Design of given oscillation index scalar controllers: modal and $H_\infty$-approaches

The algorithms of output controllers design are proposed for linear scalar plants, that ensure the desired or attainable values of oscillation index and of degree of stability, determining the settling time. Both modal control and $H_\infty$-approach are used in the design procedures. Examples are constructed, demonstrating that striving to provide the degree of stability that is much greater than the distance from the nearest left zero of the plant transfer function to the imaginary axis (even for the minimum phase plants) leads to the quite small gain and phase stability margins, that is unacceptable in practice.