Building of a class of optimal automatic control systems without using «pure» undistorted derivatives in control law

There is considered an optimal system for automatic control of a neutral object with a d-c astatic servomotor. The control law is obtained which is a nonlinear function of an error coordinate and a unit output coordinate of the kind $W(p)=a(T_0 p+1)/(a T_0 p+1)$. The control law provides the maximum high-speed of the system with null initial speed conditions and arbitrary initial conditions concerning the controlled coordinate. The peculiarity of such a system is the fact that the signal at the input of the relay element considerably differs from null during the whole control process.