Providing real closed-loop transfer functions poles for plant with interval-given parameters for overshoot elimination

The problem of providing real closed-loop poles as a part of the problem of overshoot elimination was regarded and the approach for PID-controller tuning was formulated. The presented approach is based on discriminant expression for characteristic equation of second-order plant. Analytic expressions that constrain range of acceptable tuning parameters were obtained. Next, the proposed approach was enhanced for interval-given case. The interval root-locus mapping on controller parameters plane was introduced and final constraints for controller coefficients providing strictly real closed-loop poles for every member of interval family was formulated.