Comparison of Feedback Controller for Link Stabilizing Units of the Laser Based Synchronization System used at the European XFEL

Comparison of Feedback Controller for Link Stabilizing Units of the Laser Based Synchronization System used at the European XFEL M. Heuer 1 G. Lichtenberg 2 S. Pfeiffer 1 H. Schlarb 1 1 Deutsches Elektronen Synchrotron Hamburg, Germany MOCZB3 2 Hamburg University of Applied Sciences, Germany International Beam Instrumentation Conference 07 2014/09/15 Logovarianten und Mindestabstand 01 HAW Logo

Contents 1 Introduction 2 Link Stabilizing Unit 3 Introduction to Control 4 Implementation and Experimental Results 5 Conclusion and Outlook M. Heuer et al. 2014/08/28 Page 2/30

Contents 1 Introduction 2 Link Stabilizing Unit 3 Introduction to Control 4 Implementation and Experimental Results 5 Conclusion and Outlook M. Heuer et al. 2014/08/28 Page 3/30

Introduction LSU Control Experiments Conclusion European X-ray Free Electron Laser (XFEL) Idea I Build a Camera to capture ultrafast processes in an atomic scale I E.g.: Make a movie of the folding process of biomolecules Some Numbers I Wavelength of 0.05 to 6 nm, Pulse duration of less than 100 fs (10 15 ) I Total facility length of 3.4 km with 101 accelerator modules Courtesy of http://www.xfel.eu M. Heuer et al. 2014/08/28 Page 4/30

Laser Based Synchronization System (LbSynch) Gun e I0 BAM BAM I39H A1.M{1,2,3,4} A25.M{1,2,3,4} BAM Undulator Experiment Injector Laser Pump Probe Laser System M. Heuer et al. 2014/08/28 Page 5/30

Laser Based Synchronization System (LbSynch) Gun e I0 BAM BAM I39H A1.M{1,2,3,4} A25.M{1,2,3,4} BAM Undulator Experiment Injector Laser L2RF L2RF L2RF L2RF Pump Probe Laser System MLO L L L I(t), I(l) k + 1 k k 1 k 2 x(k + 1) = 0 x(k) > 0 x(k 2) < 0 t, l M. Heuer et al. 2014/08/28 Page 5/30

Laser Based Synchronization System (LbSynch) Gun e I0 BAM BAM I39H A1.M{1,2,3,4} A25.M{1,2,3,4} BAM Undulator Experiment Injector Laser L2RF L2RF L2RF L2RF Pump Probe Laser System LSU LSU LSU LSU LSU LSU LSU MLO L L L I(t), I(l) k + 1 k k 1 k 2 OXC with Balanced Detector Piezo x(k + 1) = 0 x(k) > 0 x(k 2) < 0 t, l C LSU (s) LSU n x LSU-Control M. Heuer et al. 2014/08/28 Page 5/30

Laser Based Synchronization System (LbSynch) Gun e I0 BAM BAM I39H A1.M{1,2,3,4} A25.M{1,2,3,4} BAM Undulator Experiment Injector Laser L2RF L2RF L2RF L2RF Pump Probe Laser System LSU LSU LSU LSU LSU LSU LSU k 1 k 1 MLO L L L I(t), I(l) k + 1 k k 1 k 2 k 1 OXC with Balanced Detector Piezo x(k + 1) = 0 x(k) > 0 x(k 2) < 0 t, l C LSU (s) LSU n x LSU-Control M. Heuer et al. 2014/08/28 Page 5/30

Laser Based Synchronization System (LbSynch) Gun e I0 BAM BAM I39H A1.M{1,2,3,4} A25.M{1,2,3,4} BAM Undulator Experiment Injector Laser L2RF L2RF L2RF L2RF Pump Probe Laser System LSU LSU LSU LSU LSU LSU LSU k 1 k 1 MLO L L L I(t), I(l) k + 1 k k 1 k 2 k 1 OXC with Balanced Detector k n k n Piezo x(k + 1) = 0 x(k) > 0 x(k 2) < 0 t, l C LSU (s) LSU n x LSU-Control M. Heuer et al. 2014/08/28 Page 5/30

Laser Based Synchronization System (LbSynch) Requirements The relative jitter between all link ends should be less as possible M. Heuer et al. 2014/08/28 Page 6/30

Laser Based Synchronization System (LbSynch) Requirements The relative jitter between all link ends should be less as possible Current State Heuristically tuned PI controller New Approach Model based control 1. Model the dynamics of the system M. Heuer et al. 2014/08/28 Page 6/30

