A Formal Approach to the Design of Multibunch Feedback Systems: LQG Controllers

We formulate the multibunch feedback problem as a stan-dard control-systems design problem and solve it using Linear Quadratic Gaussian (LQG) regulator theory. Use of a specific optimality criterion allows quantitative eval-uation of different controllers and leads to the design of optimal LQG controllers. Computer simulations are used to show that, as compared to the existing Finite Impulse Response (FIR) control, LQG control can provide the same closed-loop damping for less peak power, thus making more effective use of limited kicker power. Furthermore, LQG control enables us to use more power to provide bet-ter damping without the problem of driving instabilities with higher loop gains. The code for the LQG filters dc scribed has been written for the Quick prototype installed at ALS. 1