Stability analysis and design of automatic frequency control system for in vivo EPR spectroscopy

Stability analysis and design of an automatic frequency control (AFC) system for in vivo continuous-wave EPR spectroscopy is described. The open-loop function of the feedback control system for the AFC was derived and the stability of the feedback loop systematically examined. A stability analysis of the system is demonstrated and a systematic design procedure is proposed. The design is started from the required system specifications (phase margin, steady-state error, and system bandwidth) and clear guidelines for designing an AFC system are given. A case study of the design is presented based on the specific needs of in vivo EPR measurements. A phase margin of 53 degrees, a steady-state error of 1.6%, and a system bandwidth of up to 1.8 kHz were obtained in the designed AFC system. The system specifications defined in advance are satisfied in this case study.