel 2 and 5V on channel 3. When Output ch is set to y, the PreDAC will on channel 1 output 3V, 0.2V sin(2 π f) + 4V on channel 2 and 5V on channel BPM scaling In order to keep the FPGA digital-signal-processing modules as simple as possible, the position calculation is normalized (i.e. it lies on the interval [ 1, 1]). To provide a more meaningful information to users, BPM scaling checkbox can be enabled. When enabled, the position will be multiplied by BPM dimensions, stored in /opt/caenels/best/config.ini and configurable from BEST Local GUI (please refer to BEST ). 11

12 5.2 Plots The two plots show amplitude and phase of the device-under-test. The plots get updated with new points as the frequency sweep is taking place. Multiple plots can be shown; plots can be shown or hidden by checking and un-checking the checkbox in front of the plot name in Plots list. Figure 5.3: Amplitude and phase plot The amplitude plot is showing the data in log-log scale. The unit used for y axis is dbum, i.e. a gain against 1 um. 12

13 5.2.1 Interaction The two plots use PyQtGraph plotting library and provide a lot of possibility to interact with them, such as drag-to-scale, as shown on Figure 5.4. Figure 5.4: Drag-to-scale 13

14 5.3 Import and export The BEST System Identification Toolkit provides a method to export the data in CSV file and to also import the data from a CSV file. When exporting the data to CSV file, the raw data measurements are lost. To export one or more plots, select them in Plots list and press Export meas button. For each of the selected plots in Plots list, 3 columns are created: frequency (in Hz), amplitude (in dbum) and phase (in rad). The first line of the CSV file is a header line with the names of the plots. When exporting data, the software creates the names of the columns by appending _freq, _ampl and _phase to the plot name. Example of a generated file: pltname_freq,pltname_ampl,pltname_phase 10.0, , , , , , , , , , , , , ,

15 5.4 Raw data viewer Raw data viewer can be opened by selection one of the plots in Plots list on the right side of the main window and pressing the View raw data button. Figure 5.5: Raw data viewer Raw data viewer allows user to visualize the raw data from where the measurements are derived. On the left side of the window a list of all frequencies at which the measurements were performed as well as list of all data channels stored. Please note that BPM0 posx and BPM0 posy are normalized, regardless of the BPM scaling checkbox state. 15

16 5.5 Identification Figure 5.6 shows the Identification tab. It provides a method to configure the form of the model which is then fitted using a nonlinear least-squares solver. Figure 5.6: Identification tab The Nr of poles and Nr of zeros fields allow selecting number of poles and zeros in the model. Assuming causal systems are measured, Nr of poles should be greater than nr of zeros. Delay field allows setting the model delay and whether it is fixed or if it should be determined by measurements. It is suggested to set the delay value fixed. The model is defined as: Q+1 i=0 H(s) = exp( s T ) b is i P i=0 a is i where: T is the delay of the system, P is number of poles, Q is number of zeros, and a P is fixed to 1.0 To fit the model to measurement data, select one plot in Plots list and press Run button on Identification tab. User should also provide an initial guess for parameters a i and b i. 16

17 Figure 5.7 shows the Ident (debug) tab. This tab shows the inputs to and the outputs from scipy.optimize.least_squares function, which is used to fit the model to the measurement data. Figure 5.7: Ident (debug) tab 17

18 5.5.1 Examples Example of a model (violet plot) fitted over measurement data (blue plot) of a first order filter. Figure 5.8: Model-fitting example (1st order) 18

19 There is an synthetically-generated example available in /opt/caenels/best_sys_id/example/ to experiment with model-fitting functionality of BEST System Identification Toolkit. Figure 5.9 shows the result of model fitting. Figure 5.9: Model-fitting example (higher order) 19

20 Appendix A Amplitude and phase calculation The function generator creates 3 waveforms with user-defined amplitude and offset as well as in-phase and quadrature signals with amplitude 1 and offset 0. pos, fg i and fg q are signals captured with DMA from hardware. 1. Offset is removed from position pos 0 = pos mean(pos) 2. I and Q components are calculates as: I = 2 mean(pos fg i ) Q = 2 mean(pos fg q ) 3. Amplitude and phase are calculated as ampl = I 2 + Q 2 /fg ampl ph = arctan2(q, I) where fg ampl is (user-defined) output amplitude of function generator. 4. The values shown on the plots are represented in dbum: ampl[dbum] = 20 log 10 ( ampl[um] 1um ) 20