A control system is shown in Figure AP6.3. We want the system to be stable and the steady-state error for a unit step input to be less than or equal to 0.05 (5%).
(a) Determine the range of α that satisfies the error requirement.
(b) Determine the range of α that satisfies the stability requirement.
(c) Select an α that meets both requirements.
Figure AP6.3
Third-order unity feedback system.

Y) R() (1 + ajs? + (a-1)x+ (1 a)