QUESTION In the given system, the flow rate Q is adjusted by a valve which is actuated by a field controlled DC Motor. The opening x(t) u(t) O HR KA DC Motor Hx of the valve is controlled as the DC Motor X(t) drives the rack and pinion mechanism. The Qi controller generates a controller voltage Liquid Level Sensor u(t) by comparing the measured liquid level H.(t) with the reference Ha(t). Gate Valve H(t) 例一 Water Tank T(s) DC Motor voltage-torque transfer function : G, (s) = U(s) R+Ls DC Motor torque-shaft speed transfer function : G_(s) = - @(s) T(s) Js+B : GR(s): PID Controller x(s) Controller transfer function : G,(8) = O(s) Rack-pinion transfer function H(s) : G,(s) =: K Water tank transfer function Q (s) 1+Ts Q,(s) x(s) H,(s) Valve transfer function : G, (s) = ! = K, Liquid level sensor transfer function : G;(s) = H(s) (R=10, L=0, Km=0.5 Ncm/A, K=0.4 s/cm², T=20 s, K,=0.55 cm³/s, K3=10 V/cm, J=0.25 kgcm², r=1 cm, B=0.1 Ns/cm) b) Obtain the transfer function which gives the relation between water liquid level H(s) and the reference liquid level Ha(s)