Design and implementation of IIR algorithms for control of longitudinal coupled-bunch instabilities

The recent installation of third-harmonic RF cavities at the Advanced Light Source has raised instability growth rates, and also caused tune shifts (coherent and incoherent) of more than an octave over the required range of beam currents and energies. The larger growth rates and tune shifts have rendered control by the original bandpass FIR feedback algorithms unreliable. In this paper we describe an implementation of an IIR feedback algorithm offering more flexible response tailoring. A cascade of up to 6 second-order IIR sections (12 poles and 12 zeros) was implemented in the DSPs of the longitudinal feedback system. Filter design has been formulated as an optimization problem and solved using constrained optimization methods. These IIR filters provided 2.4 times the control bandwidth as compared to the original FIR designs. Here we demonstrate the performance of the designed filters using transient diagnostic measurements from ALS and DAΦNE.