Chemical Engineering paper -Design proportional controllers

Design proportional controllers for the systems of Problem 6.1 to meet the following specifications where possible. If the design specification cannot be met, explain why and suggest a more appropriate controller.

(a) A damping ratio of 0.7

(b) A steady-state error of 10% due to a unit step

(c) A steady-state error of 10% due to a unit ramp

Problem 6.1

Sketch the z-domain root locus, and find the critical gain for the following systems: