DETERMINATION OF THE OPTIMUM RESPONSE OF LINEAR SYSTEMS

In (1) two response functions L and L₁were defined by the equations $L=∫0∞e2dτ and L1=∫0∞(dedτ)2dτ,$ where e is the error at time T. In (2) it was shown how these response functions could be used to obtain the optimum response for zero-displacement-error systems. The analysis is here applied to zero-velocity-error and zero-acceleration-error systems. The systems having the optimum response in velocity or in acceleration have a nonzero displacement lag. It is shown how the method can be extended to allow for the requirement of a zero-displacement-error in the final steady state.