The block diagram of a motor speed control system is shown i

The block diagram of a motor speed control system is shown in the figure below. (a) Determine the range of K for a stable system. (b) Determine a suitable gain so that he overshoot to a step input is

Solution

The diagram shows the range of K for negative s

The polynomial is s³+140s² +4400s + 40000+10K=0

By RH criterion, all negative roots if    44*14000 > 40000 + 10K,    57600 >K

from standard damping expression for an overshoot of 5%, we obtain   zeta of 3.3455 .

put in gain expressio 1+ 10K/(s+100)*(s+20)² =0 and solve for K

get K =-5632.46, seen to be right of the intercept on the x axis.