Problem Statement M. Heuer et al. 2014/08/28 Page 7/30

Problem Statement How to synthesis a model based controller? Has a model based controller a better performance? M. Heuer et al. 2014/08/28 Page 7/30

Contents 1 Introduction 2 Link Stabilizing Unit 3 Introduction to Control 4 Implementation and Experimental Results 5 Conclusion and Outlook M. Heuer et al. 2014/08/28 Page 8/30

Introduction LSU Control Experiments Conclusion Setup of the Link Stabilizing Unit M. Heuer et al. 2014/08/28 Page 9/30

Contents 1 Introduction 2 Link Stabilizing Unit 3 Introduction to Control 4 Implementation and Experimental Results 5 Conclusion and Outlook M. Heuer et al. 2014/08/28 Page 10/30

General Control Loop d i d o r e u y Controller System y m n u(t) output voltage applied to the piezo amplifier based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 11/30

General Control Loop d i d o r e u y Controller System y m n u(t) output voltage applied to the piezo amplifier y(t) the real timing difference based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 11/30

General Control Loop d i d o r e u y Controller System y m n u(t) output voltage applied to the piezo amplifier y(t) the real timing difference y m (t) = y(t) + n(t) timing difference measured by the OXC n(t) noise of the balanced detector based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 11/30

General Control Loop d i d o r e u y Controller System y m n u(t) output voltage applied to the piezo amplifier y(t) the real timing difference y m (t) = y(t) + n(t) timing difference measured by the OXC n(t) noise of the balanced detector d i (t) input disturbances, e.g. ripple of the piezo amplifier supply based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 11/30

General Control Loop d i d o r e u y Controller System y m n u(t) output voltage applied to the piezo amplifier y(t) the real timing difference y m (t) = y(t) + n(t) timing difference measured by the OXC n(t) noise of the balanced detector d i (t) input disturbances, e.g. ripple of the piezo amplifier supply d o (t) output disturbances, e.g. vibrations of the setup based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 11/30

General Control Loop d i d o r e u y Controller System y m n based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 12/30

General Control Loop d i d o r e u y Controller System y m n T (s) = P (s)c(s) 1+P (s)c(s) based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 12/30

General Control Loop d i d o r e u y Controller System y m n T (s) = P (s)c(s) 1+P (s)c(s) high bandwidth controller Tracking of a reference T (s) 1 based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 12/30

General Control Loop d i d o r e u y Controller System y m n T (s) = P (s)c(s) 1+P (s)c(s) S(s) = 1 T (s) = 1 1+P (s)c(s) high bandwidth controller Tracking of a reference T (s) 1 based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 12/30

General Control Loop d i d o r e u y Controller System y m n T (s) = P (s)c(s) 1+P (s)c(s) S(s) = 1 T (s) = 1 1+P (s)c(s) high bandwidth controller Tracking of a reference T (s) 1 Output Disturbance rejection S(s) 0 T (s) 1 based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 12/30

General Control Loop d i d o r e u y Controller System y m n T (s) = P (s)c(s) 1+P (s)c(s) high bandwidth controller Tracking of a reference T (s) 1 Output Disturbance rejection S(s) 0 T (s) 1 S(s) = 1 T (s) = 1 1+P (s)c(s) high bandwidth controller System output due to noisy measurements T (s) 0 based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 12/30

General Control Loop d i d o r e u y Controller System y m n T (s) = P (s)c(s) 1+P (s)c(s) high bandwidth controller Tracking of a reference T (s) 1 Output Disturbance rejection S(s) 0 T (s) 1 S(s) = 1 T (s) = 1 1+P (s)c(s) high bandwidth controller System output due to noisy measurements T (s) 0 Very large controller outputs u(t) based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 12/30

State Space Model ẋ(t) =Ax(t) + Bu(t), y(t) =Cx(t) + Du(t), based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 13/30

State Space Model ẋ(t) =Ax(t) + Bu(t), y(t) =Cx(t) + Du(t), x(t) states of the system (energy storages) u(t) input to the system y(t) output of the system based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 13/30

State Space Model ẋ(t) =Ax(t) + Bu(t), y(t) =Cx(t) + Du(t), x(t) states of the system (energy storages) u(t) input to the system y(t) output of the system A describes the dynamic behavior of the system B describes how the input acts on the state C describes how the state are combined to the output D describes which inputs have a direct influence on the output based on Skogestad and Postlethwaite (2005) M. Heuer et al. 2014/08/28 Page 13/30

Model Identification Identification Signal e.g. White Noise, Step,... System Measurement P (s) = Measurement Identification Signal Matlab System Identification Toolbox based on Ljung (1987) M. Heuer et al. 2014/08/28 Page 14/30

