Tips & Tricks for Experimentalists 1 Noise and Servo Loops An introduction to the description and control of dynamic systems Dr. Uwe Sterr Physikalisch-Technische Bundesanstalt (PTB) AG 4.31: Unit of Length Bundesallee 100 38116 Braunschweig Paschenbau Room 118a Tel: 0531 592 4310 [email protected]
45
Embed
Noise and Servo Loops - uni-hannover.de · Noise and Servo Loops ... Description of Noise Random variable V(t) ... In an amplifier, its voltage and current noise add, depending on
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Tips & Tricks for Experimentalists 1
Noise and Servo Loops
An introduction to the description and control of dynamic systems
Dr. Uwe SterrPhysikalisch-Technische Bundesanstalt (PTB)AG 4.31: Unit of LengthBundesallee 10038116 BraunschweigPaschenbau Room 118aTel: 0531 592 [email protected]
MenueNoise• description• noise types• dynamic systems
Break• hands-on experience with spectrum analyzers
Feedback Control• feedback• stability• examples
• hands-on experience with spectrum analyzers
References, Books
Noise
• E. Rubiola, V. Giordano, K. Volyanskiy, and L. Larger, Phase and frequency noise metrology, arXiv:0812.0180, (2008)
• F. Riehle, Frequency Standards: Basics and Applications, Wiley-VCH 2004• Agilent/HP Technical Notes :
Optimum: Make controller Gain as large as possible!
Loop Gain – Stability Conditions
system A(f)
controller G(f) -
-
disturbance
correction
output Y(f)
error signal reference
Optimum: Make controller Gain as large as possible!
Limit: because of phase shifts, the system eventually will oscillate
Stability conditions: • Loop gain has to circle point -1 in the complex plane (Nyquist criterion)• Phase at unity gain frequency < 180°
K. J. Aström and R. M. MurrayFeedback Systems, An Introduction for Scientists and Engineers,Princeton Univeristy Press, (2011) online at http://www.cds.caltech.edu/~murray/amwiki/index.php/Main_Page
Stability Conditions – P controller
P-Controller
system + controllerloop gain
system
phase margin
system + controllersystem and
Stability Conditions – P controller
Proportional-controller:
• rather robust• fist approach
• remaining DC-error ~ 1/loop gain
Phase margins:90°
60°
45°
Systerm response
~ 1/loop gain 45°
From first test of servo with pure P-controller:increase gain until oscillations starts • critical gain• critical frequencyhelps to estimate parameters for optimized loop filter
PI-Controller
system + controllersystem
Stability Conditions – PI controller
phase margin
system + controllerloop gain
system + controller
system
PI controller
optimize integral part:
proportional controller
optimizedPI-controller
Error Signal
PI-controller
integral part will remove remaining error for constant conditons
top: integral part too slowslow approach towards zero error
bottom:integral part too fastringing
PID-Controller
system + controllersystem
Stability Conditions – PID controller
phase margin
system + controller
system
system
PID controller
output:
• top: PI controller• bottom: PID controller
differential part:
• can compensate low- pass behaviour of the system
• allow larger bandwidth• improves phase margin
• noise issues• gain has to be limited
PID controller – more flexible
Servo design for an ultrastable laserlo
op g
ain
(dB
)
40 dB/decade
dB/decade
“multiple integrators ”
• high gain at low frequencies, where the perturbations are largest
• leads to phase shift ~ 270° at lower frequencies
• no problem for stability, as long as phase margin at unity gain (~ 3 MHz) OK
H. Stoehr, PhD Thesis (2004) frequency (Hz)
loop
gai
n (d
B)
dB/decade
dB/decade
dB/decade
dB/decade
OK
• poor transient behaviour – to lock, first use fewer and gain-limited integrators
Laser frequency stabilization
“Servo Bump ”
noise increasesaround unit-gain frequency
noise will further increase
out-of loop error spectrum
H. Stoehr, F. Mensing, J. Helmcke and U. Sterr, Diode Laser with 1 Hz Linewidth,Opt. Lett. 31, 736-738 (2006)
noise will further increase and finally system oscillates there with increasing gain
Servo loop for an ultrastable laser
“Simulation Tool ”
sophisticated tools for frequency, noise and time-domain analysis are freely available,
e.g. LTSpice, PSpice
Temperature controller
Temperature controller
Temperature Sensor interfaceprovides 100 mV/°CAD590
sensor1 µA/K
Temperature controller
Temperature set pointprovides 100 mV/°C
set point knob
Temperature controllerPI controllertwo OP amps
Temperature controllerPower amplifier for thermo-electric elements