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Unformatted text preview: H I) Name: Student #:
01 ____Q2 __Q3 ___Q4=____QS ____Q6 __
Total __ UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING
FINAL EXAMINATION, APRIL 2001
CHE322$  PROCESS DYNAMICS AND CONTROL
Examiner  W.R. Cluett Closed Book All work to be marked must appear on front of page. Use back of page for rough
work only. 1. (l5 marks) (3) Define the regulation control problem. (b) Define the servo control problem. loflo II II (c) Describe several reasons why automatic control might be beneficial in the chemical
or mineral processing industries. (d) Consider the following statement: “Process control strategies, like feedback and feedforward. do not actually remove
process variabilityr they simply transfer variability from important variables (controlled
output variables) to less important variables (manipulated input variables). Do you agree or disagree with this statement? Give some justification for yottr argument using your experience in the laboratory associated with this course in which you studied
the control of a stirredtank heater process as an example. Ettflb i l H 2. (15 marks) The primary control objective for a certain industrial reactor is to control the quality of
the produced polymer producr as measured by its melt viscosity The two feed streams
shown are monomer and chain transfer agent that react exothennically to produce the
polymer product. The key manipulated variable is the control valve on the jacket cooling
water ﬂowrate. which affects the reactor temperature. which in turn affects the product
melt viscosity. (a) Consider two disturbances that affect this process: cooling water supply temperature
and cooling water supply pressure. Describe how the basic feedback strategy for
controlling the prodUCt viscosity shown below will work to counteract the effect of
these two diswrbances. considering the effect of each diSturbance separately. 3oflo H H U H Ii (b) Consider the cascade control strategy shown below that has inserted a temperature
controller between the viscosity controller and the jacket cooling water valve.
Describe why this control strategy should be able to improve upon the performance of the basic Strategy in part (a). 4oll6 H H (c) Describe a stepbystcp experimental pr0cedure for designing the cascade control strategy shown in part (b). Be very speciﬁc about the process variables you make
changes to and the process variables you measure, Sol l6 H H H 3. (30 marks) The temperature at a critical point in a fractionator (separator) unit (T ) is to be controlled
as indicated in the diagram below using a feedforward controller that manipulates the
reﬂux ﬁowate (R ) 0n the basis of feed ﬁowrate measurements (F ) (the feed valve is not available for manipulation). The following transfer function models have been obtained
for the effect of changes in R and F on T: 20e'm
T' = F'
(S) 363 +1 m
_4e4s
T' )= R'
(S 65 4»! (S) (a) Design a gainonly feedforward controller to provide offsetfree performance in the
critical temperature (T l in the presence of step disturbances in feed ﬂowrate ( F ). 601“ [6 H H H H (1)) Draw a block diagram representation of the fractionator along with the feedforward
controller designed in part (a) showing all variables and related transfer functions. to) Develop the overall transfer function for this feedforward controlled system that
relates changes in the feed flowrate ( F ) to changes in the critical temperature (T ). 70fl6 l I H H H (d) Is this controlled system stable for all values of the feedforward controller gain? Give
somejustificalion for your answer. (e) Consider a unit step disturbance in the feed ﬂowrate. How would your feedforward
controller adjust the reﬂux flowrate? Sol‘lé l l H (D Consider again a unit step disturbance in the feed ﬂowrater However, this time
assume that the process operator is manually doing the necessary feedforward control
actions by watching a readout of the measured feed flowrate. How would you go about helping the operator figure our how to change the reﬂux ﬂowate in order to
achieve perfect control? (g) Assume that you change the control configuration to implement instead a feedback
controller that measures the critical temperature directly and manipulates the reﬂux
ﬂowrate. Discuss the inherent performance limitations and advantages of this feedback strategy in comparison to a feedforward control strategy in the presence of
step disturbances in feed ﬂowrate. Out 16 H 4. (20 marks) An approximate model has been identified for an industrial process: 0.8
h 0.55 —.01 m2
4s+1 3.Ss+l (a) Does this model show any evidence of interactions between the process variables? If
so, which output variable is expected to be more susceptible to the effect of
interactions and why? (b) Calculate the RGA for this process. What does this suggest in terms of inputfoutput pairing?
1
Note: 1,1 =—————
' 1_K12K21
Kllk'22 1001'”) H H H (c) Assuming a yl —m1/y2 —m2 pairing, the objective is to design two singleloop
feedback PI controllers for this process. Beginning with the y, controller, design a
PI controller that will give a first order closedloop response to a step change in yup
with a time constant of 3 and zero offset. (d) Draw a block diagram for this system that shows the process interconnected with just
the y, controller using the given process transfer functions and the controller transfer
function designed in part (c). Ilofl6 (e) With just the yl controller connected to the process. what would be the effect on y:
if a unit Step change in yup was introduced? (Hint: derive the transfer function relating yup to yz from your block diagram in pan (d).) 12:)fl6 H 5. (10 marks) Consider a first order process with inputoutput characteristics that have been
approximated by the following transfer function model: 5
103+1 Gp.mod€l (S) :3 This model is to be used for feedback centroller design purposes. The objective is to
design a feedback controller for this process that will yield the following closedloop
transfer function: y l y,p Ids +1 Suppose that the true process is nonlinear, and that the true inputoutput characteristics
can be represented by: K
105+] Gerue (S) = where K varies depending on the steadystate around which the process is operating. (a) Design the feedback controller that will yield the desired closed100p transfer
function when applied to the process model given by Gp‘moddw). lSol‘lﬁ (b) Derive the true closedloop transfer function relating y”, to _v ,by using the feedback controller designed in part (a) and the true process description given by
GPJMU)‘ Using this result, determine whether the feedback controller will provide offset~free servo comrol performance when applied to the true process. (c) Show that when the feedback controller designed in part (a) is implemented on the
true process. the overall closedloop system will always be stable for all values of “rd > 0 provided the true procass gain K remains positive. Moflb H H 6‘ (l0 marks)
An unsmblc first order process, with transfer function:
_3_
s  4
is to be controlled using a proportional (P) controller.
(a) How would this process reSpond to a unit step input change without any feedback control action? Note: the inverse Laplace transform of ——£—— is K(1 9"” ). s(ts +1) l50llﬁ H II (b) The P—controller has now been installed around this unstable process. The engineer
responsible for selecting the ‘right' controller gain (Kc) believes that the best choice is a small value fo. Kc because this person recalls from a process control course taken as an undergraduate student that a large value for the feedback controller gain
K will liker produce oscillatory, and possibly even unstable closedloop behaviour. However. this person has turned to you for advice. What range of values for Kc C would you suggest to ensure a stable. nonoscillatory closedloop response? (c) Choose a specific value for Kc that produces a stable. nonoscillatory closedloop response. Sketch the response of the process output to a unit step change in the
setpoint value. showing as much detail as possible (shape of the response,
approximate time to reach steadystate, any offset from the setpoint value, etc.). loot‘lo ...
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