Digital Feedback System for Orbit Stabilization at theSIBERIA- 2 Light Source
A.Batrakov, S.Kuznetsov? , E.Levichev, V.Sajaev, V.Shilo
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia?
Kurchatov Institute, Moscow 123182, Russia
Abstract
An implementation of global/local feedback system on the 2.5 GeV SIBERIA-2 storage ring is reported.
This project is based on parallel data handling in BPM modules and VME crate for communication and magnet
correction control. We present special own-made beam position monitor data acquisition module, which includes
ADC, DSP TMS320C31 and high-speed serial link. Paper describes software for simulation of feedback control
and digital filtration. The motivation, approaches, results and future plans of this project are discussed.

1INTRODUCTION

In the design of a high-brightness light source, the electron beam emittance is a parameter of prime importance.
Any vibrations that lead to distortions in the closed orbit will result in a larger effective emittance. Together withthe brightness reduction, unwanted beam motion that causes the incident light position and angle to variy candegrade the experimental advantages of synchrotron radiation.
SIBERIA-2 is a dedicated light source with an electron energy of 2.5 GeV that was developed by the Budker
Institute of Nuclear Physics (Novosibirsk) for the Kurchatov Institute (Moscow) and commissioned at the beginning of 1995 in Moscow [1]. The typical beam stability tolerance for modern light sources is about 10% of thebeam size and divergence. For SIBERIA-2 this criterion means that we have to position the beam orbit accurately
to the 10-15 µm level. An active feedback system, which detects and counteracts undesired beam fluctuations
by correcting the closed orbit, is essential to achieve the necessary beam stability [2]. Potential sources driving
the variation in electron beam are: ground vibrations, magnet power supply ripple and thermal drift. A specificfeature of the low-emittance light source magnetic lattice is the significant amplification factor for any mechanicalvibrations of the magnetic elements. For example, for SIBERIA-2 due to the strong focusing, quadrupole lensmotion will transfer to beam motion with the amplification factor (rms) Mx,z ' 30. To stabilize the orbit oscillations, a fast digital feedback system is proposed. A single module composed of a DSP (digital signal processor)
board together with 4-channel 10-bit ADCs and 12-bit DACs has been developed. The module was linked to a
standard pick-up station and the beam measurements which are necessary to design the feedback system (suchas the low-frequency beam noise spectrum, system transfer function, etc.) were performed. A reference modelthat includes the real measurement results was prepared to test the beam stabilizing system. Using this model, aclassical PID algorithm was implemented and a significant reduction of modelling beam motion was achieved ina frequency bandwidth up to 60 Hz.

2 LOCAL FEEDBACK SYSTEM
The local feedback system is intended to stabilize the beam at a single orbit point (where the radiation is emitted)
without disturbance of the remainder of the beam trajectory. We use digital signal processing to avoid the problems
connected with analog circuits, such as drift, offset, etc. and to increase the flexibility of the system. The local
feedback system consists of a fast digital controller, an existing pick-up station, three steering magnets and power
supplies. A block diagram of the feedback system is shown in Fig.1. The controller is a DSP system which iscomposed of a 32-bit floating point TMS320C31 board, a 4-channel ADC board with 10-bit resolution and a 3channel DAC board with 12-bit resolution. The sampling rate of the system is 2.5 kHz. The sampling period
may be divided into three parts. During the first part the ADC provides the measurements of 600 turns of thebeam (414 nsec per turn) and stores the data into the memory. Then the TMS computes the average beam centroidcoordinates for the vertical and horizontal planes. This procedure provides us with a significant electronics noise
reduction and enhanced accuracy in comparison with a single ADC reading. During the third part the output signal
is produced using the PID controller and the system transfer function, and the steering magnets make a closed
orbit bump to cancel the beam position displacement detected by the monitor. A digital bandlimiting filter (BLF)
is inserted into the loop before PID controller for stability reasons.

