Optimization of Synchrotron Beam Alignment using a Linguistic
Control Scheme
Roberto Pugliese and Roberto Poboni*Electronic Technology Laboratory, Scientific Division, Sincrotrone Trieste.
*Department of Electrotechnics, Electronics and Informatics, University of Trieste.
Abstract: The project deals with the design and the implementation of an adaptive controller which optimizes thebeam alignment at the SuperESCA beamline, using a behavioural model based on fuzzy logic. The operating
environment is an extension of the FuzzyCLIPS1 expert system shell, integrated in the ELETTRA Beamline
Control System.

1. INTRODUCTION
The Sincrotrone Trieste is a research laboratory which built ELETTRA, a “third generation” machine, witha 2GeV state-of-the-art storage ring. ELETTRA is a high brilliance synchrotron radiation facility covering a large
spectrum of wavelength from the VUV to hard X-ray region. This radiation can be used for chemical, physical andbiological experiments.
According to the requirement of the experiments, the light has to be collimated, monochromatized andfocussed on the sample under test; this is realized by a highly sophisticated beamline working in ultra-high vacuum.
The Super-ESCA beamline [1] has been designed for high-resolution core-level spectroscopy using soft x-ray
synchrotron radiation. It receives the light from an undulator in the storage ring ELETTRA. The tunability of thisinsertion device and the connected SX700 monochromator allow experiments in the photon energy range 1001400eV. This beamline, operational since 1994 has shown a resolving power varying from 10000 to 8000 forphoton energies between 240 and 850 eV.
The performance of the Super-ESCA beamline is strongly affected by the alignment conditions i.e. all theoptical components must be set to optimize the flux and resolving power at the experimental station.
The propagation process of the photon beam through the beamline has a complex structure. Many optimization
schemes can be applied under the assumption of the existence of a mathematical model of the process [12]. However
such a model may be too complex, it may not be precise or it may not even exist.
Soft Computing methodologies such as neural networks, genetic algorithms, and fuzzy sets theory have been applied
to a broad class of such real-world problems. In this work, optimizing control is performed by using a rule-based
look-up table which can be learned from operating experience without the need of a process model.

1 FuzzyCLIPS was developed by the Knowledge System Laboratory, National Research Council of Canada

2. THE BASICS OF FUZZY LOGIC
Fuzzy logic introduced by Lofti Zadeh [2,3] brings reason to the vagueness found in human experiences orto the unclear boundaries in physical processes. For example, even a concept like "normal height" is difficult toexpress by standard "crisp" computing, but easily described by a characteristic function that has a continuous grade
between 0 and 1. This "fuzzy set" or membership function can take various shapes (bell-curve, trapezoidal,
triangular, and other).
Rule 1:

if

X is X1

Y is Y1,

Y is Y1

X is X1

1andthen

Z is Z1
Z is Z1

10.4
0.2

00

Rule 2:
1

X is X2

if

X is X2

andY is Y2,

Y is Y2

then1

Z is Z2
Z is Z2

0.8
0.6

001

X is x

Y is yfuzzy inference inputs

0

center of gravity location
fuzzy inference ouput

Z is zFig.1: Stages of Fuzzy Processing

Fuzzy Logic theory allows one to work on a linguistic description of the reality, representing information bylinguistic variables. Linguistic variables are entities whose values are fuzzy sets. Fuzzy Logic represents a new
approach to system modeling. The first known applications of Zadeh's theory were reported by Mamdani [4,5] .

The stages of fuzzy processing are illustrated in Fig.1 for a simple case of two linguistic variables (X,Y)
combined by means of two rules to form the result Z. Inputs are compared to membership functions by a process
called "fuzzification", so a membership grade is assigned to each linguistic term. Logic combinations of linguistic
terms are then evaluated by application of Fuzzy Logic operators: usually the minimum grade of the conditions isselected as the fitness grade of the rule left-hand side. Fuzzy values of the rule right hand side are adjusted to reflect
the rule fitness grade and then combined with the fuzzy values of the other rules. Center of gravity or other averaging
methods are used for "defuzzyfication", that is, to obtain a single value for each output variable. Many
implementations of this kind of inference can be found in literature [9].
So far Fuzzy Logic has been exploited mainly in Knowledge Based Systems and in Control Systems [6-8].
We say that a control system is "fuzzy" when the value of the controlled variables is determined by the input signals
through a fuzzy inference. In the same way we talk about Fuzzy Optimization when the optimization process isdriven by fuzzy inference.

