(Solved): The open-loop transfer function (OLTF) of a unity feedback control system is given by: \[ G(s) H(s ...

The open-loop transfer function (OLTF) of a unity feedback control system is given by: \[ G(s) H(s)=\frac{K}{s\left(T_{1} s+1\right)\left(T_{2} s+1\right)} \] where \( K \) is the open-loop gain, \( T_{1} \) and \( T_{2} \) are the time constants of the poles. (i) show that the frequency \( \omega_{2} \) at which the Nyquist plot crosses the imaginary axis occurs at: \[ \omega_{2}=\frac{1}{\sqrt{\left(T_{1} T_{2}\right)}} \] [7 marks] (ii) hence, deduce the magnitude of the real part at the frequency \( \omega_{2} \) (given in part b(i)). Hint: deduce in terms of \( K, T_{1} \) and \( T_{2} \).