.
Figure 1: Block diagram of the closed loop.
The transfer function of the feedback system is composed of two components: G(z) which corresponds to thecontroller and H(z) which describes in the z-domain the transfer function of the rest of the system. In the case ofSIBERIA-2 the last term is mainly determined by eddy currents in the aluminum vacuum chamber. To determine
this transfer function we have measured the attenuation of the corrector field by the vacuum chamber with a low
electron current. The electron beam was excited by a sinusoidal current in the frequency range of 0 to 150 Hz; thebeam displacement was measured at the monitor and an FFT of this signal was performed. Fig.2 shows the transfer
function of the system with the controller excluded. One can see that at a frequency of 100 Hz the attenuation isabout -20 dB.

.
Figure 2: Amplitude- frequency dependence of a system consisting of corrector magnet and vacuum chamber of
the SIBERIA-2.
The digital filter function of the PID controller G(z) is decided by the control program. We use a classicalPID controller algorithm with anti-windup reset and limitation of derivative gain [3]. In the z-domain G(z) can bewritten as:
KiG(z) = Kp ++ Kd (1 − z−1 ),(1)1 − z−1
where Kp , Ki , and Kd are the proportional, integral, and derivative constants of the controller. A control program
based on the PID controller algorithm was coded in C and downloaded to the DSP. The feedback system wastested with the model that takes into account the results of response measurements that was done at the SIBERIA2 (Fig.2). To describe the vacuum chamber influence, a digital filter H(z) with four poles and four zeros wasdeveloped and implemented in the simulation code. The noise attenuation obtained from the simulation is plottedin Fig.3. It can be seen that at a frequency of 10 Hz the attenuation is around -30 dB, while for 60 Hz this value
is decreased to -10 dB. For this test, the controller coefficients were: Kp = 1.0, Ki = 0.003, and Kd = 8.0.

.
Figure 3: Noise attenuation of the closed loop with Kp = 1, Ki = 0.003, Kd = 8 and Ts = 0.0004.

3 GLOBAL FEEDBACK SYSTEM
A global orbit correction system includes 24 BPMs and 48 correctors in each plane. The global orbit correction
may be considered as the extension of the local feedback correction after using the technique of singular value
decomposition (SVD) [4] of the response matrix Rij that connects the beam motion at the i-th pick-up station withthe changing of the j-th steering magnet strength:
Rij =pβ βi j2sinπν

cos(|ψi − ψj | − πν ),(2)where (βi , ψi ) are the beta and phase functions for i-th beam position monitor, and similarly for j-th corrector(βj , ψj ), and ν is the betatron tune. The response matrix is usually obtained by reading beam position displacement
while varying the corrector strengths one by one. SVD reconfigures the BPMs and correctors into the same numberof "pseudo" BPMs and "pseudo" correctors. In this new configuration space each BPM is coupled with a single
corrector and vice versa. For each "BPM-corrector" pair the solution to the problem can be found by the method
described above for the local feedback system. Then the backward transformation lets us know the strengths of
the real correctors. As in the SVD technique, only matrix transformations take place so it looks very attractive toimplement this method in a DSP.
At the local level, each BPM station electronics includes a 4-channel ADC and a DSP TMS320C31 whichis connected via a serial data link with a Central Processor Board (CPB), located in a VME crate. The CPB,
where we expect to use a TMS320C40, treats all the information and produces the output signal through a DAC
to the corrector power supplies. The work of the CPB module includes the communication of the C40 with every
BPM station. The performance of the C40 allows us to operate with the expected dataflow. We propose using aMC68030 or MC68040 VME master processor under the OS-9 operating system to provide the supervisory, I/Oand file managment functions. The system software for OS-9 has been developed.

