Shape control of phase-front correctors in large radiotelescopes

With special reference to shape control of the reflecting surface of phase front correctors in large telescopes the paper is concerned with shape control of distributed mechanical systems such as diaphragms, plates, or hulls by using a finite number of control signals. The solution which is found by decomposing the system state into eigen forms leads to optimal laws of static eigen state feedback control. The performance index is the expected weighed r.m.s. deflection of the actual shape from the desired one; this makes it possible to recognize the effect of various parts of the surface on the control objective in generation of the control equation. The solutions also lead to advice on choice of the number of sensors and actuators and their positioning on the surface to be shaped.