3. THE PROBLEM STATEMENT
The schematic diagram in Fig.2 is a simplified description of the beamline Super-ESCA. In the drawing
only the components relevant to the optical alignment are present; optical components are represented with roundedborder. A detailed discussion of each component of the beamline is beyond the scope of this document, but to feelthe complexity of the system requires a brief description of the beam path. As the synchrotron radiation beam leaves
the undulator, it passes through two photon Beam Position Monitors and then through the Double Slits where thecentral part of the beam is selected; it then reaches the Switching Mirror, a plane mirror used to switch between thebranch lines2 . Before reaching the SX700 Monochromator, the light beam passes the Prefocusing Mirror, acylindrical mirror which focusses the beam in the vertical plane onto the Entrance Slit. The Monochromator is themost complex optical component of the beamline, consisting of a plane mirror, a plane grating and an ellipticalfocusing mirror. The plane grating spreads the incoming radiation in the vertical plane according to energy. Only one
selected energy follows the right path to the elliptical mirror, which focusses the radiation on the Exit Slit. The
Refocussing Mirror, an elliptical mirror, refocusses the monochromatized light onto the sample in the ExperimentalChamber. A photo-diode supplies a signal proportional to the quantity of photons leaving the Exit Slit.
The complexity of the optical path makes it difficult to determine the equations relating the quality of thesynchrotron light spot at the experimental chamber with the position of the optical components of the beamline.
One may realize that the alignment optimization, that is the process of setting the positions of all the opticalcomponents to optimize the flux and resolving power at the experimental station, is a very difficult. In practice it isseveral hour job for a pair of trained operators.

2 The Super-ESCA and ESCA-microscopy beamlines share the so-called "front-end", i.e. the part of the beamline

from the source to the switching mirror.

Undulator
BPMs
DoubleSlits
SwitchingMirrorPrefocus.
Mirror
Entr.
Slit
Monocrom.
SX700
Exit
Slit
Photodiode
Refocus.
MirrorExperimental

stationFig.2: Simplified scheme of the Super-ESCA Beamline

The problem we have actually considered, a non-trivial subproblem of the global alignment optimization, can beformalized as follows: determine the positions of Prefocussing and Switching mirrors which maximize the flux ofphotons at the photo-diode, assuming that the Monochromator is aligned. Namely, we have considered only thedegrees of freedom of the mirrors which can be considered optically critical: the Pitch and the Roll angular positions.
Formally we have to find the maximum of the following function:y = f(x1,x2,x3,x4)
where y is the photo-diode current, x1 is the Switching Mirror Pitch, x2 is the Switching Mirror Roll, x3 is thePrefocusing Mirror Pitch and x4 is the Prefocussing Mirror Roll.

4. THE OPERATING ENVIRONMENT
The Beamline Control System [14] provides supervision and control of the beamline equipment: it has theresponsibilities to assure a "safe behaviour of the beamline" and to give the operator a uniform access to theinstrumentation.
The system has a distributed multi-layer architecture (Fig.3). The presentation level is based mainly on
UNIX graphical workstations (such as DEC-ultrix, DEC-alpha, HP9000): a synoptic interface implemented with
DataViews3 and Motif enables graphical navigation through the beamline instrumentation.

WSWSPC

RPC, TCP/IPBCSBeamlineEquipment

VMEEIBEIBEIBEIB

Fig.3: The Beamline Control System architecture

The core of the system, called BCS, is the process control level, based on VME embedded systems using theMotorola 68030 processor (MVME147) and the LynxOS real-time operating system. These two layers are connectedby an ethernet LAN via Remote Procedure Calls4. The equipment interface level, connected with the BCS by theVME bus, is based on standard data acquisition boards 5. The application software can be developed both at thepresentation level and at the process control level by means of well defined libraries.

3 Is a graphical visualization package developed by V.I. Corporation
4 In the current release the CERN network compiler has been used.
5 We have named such boards Equipment Interface Boards (EIB).