State Feedback Controller ẋ(t) =Ax(t) + Bu(t), y(t) =Cx(t) + Du(t), based on Zhou et al. (1996) M. Heuer et al. 2014/08/28 Page 15/30

State Feedback Controller ẋ(t) =Ax(t) + Bu(t), y(t) =Cx(t) + Du(t), u(t) = F x(t), based on Zhou et al. (1996) M. Heuer et al. 2014/08/28 Page 15/30

State Feedback Controller ẋ(t) =Ax(t) + Bu(t), y(t) =Cx(t) + Du(t), min V = 0 u(t) = F x(t), x(t) T Qx(t) + u(t) T Ru(t) dt, based on Zhou et al. (1996) M. Heuer et al. 2014/08/28 Page 15/30

State Feedback Controller ẋ(t) =Ax(t) + Bu(t), y(t) =Cx(t) + Du(t), min V = 0 u(t) = F x(t), x(t) T Qx(t) + u(t) T Ru(t) dt, Q and R are tuning parameter. e.g. Q = C T C and tune the response speed with R based on Zhou et al. (1996) M. Heuer et al. 2014/08/28 Page 15/30

State Feedback Controller ẋ(t) =Ax(t) + Bu(t), y(t) =Cx(t) + Du(t), min V = 0 u(t) = F x(t), x(t) T Qx(t) + u(t) T Ru(t) dt, Q and R are tuning parameter. e.g. Q = C T C and tune the response speed with R F = -lqr(a,b,c *C,R); based on Zhou et al. (1996) M. Heuer et al. 2014/08/28 Page 15/30

State Feedback Controller ẋ(t) =Ax(t) + Bu(t), y(t) =Cx(t) + Du(t), min V = 0 u(t) = F x(t), x(t) T Qx(t) + u(t) T Ru(t) dt, Q and R are tuning parameter. e.g. Q = C T C and tune the response speed with R F = -lqr(a,b,c *C,R); x(t) is not measured in most cases. based on Zhou et al. (1996) M. Heuer et al. 2014/08/28 Page 15/30

State Estimation d i d o u System y B 1 s C ỹ A x based on Zhou et al. (1996) M. Heuer et al. 2014/08/28 Page 16/30

State Estimation d i d o u System y L B 1 s C ỹ A x based on Zhou et al. (1996) M. Heuer et al. 2014/08/28 Page 16/30

State Estimation d i d o u System y L B 1 s C ỹ A x The dual problem to state feedback based on Zhou et al. (1996) M. Heuer et al. 2014/08/28 Page 16/30

State Estimation d i d o u System y L B 1 s C ỹ A x The dual problem to state feedback Q obsv and R obsv are again tuning parameter. e.g. Q obsv = B B T and tune the filtering of the noise with R obsv based on Zhou et al. (1996) M. Heuer et al. 2014/08/28 Page 16/30

State Estimation d i d o u System y L B 1 s C ỹ A x The dual problem to state feedback Q obsv and R obsv are again tuning parameter. e.g. Q obsv = B B T and tune the filtering of the noise with R obsv L = -lqr(a,c,b*b,robsv); based on Zhou et al. (1996) M. Heuer et al. 2014/08/28 Page 16/30

Contents 1 Introduction 2 Link Stabilizing Unit 3 Introduction to Control 4 Implementation and Experimental Results 5 Conclusion and Outlook M. Heuer et al. 2014/08/28 Page 17/30

Matlab VHDL Toolbox Extends the Xilinx System Generator Toolbox Automatic code generation from a Simulink model (no VHDL knowledge required) Simulation of the real behavior (saturation, overflow, fixed point precision, etc.) M. Heuer et al. 2014/08/28 Page 18/30

Model Identification 0.1 y(t) u(t) y Model (t) Voltage [V] 0 0.1 0 0.5 1 1.5 2 2.5 Time [ms] M. Heuer et al. 2014/08/28 Page 19/30

Model Identification 0.1 y(t) u(t) y Model (t) Voltage [V] 0 0.1 0 0.5 1 1.5 2 2.5 Time [ms] The model fits well to the dynamic behavior of the real plant. M. Heuer et al. 2014/08/28 Page 19/30

Identification A = 253.8 1.133 10 5 935.9 1.133 10 5 1138 2017 935.9 4035 1.346 10 5 [ ] B = 112.9 237.9 209.5, [ ] C = 225.8 475.9 418.9, M. Heuer et al. 2014/08/28 Page 20/30

