Question

Solve problem B-4-10. Then answer the following: 1. If the head h is the input to the hydraulic controller and the output from the controller is y, derive the transfer function of the controller? 2. What is the control action of this controller? Screen Shot 2019-06-03 at 10.49.13 PM Q Search B-4-10. Consider the liquid-level control Figure 4-52. The inlet valve is controlled by a hydraulic integral controller. Assume that the steady-state inflow rate is Q and steady-state outflow rate is also Q, the steady-state head is H, steady-state pilot valve displacement is X = 0, and steady-state valve position is Y. We assume that the set point We assume that is proportional to pilot-valve displ shown K1- dt where K is a positive constant. enange e el is negat opening y, or corresponds to the steady-state head . The set poir which is a small quantity, is applied to the water tank at i =0.This disturbance causes the head to change from A to h. This change results in a change in the outflow rate by qo.Through the hydraulic controller, the change in head causes a change integral controller tends to keep the head constant as much s possible in the presence of disturbances) We assume that all changes are of small quantities. q-K,y where K, is a positive constant. Assuming the following numer C 2 m2 the inflow rate from Q to Q + - (The R 0.5 sec/m a 0.25 m, b 0.75 m, obtain the transfer function H(s), y Tb+@ C (Capacitance) H+h T O+ae (Resistance)

The figure for 4-52 is the image below.

Answer 1

Daie: go n B-4-10 Sclution:Simee the imcteale of usatee im the tomk 4ual durimg the same dt ucends the met imle durimg dt 8.econds to the tomk to We hoke cdhz(9it 9-9o) dt uhitey h Vo Eot the ludhock lusel mechamism at b fallowss Equation A Com be usittem As NOWY Cdh - 9i t 9-9/a Cdh dt Note that dy dt k, a C dt at b Ry ubstitutimg the givem numetical valuus imto iquatien 3 C C-2m2 R-O.5 Stcfm Kv=1m2/sic. a-0.25 m 6-075m KI 4 Sec

Daba: Paga no; uee cbtaim 2 dh dt - 2h h the Percudimg imitial Cenditions Takimg the laplac teamiletm of ture equations, asumimg zero leee obtoim 2 S H(s2 =-Y(s)+Qa (s) -2 H(S) HCs Sy(s) By alimimating ys) feem the lait ture iquations get 252 HCS)- H (s) +sad s ) -28 H(s 2s228 £) H(s) = SRd (s) liom which use git H (s) AMs 2S2 + 2S + ad Cs) ACS) YIs) 1 Tt sod CRICIS+)k R The manmetm uhich the Conteelles P&aducar centtel iga I& called the Contiol acction