FuzzyCLIPS is an extended version of the CLIPS rule-based shell6 for representing and manipulating fuzzy facts andrules. In addition to the CLIPS functionality, Fuzzy CLIPS can deal with exact, fuzzy, and combined reasoning,allowing fuzzy and normal terms to be mixed freely in the rules and facts of the knowledge based system. Thesystem uses two basic inexact concepts, fuzziness and uncertainty.
We have developed an extended version of FuzzyCLIPS which allows one to perform the basic read andwrite actions on the BCS controlled variables. The optimization application was implemented at the process controllayer.

5. THE FUZZY OPTIMIZER
The design of the optimizer was guided by the domain knowledge of the expert operator and by the analysisof the qualitative behaviour of the objective function; an operational model of the beamline was implemented withthe Ray Tracing Shadow7 simulation program.

OCIa

A(k)

S(k-1)∆ y / ∆ x (k)FIuU(k)S(k)*D∆ x (k+1)+x(k)

Optical System

Fig.4: Simplified block diagram of the controller.

The optimization control scheme we have developed is a modified version of the linguistic control scheme developed

6 CLIPS was developed by the Artificial Intelligence Section, Lyndon B. Johnson Space Center, NASA.
7 Ray Tracing Shadow was developed by the University of Wisconsin.

by Procyk and Mamdani [10,11]. The independent variables, namely the mirror positions, are optimized in asequence determined by a knowledge based planner. Each variable is optimized by a sophisticated hill climbing
technique: a simplified block diagram is shown in Fig.4.
At each step the block F processes the slope of the objective function by performing normalization andfuzzification. The block Iu takes the normalized slope at the current and previous step and by fuzzy inference
provides the magnitude of the correction of the mirror position (angle change) which is then defuzzyfied by block D.
The direction of the correction is determined in the natural way by the sign of the current slope. If we call S(k) thenormalized slope and U(k) the angle change, a typical linguistic rule can then be written in the following form:

if S(k) is Si and S(k-1) is Sj then U(k) is Uh.

The fuzzy sets of the normalized slope and angle change are shown in Fig.5. The linguistic rule set can be

Membership grade

represented by the relation matrix or look-up table of Fig.6.

1.0ZS

M

0.00

0.20

0.40

VBB

0.5

0.0
0.60

0.80

1.00

Membership grade

Normalized slope

1.0ZVSSMB

VB

0.40

0.60

0.80

0.5

0.00.000.20

1.00

Normalized angle change

Fig.5: Normalized slope (S) and angle change (U) membership functions. The labels can be read as follows: Z aszero, VS as very small, S as small, M as medium, B as big and VB as very big.

We have also introduced an adaptive component in the fuzzy controller. The method described in Maeda-Murakami[13] consists of realizing an adjustment function which determines, depending on the operational conditions of thecontroller, a scaling factor for the angle change. As shown in the block diagram shown in Fig.4, the module Ia takes

the normalized slope at the current and previous step and depending on the operational conditions OC, determines byfuzzy inference the scaling factor A(k). A knowledge based module sets OC by observing the optimization process.

U(k)

S(k)

S(k-1)
n.a.

Z

S

M

B

VB

Z

VS

Z

Z

VS

Z

VS

S

VS

Z

VS

VS

VS

Z

M

S

VS

S

M

VSS

B

M

S

VB

B

B

S

VB

S

M

B

M

M

SFig.6: Linguistic control rules

An example of the behaviour of the controller with and without the adaptive component is shown in Fig.7; theperformance gain provided by the adaptive module is generally valuable.

6432
normaladaptiv e

1step

Fig.7 the behaviour of the optimizer

2927252321

19171513

1197

530

1

photo-diodecurrent(uA)5

6. CONCLUSION
We have implemented an adaptive controller which optimizes the beam alignment at the beamline SuperESCA by using a behavioural model based on the fuzzy logic. The system is now under test and its behaviour isquite satisfactory both on the simulator and in the field.
Further improvements could be obtained by using the beam status information provided by the BeamPosition Monitors; fuzzy logic could be used as a tool to implement a qualitative optical reasoning component.
The introduction of soft computing techniques can be considered a meaningful step in the extension of theapplication areas of the Beamline Control System.

Acknowledgements
Special thanks are due to the staff of the beamline Super-ESCA, in particular to Daniele Cocco and to the staff of theElectronic Technology Laboratory, in particular to Rudi Sergo and Fulvio Billè.

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