Closed orbit feedback with digital signal processing

The closed orbit feedback experiment conducted on the SPEAR using the singular value decomposition (SVD) technique and digital signal processing (DSP) is presented. The beam response matrix, defined as beam motion at beam position monitor (BPM) locations per unit kick by corrector magnets, was measured and then analyzed using SVD. Ten BPMs, sixteen correctors, and the eight largest SVD eigenvalues were used for closed orbit correction. The maximum sampling frequency for the closed loop feedback was measured at 37 Hz. Using the proportional and integral (PI) control algorithm with the gains Kp = 3 and K{sub I} = 0.05 and the open-loop bandwidth corresponding to 1% of the sampling frequency, a correction bandwidth ({minus}3 dB) of approximately 0.8 Hz was achieved. Time domain measurements showed that the response time of the closed loop feedback system for 1/e decay was approximately 0.25 second. This result implies {approximately} 100 Hz correction bandwidth for the planned beam position feedback system for the Advanced Photon Source storage ring with the projected 4-kHz sampling frequency.