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

Due to the time-varying nature of the radio-frequency (RF) accelerator, RF field amplitude and phase parameters must be precisely controlled in order to confine and accelerate the charged particle beam. Typically, a feedback control system regulates the RF field, rejects noise and disturbances, and maintains operational stability over changes in the electrical structure of the accelerator. This paper describes 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 and Q) variables. These orthogonal variables have simple mathematical relationships, and can be analyzed using linear transfer function matrices. The transfer matrix theory has been applied to the design of the multivariable control system that regulates the RF field in-phase and quadrature components. Frequency-domain controllers compensate these two signals to provide desired frequency response characteristics. A control predistorter performs an inverse coupling function, so that the I and Q components are effectively decoupled by the accelerator. Furthermore, computer interface circuitry allows the adaptive optimization of the mathematical transfer functions of the compensators.