Shape control of phase-front correctors in large radiotelescopes (Q1072981)

By an example of shape control for the reflecting surface of phase-front correctors in large radio telescopes, the authors discuss the problem of controlling the shape of distributed mechanical systems of the diaphragm, plate, or shell type using a finite number of control actions. The solution, which is found by decomposing the state of the system into eigenforms, leads to optimal static control laws with feedback for the measured state of the system. The performance index is the expected weighted r.m.s. deviation of the actual shape from that desired, thereby making it possible to recognize the amount of influence various parts of the system's surface have in the control circuit when formulating the control laws. The solutions also lead to practical recommendations for choosing the number of sensors and actuators as well as their positioning on the controlled surface.