4 DIGITAL SIGNAL PROCESSING
The intelligent BPM controller is based on the TMS320C31-40 Texas Instruments floating point DSP. The structureof the controller is shown in fig.4. The DSP has 32 KWords of local static memory and 32 KWords of dual portedmemory (DPM). Both memories have an access time of 50ns. The DPM is shared by the processor and ADCs. The.
Figure 4: Structure of the DSP controller.
useg of a DPM allows the ADC to write the data directly to the processor address space. This allows the use of theADC data without an additional time penalty for data transfer. Peripherial registers to control an external board
with a programmable delay generator, DACs and sample-and-hold registers are mapped into the DSP addressspace. A 64 kbyte ROM contains the primary bootloader and some application codes. These codes can be loaded
into local memory during program execution. All on-board devices are managed by a dedicated control unit,
implemented inside the INTEL Flex Logic PGA. The hardware interrupts are used by the DSP to synchronize theaplication software with external events. Interrupts when the ADCs have data for writing to the DPM and when
the DPM is full are possible.
Ten-bit ADCs with common simultaneous synchronization and a maximum sample rate of 15 million samples
per second are installed on the small piggy-back module at the moment. The six least significant bits in the DSP
are reserved to increase ADC’s resolution in future without software modification. The control unit drives theDPM address bus during the write process of ADC data to DPM.

Vertical beam position (mm)Kick#13, vert. motion

FFT of beam position

235

130

025-1
20-2
15-3
10-4

5-5-6.

00400

800

1200
Turns

1600

2000

.

00.05

0.1
0.15
Vert. betatron tune

0.2

0.25

Figure 5: Beam position as a function of revolution number and its Fourier transform after vertical kick.
The INMOS serial link interface IMSC012 is used to provide I/O functions with the host computer and code
downloading with a physical data rate of 10 or 20 Mbit/s. All signals can be transmitted/received up to a distanceof 200 meters via 50 ohm coaxial cable using a home-made interface. The link speed for this distance is 10Mbit/sec. Choice of the INMOS serial data interfaces allows the use of the transputer host software to load DSPs
and to implement host I/O functions without development of additional host hardware or software.

In addition to the feedback system development, the DSP board provides the possibility of using various beamdiagnostic techniques. Fig.5 displays the sampled signal as a function of revolution number and its discrete Fouriertransform after the beam was excited vertically by fast kicker. The subsequent decay is clearly seen. This modecan be used for experimental nonlinear phase space study and dynamic aperture investigation. We expect that turnby-turn measurements of beam position and current can be useful for the investigation of fast processes: beamloss during injection, ion accumulation, some kinds of coherent instabilities, etc. Fig.6 demonstrates the injection
into the VEPP-3 storage ring. A "slow wave" corresponds to the energy oscillations. Due to the high computation
capability of the DSP (2.5 ms for a 1024 point FFT) we can perform the various algorithms for signal treatment
and investigate dynamic processes.
Inj#S31, hor. motion
10Hor. beam position (mm)98765430.

400

800

1200

1600

2000

Turns

Figure 6: Injected beam: horizontal position vs. turn number.

5 Conclusion and acknowledgments
The development of the orbit correction feedback system for the SIBERIA-2 light source is in progress. The homemade DSP module which combines a TMS-processor and ADC and DAC boards was tested with the electron beamusing the existing pick-up station. The necessary measurements of the system response, including the influenceof the vacuum chamber, corrector magnet and power supply were carried out. A model of the full system wasdeveloped and a PID-controller was implemented in that DSP. The results of the simulation indicate an adequate
suppression of the beam motion. We expect that the steering magnet and power supply unit with an improved
bandwidth (up to 250 Hz) will be manufactured by the end of October and the total feedback system (in a localmode) will be tested with beam by the end of 1995.
The authors would like to thank Dr. A.Kalinin and Dr. V.Smaliuk who kindly help them to carry out the orbit
measurements and also to Dr. S.Kovalev for developing the bootloader for the DSP.

References[1] V.N. Korchuganov et al., NIM 208 (1983), pp.11-18.
[2] J.N.Galayda, Y.Chung, and R.O.Hettel, in "Synchrotron Radiation Sources - A Premier", ed.H.Winick, World
Scientific, 1994, pp.344-376.
[3] K.J. Astrom and B. Wittenmark (1990): Computer Controlled Systems -Theory and Design, second edition,
Prentice-Hall, Englewood Cliffs, NJ.
[4] W.Press et al., Numerical Recipes in C, Cambridge University Press, p.60, 1989.