Simulating the weather files with noise and delay on the sensors makes the final test of
the controllers. Apart from the noise and delay nothing else is changed from former
simulations. First the dryinfluent file is simulated with a controller having one fixed
parameter pair from the identification around the working point DO
ref= 1.5 [ g/m ] and a
3pole in = 0.74 . As seen in the lower plot in Figure 5.9 the value of DO
refspans almost
over the entire interval from zero to five [g/ m ].
30 2 4 6 8 10 12 14 0
2 4 6 8
SNH,5 [g/m3]
0 2 4 6 8 10 12 14
0 1 2 3 4 5
Time [days]
SO,5 [g/m3]
)LJXUH
Upper plot shows ammonia concentration in zone five and lower plot shows DOref and DO concentration in zone five. The file dryinfluent is simulated with noise and delay on the sensors. The controller has one fixed parameter pair calculated from the model around the working pointref 1.5
DO =
[
g/m3]
and a pole in =0.74.The master controller should not be too fast since the slave controllers might have
problem to track a reference value that changes too quickly. Therefore it would be
desirable to have a reference value that changes less. The master controller obviously has
to be made slower. The same simulation is therefore carried out, but this time a parameter
pair based on a pole placed in = 0.85 is used. As seen in Figure 5.10 the slower pole
gave the desired effect.
0 2 4 6 8 10 12 14 0
2 4 6 8
SNH,5 [g/m3]
0 2 4 6 8 10 12 14
0 1 2 3 4 5
Time [days]
SO,5 [g/m3]
)LJXUH
Upper plot shows ammonia concentration in zone five and lower plot shows DOrefand DO concentration in zone five. The file dryinfluent is simulated with noise and delay on the sensors. The controller has one fixed parameter pair calculated from the model obtained around the working pointref 1.5
DO =
[
g/m3]
and a pole in =0.85.The peaks in the nitrate concentration in zone five are also lower, but still far too high. If the airflow rate in zones three to five is kept constant at a level of 500 [ m /h], which is
3the maximum capacity, the peaks are only lowered marginally. On the basis of this fact the performance of the controller is after all quite good. Next the same simulation is run, but this time with variable parameter pairs based on a real double pole in = 0.85 . When gain scheduling is used the master controller is too fast despite the fact that a pole in
= 0.85 is used in all working points, see Figure 5.11.
0 2 4 6 8 10 12 14 0
2 4 6 8
SNH,5 [g/m3]
0 2 4 6 8 10 12 14
0 1 2 3 4 5
Time [days]
SO,5 [g/m3]
)LJXUH
Upper plot shows ammonia concentration in zone five and lower plot shows DOrefand DO concentration in zone five. The file dryinfluent is simulated with noise and delay on the sensors. The controller has variable parameter pairs based on the model obtained around the working pointref 1.5
DO =
[
g/m3]
and a pole in =0.85.In Figure 5.10 where one fixed parameter pair corresponding to the slower pole in
= 0.85 is used it can be seen that the controller output, or DO
ref, centers around approximately 4 [g/ m ]. The parameter pair is calculated from the model around the
3working point DO
ref= 1.5 [g/ m ], which means that the controller is faster for working
3points below 1.5 [g/ m ] and slower for working points above 1.5 [g/
3m ] due to the
3nonlinear characteristic of the process. The DO
refvalue increases quicker than the speed corresponding to a pole in = 0.85 below 1.5 [ g/m ], and then when the 3 DO
refreaches values around 4 [ g/m ] the speed of the controller is slower than the original design. 3 This behavior that the DO
refrelatively quickly passes low values and then centers around a higher mean value and do not deviate from this too much is actually a good behavior, and can not be achieved with gain scheduling. With variable parameter design it takes a very slow pole to keep the deviations down, but with such a slow pole the controller output never reaches values up to 4 [g/ m ] during the fourteen days. A controller with
3one fixed parameter pair calculated from the identified model around the working point
ref 1.5
DO = [ g/m ] and a pole in 3 = 0.85 , is chosen as the final controller design, and will be used in all remaining simulations. Next the file raininfluent is simulated.
