GAZI UNIVERSITY FACULTY OF ENGINEERING AND ARCHITECTURE 2011-12 FALL SEMESTER KM 473 PROCESS CONTROL (İO-01) PROBLEM SET 2 1) The following transfer function is not written in a standard form G(s) 3 ( s 2) exp( 5s) s 3 (3s 2) _ (a) Put it in standard gain/time constant form (b) Determine the gain, poles and zeros (c) If the time delay term is replaced by a 1/1 Pade approximation repeat part b) 2) A process has the transfer function of Eq. 6-14 with K=4, 1 12 , 2 3 . If a has the following values: Case i : a =15 a =3 ii(b): a =2 iii: a =-4 Case ii(a): Case Case Calculate the responses for a step input of magnitude 0.8 and plot them in a single figure. What conclusions can you make concerning the effect the zero location? Is the location of the pole corresponding to 2 important so long as 1 > 2 ? 3) A pressure measuring device has been analyzed and can be described by a model with the structure shown below 5 2 6s 4s 1 P’(s) 4 25s 2 R’(s) Pm’(s) Q’(s) In other words, the device responds to pressure changes as it were a first order process in parallel with a second order process. Preliminary tests have shown that the gain of the first order process is -4% psi and the time constant equals 25 min. a)Plot Pm as a function of time resulting from a step change in P from 5 to 9 psi b)What is the overall transfer function for the measurement device P’m(s)/P’(s)? c)Find the value of the overall transfer function 1) The following transfer function is not written in a standard form G( s) 2 ( s 4) exp( 7 s) s 2 (2s 1) (a) Put it in standard gain/time constant form……….15pts (b) Determine the gain, poles and zeros……………10pts (c) Convert the transfer function into first order plus time delay model by Skogestad’s half rule method and Taylor series……15pts (d) Compare the actual output with Taylor series, skogestad’s rule approximations for a unit step input……….10 pts 4) A second order critically damped process has the transfer function Y (s) K U ( s ) .s 12 i. For a step change in input of magnitude M, what is the time (ts) required for such a process to settle to within 5% of the total change in the output? Time constant is 2 seconds. 10 pts ii. For K=1 and a ramp change in input, u(t)=at, by what time period does y(t)lag behind u(t) once the output is changing linearly with time? 10pts 5) A mixing process consists of a single stirred tank instrumented as shown in Figure below. The concentration of a single species A in the feed stream varies. The controller attempts to compensate for this by varying the flow rate of pure A through the control valve. The transmitter dynamics are negligible. (a) Draw a block diagram for the controlled process …….15 pts (b) Derive a transfer function for each block in your block diagram. ……15pts Process: (I) The volume is constant (5m3) (II) The feed flow rate is constant (qF=7m3/min) (III) The flow rate of the A stream varies but is small compared to qF (qA=0.5m3/min). (IV) CF=50kg/m3 and CA=800kg/m3 (V) All densities are constant and equal Transfer line I) The transfer line is 20m long and has 0.5 m inside diameter. II) Pump volume can be neglected. Composition Transmitter Gain, Km= 0.08 mA.m3/kg (Transmitter dynamics are negligible) Controller : PI controller I/P transducer Gain , KIP = 0.75 psi/mA Control valve: An equal percentage valve is used, which has the following relation: q A 0.17 0.03 (20) Pv3 12 , for a step change in the input pressure, the valve requires approximately 1 min to move to its new position.