Design of a multivariable RF control system using gain-shaping in the frequency domain

The authors describe a multivariable control system that compensates the electrical structure of the accelerator by using gain-shaping in the frequency domain. The amplitude and phase quantities have been resolved into in-phase and quadrature (I&Q) variables. These orthogonal variables have simple mathematical relationships, and can be analyzed using linear transform function matrices. The transfer matrix theory has been applied to the design of the multivariable control system that regulates the RF field (I+Q) components. Frequency-domain controllers compensate these two signals to provide desired frequency response characteristics. A control pre-distorter performs an inverse coupling functions, so that the I&Q components are effectively decoupled by the accelerator. Computer interface circuitry allows the adaptive optimization of the mathematical transfer functions of the compensators.<>