Synthesis of discrete modal siso controllers by engineering performance indices

The linear discrete minimum-phase plant with one control input, one measured output and with an unmeasured external disturbance is considered. The problem is stated of the design of the discrete output controller that provides the preset engineering performance indices: control error, settling time, stability margins radius. Analytical formulas are obtained that allow to relate the engineering performance indices with the desired closed system characteristic polynomial roots in the modal control problem when choosing real non-negative roots. At the same time, the specified control error and the settling time lead to the constraints on the maximum absolute value of the desired roots, while the values of the desired roots, providing the given radius of stability margins, may not satisfy these constraints, so the specified values of the performance indices should be revised. Examples are given showing the effectiveness of the approach proposed.