Use of digital control theory state space formalism for feedback at SLC

The algorithms used in the database-driven SLC fast-feedback system are based on the state-space formalism of digital control theory. These are implemented as a set of matrix equations which use a Kalman filter to estimate a vector of states from a vector of measurements and then apply a gain matrix to determine the actuator settings from the state vector. The matrices used in the calculation are derived offline using linear quadratic Gaussian minimization. For a given noise spectrum, this procedure minimizes the RMS of the states (e.g., the position or energy of the beam). The offline program also allows simulation of the loop´s response to arbitrary inputs and calculates its frequency response.<>