Around day eight to eleven there is a sustained rain event that results in a constant
increase in influent flow. During this time period the effluent concentrations of ammonia
are higher and the DO concentration is close to its upper bound of five [g/ m ], see Figure
35.12
.
0 2 4 6 8 10 12 14
0 2 4 6 8
SNH,5 [g/m3]
0 2 4 6 8 10 12 14
0 1 2 3 4 5
Time [days]
SO,5 [g/m3]
)LJXUH
Upper plot shows ammonia concentration in zone five and lower plot shows DOref and DO concentration in zone five. The file raininfluent is simulated with noise and delay on the sensors. The controller has one fixed parameter pair calculated from the model obtained around the working pointref 1.5
DO =
[
g/m3]
and a pole in =0.85.The effluent constraint of the ammonia concentration was violated at five different occasions from day seven to day fourteen.
Finally the last weather file storminfluent is simulated and the result can be seeen in
Figure 5.13. Nothing drastic happens when the storminfluent file is simulated.
0 2 4 6 8 10 12 14 0
2 4 6 8
SNH,5 [g/m3]
0 2 4 6 8 10 12 14
0 1 2 3 4 5
Time [days]
SO,5 [g/m3]
)LJXUH
Upper plot shows ammonia concentration in zone five and lower plot shows DOref and DO concentration in zone five. The file storminfluent is simulated with noise and delay on the sensors. The controller has one fixed parameter pair calculated from the model obtained around the working pointref 1.5
DO =
[
g/m3]
and a pole in =0.85.The limit of the effluent ammonia concentration was violated at six different occasions and the limit of the maximum effluent total suspended solids was violated at 2 different occasions.
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This section treats the same problem as in section 5, namely how to control the aeration in an activated sludge process with nitrogen removal. Recently attempts have been made to use the aerated volume as control variable, see Samuelsson and Carlsson 2000. When the aerated volume is fix the DO set point must be set in relation to the volume. If the volume for example is too small it might be necessary to choose the DO set point very high to reach the desired results. With a variable aerated volume that problem is avoided and the DO set point can to a greater extent be set in relation to other aspects. The
strategy with a variable aerated volume does not solve the problem of choosing a suitable
DO set point, but widen the range of possible DO set points. It is not straightforward to
implement a strategy with variable aerated volume since a continuous change in volume
over time is impossible. Wastewater treatment plants are divided into compartments that
can be aerated or not and only discrete changes in volume are possible. This is a major
drawback especially if the plant only has few compartments. The aim of the volume
controller that will be developed in the following sections is to keep the ammonia
concentration in zone five at a constant pre specified level by adjusting the aerated
volume.
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The ammonia dynamic is not linear with respect to the DO concentration. An exact linearization will be made and the system is linearized via feedback, which is customary.
Consider the following general nonlinear system of order n.
( ) ( ) [ J [ X GW I
G[ = + , (6.1)
( ) [ K
\ = (6.2)
x is a vector containing the states of the system, u is the external input to the system and y is the output of the system. The idea is to differentiate the output y until the input u appears explicitly. If the output y and its derivatives are continuously differentiable the following expression is obtained after successive differentiation of the output.
( ) [ I ( ) ( ) [ X W P I
GW P \ G
1
0 +
= (6.3)
m is called the relative degree of the system and is the number of derivations required making y appear explicit. Chose the input as:
( ) ( ) ( ) (
0)
1
1
[ X ˆ W I
I W
X =
−− (6.4)
Then the non-linearities are cancelled, which is seen by inserting equation (6.4) in equation (6.3). The choice of uˆ ( ) t can be made in many ways and here a simple PI-controller will be chosen.
Next consider a completely mixed aerobic compartment in an activated sludge process see Figure 6.1 .
Snh,in Snh,out
Q Q
V
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A completely mixed aerobic compartment. The volume of the compartment is V and the incoming flow rate Q is equal to the outgoing flow rate.Using the notation in Figure 6.1 the mass balance of the ammonia concentration is:
(
1+LQ 1+RXW)
1+