Effect of State Feedback Voltage [V] 4 10 2 2 0 y pid (t) u pid (t) y lqg (t) u lqg (t) 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [ms] M. Heuer et al. 2014/08/28 Page 21/30

Effect of State Feedback Voltage [V] 4 10 2 2 0 y pid (t) u pid (t) y lqg (t) u lqg (t) 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [ms] Its possible to change the dynamic behavior e.g. increase the damping. M. Heuer et al. 2014/08/28 Page 21/30

Control Startup 0.05 Voltage [V] 0 0.05 0.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time [ms] y pid (t) u pid (t) y lqg (t) u lqg (t) M. Heuer et al. 2014/08/28 Page 22/30

Control Startup 0.05 Voltage [V] 0 0.05 0.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time [ms] y pid (t) u pid (t) y lqg (t) u lqg (t) The model based controller reaches the steady state faster... M. Heuer et al. 2014/08/28 Page 22/30

Dynamic behavior of an input disturbances 10 2 Voltage [V] 5 0 y pid (t) u pid (t) y lqg (t) u lqg (t) 5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time [ms] M. Heuer et al. 2014/08/28 Page 23/30

Dynamic behavior of an input disturbances 10 2 Voltage [V] 5 0 y pid (t) u pid (t) y lqg (t) u lqg (t) 5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time [ms]... and rejects disturbances much better than the PID controller. M. Heuer et al. 2014/08/28 Page 23/30

Dynamic behavior of a coarse tuning step 10 2 Voltage [V] 5 0 y pid (t) u pid (t) y lqg (t) u lqg (t) 5 0 20 40 60 80 100 120 Time [ms] M. Heuer et al. 2014/08/28 Page 24/30

Dynamic behavior of a coarse tuning step 10 2 Voltage [V] 5 0 y pid (t) u pid (t) y lqg (t) u lqg (t) 5 0 20 40 60 80 100 120 Time [ms] Effects measurable with PID controller but not with LQG. M. Heuer et al. 2014/08/28 Page 24/30

Contents 1 Introduction 2 Link Stabilizing Unit 3 Introduction to Control 4 Implementation and Experimental Results 5 Conclusion and Outlook M. Heuer et al. 2014/08/28 Page 25/30

Statements M. Heuer et al. 2014/08/28 Page 26/30

Statements Use model based control approaches to a better performance M. Heuer et al. 2014/08/28 Page 26/30

Statements Use model based control approaches to a better performance It is possible to achieve good control results for the LSU with a LQG controller M. Heuer et al. 2014/08/28 Page 26/30

Conclusion Conclusion M. Heuer et al. 2014/08/28 Page 27/30

Conclusion Conclusion An overview of the LbSynch System was given M. Heuer et al. 2014/08/28 Page 27/30

Conclusion Conclusion An overview of the LbSynch System was given It was shown how to synthesis a LQG controller M. Heuer et al. 2014/08/28 Page 27/30

Conclusion Conclusion An overview of the LbSynch System was given It was shown how to synthesis a LQG controller The design controller was tested in an experimental setup M. Heuer et al. 2014/08/28 Page 27/30

Conclusion Conclusion An overview of the LbSynch System was given It was shown how to synthesis a LQG controller The design controller was tested in an experimental setup Outlook Test other model based controller types M. Heuer et al. 2014/08/28 Page 27/30

Final Slide References Additional Slides The End Thank you very much for your attention M. Heuer et al. 2014/08/28 Page 28/30

Final Slide References Additional Slides Further Reading L. Ljung. System identification: theory for the user. Prentice-Hall information and system sciences series. Prentice-Hall, 1987. ISBN 9780138816407. URL http://books.google.com/books?id=gpvraaaamaaj. S. Skogestad and I. Postlethwaite. Multivariable Feedback Control - Analysis and Design. John Wiley & Sons, Ltd, 2nd edition, 2005. ISBN 978-0-470-01168-3. K. Zhou, J.C. Doyle, and K. Glover. Robust and Optimal Control. Feher/Prentice Hall Digital and. Prentice Hall, 1996. ISBN 9780134565675. URL http://books.google.com/books?id=rpsoqgaacaaj. M. Heuer et al. 2014/08/28 Page 29/30

Final Slide References Additional Slides LQR via algebraic riccati equation min V = ẋ(t) =Ax(t) + Bu(t), y(t) =Cx(t) + Du(t), 0 u(t) = F x(t), x(t) T Qx(t) + u(t) T Ru(t) dt, F = R 1 B T P A T P + P A P BR 1 B T P + Q = 0 M. Heuer et al. 2014/08/28 Page 30/30