Feedback Characterization

Besides the different components in the feedback loop like corrector magnets, vacuum chambers, BPM system and global BPM data distribution, the overall performance of the feedback system depends on the type of the digital controller. Presently, a simple PID controller has been implemented. The horizontal and vertical open loop transfer functions from a corrector magnet to its closest BPM (nearly no phase advance) have been measured (see Fig. 1) in order to optimize the feedback parameters.

Figure 1: Horizontal and vertical open loop transfer functions of the fast orbit feedback. The model of the fit consists of a series of a first (bandwidth 1) and fifth order (bandwidth 2) low pass filters and a time delay.

The underlying model of the fitted data comprises a first order low pass filter representing DDC filters, corrector magnet, vacuum chamber and eddy currents, a fifth order low pass filter for the digital power supplies and a time delay for the digital processing. The fit predicts first order low pass bandwidths of $\approx$ 355 Hz horizontally and $\approx$ 830 Hz vertically indicating the asymmetry of the SLS storage ring vacuum chamber. Independent laboratory measurements of the digital power supplies showed a fifth order low pass filter characteristics with a small signal bandwidth [5] of 2 kHz. Delay times through the digital processing chain were determined to $\approx$ 300 $\mu$s for the digital receivers, $\approx$ 60 $\mu$s for the first DSP for beam position calculations, $\approx$ 70 $\mu$s for the feedback algorithm in the second DSP and $<$ 160 $\mu$s to transfer the correction values to the power supplies. A maximum of 250 $\mu$s have to be accounted for the global data exchange due to the asynchronous transfer. Therefore a total digital time delay of around 700 $\mu$s corresponding to 3 correction cycles were used in the fit.