Our control objective for the jacketed stirred reactor process is to minimize the
impact on reactor operation when the temperature of the liquid entering the
cooling jacket changes.
We have previously explored
modes of operation and
dynamic CO-to-PV behavior
of the reactor. We also have established the performance
of a single loop
PI controller and a
PID with CO Filter controller in this disturbance rejection application.
Here we consider a
cascade architecture as a means for improving the disturbance rejection
performance in the jacketed stirred reactor.
The Single Loop Jacketed Stirred Reactor
As shown in the process graphic below (click for large view),
the reactor exit stream temperature is controlled by adjusting the flow rate
of cooling liquid through an outer shell (or cooling jacket) surrounding the
As labeled above for the single loop case:
CO = signal to valve that adjusts cooling jacket liquid flow rate
(controller output, %)
PV = reactor exit stream temperature (measured process variable,
SP = desired reactor exit stream temperature (set point, oC)
= temperature of cooling liquid entering the jacket (major
The control objective is to maintain the reactor exit stream temperature
(PV) at set point (SP) in spite of unmeasured changes in the temperature of cooling
liquid entering the jacket (D).
We measure exit stream
temperature with a
sensor and transmit the signal to a temperature controller (the TC inside
the circle in the diagram). After comparing SP to PV, the temperature
computes and transmits a CO signal to the cooling jacket
liquid flow valve.
As the valve opens and closes, the flow rate of liquid through the jacket
increases and decreases. Like holding a hot frying pan under a water faucet, higher flow rates of cooling
liquid remove more heat. Thus, a higher flow rate of cooling liquid through
the jacket cools the reactor vessel, lowering the reactor exit stream temperature.
Problems with Single Loop Control
The single loop architecture in the diagram above attempts to achieve
our control objective by adjusting the flow rate of cooling liquid through
If the measured
temperature is higher than set point, the controller signals the valve to
increase cooling liquid flow by an
appropriate percentage with the expectation that this will decrease reactor
exit stream temperature accordingly.
A concern discussed in detail
in this article is that the temperature of the cooling liquid entering
the jacket (D) can change, sometimes rather quickly. This can disrupt
reactor operation as reflected in the measured reactor exit stream temperature PV.
So reactor exit stream temperature PV is a function of two
▪ cooling liquid flow rate, and
▪ the temperature of the cooling liquid entering the cooling jacket
To explore this, we conduct some thought experiments:
Thought Experiment #1: Assume that the temperature of the
cooling liquid entering the jacket (D) is
time. If the cooling liquid flow rate increases by a certain amount, the
reactor exit stream temperature will decrease in a
predictable fashion (and vice versa). Thus, a single loop structure
should provide good temperature control performance.
Thought Experiment #2: Assume that the temperature of cooling
liquid entering the jacket (D) starts rising over time. A warmer cooling liquid
can carry away less heat from the vessel. If the cooling liquid flow rate
is constant through
the jacket, the reactor will experience less cooling and the exit stream
temperature will increase.
Thought Experiment #3: Now assume that the temperature of
cooling liquid entering the jacket (D) starts to rise at the same moment
that the reactor exit stream temperature moves above set point. The
controller will signal for a cooling
liquid flow rate increase, yet because the cooling liquid
temperature is rising, the heat removed from the reactor vessel can
actually decrease. Until further corrective action is taken, the reactor exit stream
temperature can increase.
As presented in Thought Experiment #3, the changing temperature of
cooling liquid entering the jacket (a
disturbance) can cause a contradictory outcome that can confound the
controller and degrade control performance.
Cascade Control Improves Disturbance Rejection
As we established in our study of the
an essential element for success in a cascade (nested loops) design is the measurement and
control of an "early
warning" process variable, PV2, as illustrated in the block diagram
below (click for a large view).
Since disruptions impact PV2 first, it provides our "early warning" that
a disturbance is heading toward our outer primary process variable, PV1. The inner secondary controller can
begin corrective action immediately. And since PV2 responds first to valve
manipulations, disturbance rejection can begin before PV1
has been visibly impacted.
A Reactor Cascade Control Architecture
The thought experiments above highlight that it is problematic to control
exit stream temperature by adjusting the cooling liquid flow rate.
An approach with potential for "tighter" control
is to adjust the temperature of the cooling jacket itself. This
provides a clear process relationship in that, if we seek a higher reactor
exit stream temperature, we know we want a higher cooling jacket
temperature. If we seek a lower reactor exit stream temperature, we want a
lower cooling jacket temperature.
Because the temperature of cooling liquid entering the jacket changes,
cooling jacket temperature by a precise
amount may mean decreasing the flow rate of cooling liquid a lot, decreasing
it a little, and
perhaps even increasing the flow rate a bit.
and easy" proxy for the cooling jacket temperature is the
temperature of cooling liquid exiting at the jacket outlet. Hence, we choose
our inner secondary process variable, PV2, as we work toward the
construction of a nested cascade
Adding a temperature sensor that measures PV2 provides us the early warning
that changes in D, the temperature of cooling liquid entering the jacket,
are about to impact the reactor exit stream temperature, PV1.
The addition of a second temperature controller (TC2) completes construction
of a jacketed
reactor control cascade as shown in the graphic below (click for a large view).
Now, our inner secondary control loop measures the temperature of cooling
liquid exiting at the jacket outlet (PV2) and sends a signal (CO2) to the
valve adjusting cooling jacket flow rate. The valve increases or
decreases the flow rate of cooling liquid if the jacket temperature needs to fall
or rise, respectively.
Our outer loop maintains reactor exit stream temperature (our process
variable of primary interest and concern) as PV1. Note in the graphic above
controller output of our primary controller, CO1, becomes the set point of
our inner secondary controller, SP2.
If PV1 needs to rise, the primary
controller signals a higher set point for the jacket temperature (CO1 = SP2).
The inner secondary controller then decides if this means opening or closing the valve and
by how much.
Thus, variations in the temperature of cooling liquid entering the jacket
(D) are addressed quickly and directly by the inner secondary loop to the
benefit of PV1.
The cascade architecture variables are identified on the above graphic
and listed below:
PV2 = cooling jacket outlet temperature is our "early warning"
process variable (oC)
CO2 = controller output to valve that adjusts cooling jacket liquid flow rate
SP2 = CO1 = desired cooling jacket outlet temperature (oC)
PV1 = reactor exit stream temperature (oC)
SP1 = desired reactor exit stream temperature (oC)
= temperature of cooling liquid entering the jacket (oC)
The inner secondary PV2 (cooling jacket outlet temperature) is a proper early
warning process variable because:
▪ PV2 is measurable with a temperature sensor.
▪ The same valve used to manipulate PV1 also manipulates PV2.
▪ The same disturbance that is of concern for PV1 also disrupts PV2.
▪ PV2 responds before PV1 to the disturbance of concern and to valve
Reactor Cascade Block Diagram
The jacketed stirred reactor block diagram (click for a large view)
for this nested cascade architecture is shown below.
As expected for a nested cascade, this architecture has:
▪ two controllers (an inner secondary and outer primary
▪ two measured process variable sensors (an inner PV2 and outer PV1)
▪ only one valve (to adjust cooling liquid flow rate)
Tuning a Cascade
With a cascade architecture established, we apply our
implementation recipe for cascade control and
explore the disturbance rejection capabilities of this structure.
Return to the
Table of Contents to learn more.
Copyright © 2007 by Douglas J. Cooper. All Rights Reserved.