1. Modern Control for quantum optical systems
ISC-Meeting Hannover
Maximilian Wimmer
Quantum Controls Group

2. Outline Traditional and Modern Control Control Theory Nomenclature
LQG Method
Our Plans

3. Control History First mentioned control: water clocks (1500 ac)
Serial production of governor controllers for steam engines started 1769
Begin of mathematical description of control problems by Maxwell (late 19th Century)
Development of Bode- and Nyquist-plots and root locus method (beginning of 20th Century)
1967 Kalman Filter, first used for Apollo missions in 70s
Since 80s Digital Signal Processing, with new numerical methods

4. Traditional and Modern Control
- Ideal for systems with few inputs/outputs
- Bode plots, Nyquist stability criteria
Modern
- Ideal for MiMo-systems with nested loops
- Robust control
- Optimal control (LQG-Method)

5. Control Theory Nomenclature (I)
State Space model
with disturbance vector w(t)
observation vector z(t) with measurement noise v(t)

6. Control Theory Nomenclature (II)

7. Control Of A Linear Cavity
Using:
- Linear Quadratic
Gaussian controller
- Kalman filtering
- subspace filtering
and model reduction
Frequency locking of an optical cavity using linear–quadratic Gaussian integral control
S Z Sayed Hassen1, M Heurs1, E H Huntington1, I R Petersen1 and M R James2
Example to show methology and techniques of modern control

8. LQG Design (I) Get the state space model
- by theoretical models (eg. linear cavity,
homodyne detection, laser white noise…)
- via frequency response
measurements
- fit model with sub space
system identification

9. LQG Design (II) Choose general performace criteria Cost functional
With design parameters Q and R
Which correspond to small detuning and control effort

10. LQG Design (III) Minimize cost functional
J includes the laser noise z(t) in an integral Form L(z) with a new design parameter Q
Design a Kalman-Filter for good estimation of system
variables including quantum ones

11. LQG Design (IV) Set design parameters Discretise (eg. sampling)
Full (15th) and reduced-order (6th) continuous LQG controller Bode plots
phase (°) magnitude (dB)
frequency (Hz)
Set design parameters
Discretise (eg. sampling)
Solve equations (MatLab)
Finally you get
the controller

12. Results Closed loop transfer function (disturbance
angle (°) gain (dB)
freq (Hz)
Closed loop transfer
function (disturbance
supression function)

13. Plans Build a squeezer (MIMO-System)
Design a digital controller (LQG, dSPACE)
Show the advantages of modern approach
But first get rid of problems getting started with new lab

14. Our Group Imagine Photo here Michéle Heurs Timo Denker Dirk Schütte
Maximilian Wimmer
Imagine Photo here

15. Thank you for your attention

16. Anhang Cost functional is minimized if
P is determined by solution of Riccati equation