4 Model Predictive Control of crystallisers
4.5 MPC of a vacuum crystalliser
4.5.4 Control study
4.5.4.2 MPC control of vacuum crystalliser with OPC connection
4.5.4.2.4 Control with disturbance
To test the controller in regulatory mode the disturbance can be the inlet concentration win, kg/kg solute. In Figure 4.26 and 4.27 the controller is on, the MVs compensate for the change. In Figure 4.28 the controller is turned off, the MVs don’t change, the object settle down to another operating point. The first hump, the negative is smaller when the controller is on, but in the second hump, the positive is bigger, because the controller overcompensates a little.
0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18
12:15:00 13:15:00 14:15:00
0.15 0.2 0.25 0.3 0.35
CV1*10^3 (left axis) CV1 SETPOINT (left axis) CV2*10^7 (right axis) CV3*10^3 (right axis) CV3 HIGHLIMIT (right axis) CV3 LOWLIMIT (right axis) win (right axis)
Figure 4.26 Changing of CVs with disturbance (win) when MPC is on
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
12:15:00 13:15:00 14:15:00
900 1000 1100 1200 1300 1400 1500
1000*MV1 (left axis) MV2 (left axis) MV3 (right axis)
Figure 4.27 Changing of MVs when MPC is on
0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18
12:00:00 12:20:00 12:40:00 13:00:00 13:20:00 13:40:00 14:00:00 14:20:00
0.15 0.2 0.25 0.3 0.35
CV1*10^3 (left axis) CV1 SETPOINT (left axis) CV2*10^7 (right axis) CV3*10^3 (right axis) CV3 HIGHLIMIT (right axis) CV3 LOWLIMIT (right axis) win (right axis)
Figure 4.28 Changing of CVs with disturbance (win) when MPC is off
CV1 (size) oscillation can be reduced, if the disturbance is incorporated to the controller as a feed forward variable, as a DV. See Figure 4.29, the enlarged model matrix. The MVs can react to the change of the DV, don’t have to wait for the reactions of the CVs.
The results are shown on Figure 4.30 and 31.
Figure 4.29 The enlarged model matrix including DV models
0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18
12:15:00 13:15:00 14:15:00 15:15:00
0.15 0.20 0.25 0.30 0.35
CV1*10^3 (left axis) CV1 SETPOINT (left axis) CV2*10^7 (right axis) CV3*10^3 (right axis) CV3 HIGHLIMIT (right axis) CV3 LOWLIMIT (right axis) win (right axis)
Figure 4.30 Changing of CVs with disturbance (win) when MPC is on and model include the disturbance
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
12:15:00 13:15:00 14:15:00 15:15:00
900 1000 1100 1200 1300 1400 1500
1000*MV1 (left axis) MV2 (left axis) MV3 (right axis)
Figure 4.31 Changing of MVs when MPC is on and model includes the disturbance
4.5.4.2.5 Comparison with PID controllers
To compare the advanced, model predictive controller results, basic level, PID controllers were set up and tuned for the vacuum crystalliser.
One main advantage the MPC to the set of PIDs is that the structural problems are solved inherently, MPC handles the assigning loops. There is a difference in complexity between the two controllers. According to engineering experience the more complex the technology the more complex the control system, but the slope of the relation depends on the kind of controller. See Figure 4.32. For simple cases, PID is easier, but for a difficult one MPC can be the easier controller to implement. Already for this 3 input, 3 output case the decoupling is difficult, MPC can handle the MIMO object without problem.
Complexity of the technology Complexity of
the controller PID
MPC
Figure 4.32. The relationship between the complexity of the technology and the controller
PID is a single input single output (SISO) controller and as it is shown in the control studies, the crystallisers are MIMO object with strong coupling.
Like in Section 3.3.2.3 for isotherm crystalliser, the relative gain array was calculated to decide the best pairings.
Since its proposal by Bristol in 1966, the relative gain technique has not only become a valuable tool for the selection of manipulative-controlled variable pairings, it has also been used to predict the behaviour of controlled responses. The relative gain array (RGA) can be easily calculated from the gains of the model matrix (K):
) 1
( .∗ −
=K KT
Λ (4.15)
The result of the calculation from the used model matrix (see Figure 4.10):
⎥⎥
It is an obvious proof of strong coupling.
Since the best value for pairing is 1 but it shouldn’t be negative and 0 (Cooper and Douglas, 2004) the only pairing is the following, showed with bold numbers:
⎥⎥
So MV1 controls CV3, MV2 controls CV1 and CV2 is controlled by MV3.
The starting points of the PID tunings were calculated with the strategy based on Internal Model Control (IMC). (Cooper and Douglas, 2004)
PID controller in IMC structure: ⎥
⎦ The filter:
1
The parameters of the PID controllers were fine-tuned, the MVs were limited, the control structure can be seen in Figure 4.33.
Figure 4.33 The structure of PID control of the crystalliser model
In the simulation run the setpoints are the same like the steady state values were in the study of MPC. The result shows (Figure 4.34, 4.35) that the coupling is strong, PID controllers can not really handle this MIMO object. The new setpoint of CV1 couldn’t reach, but for CV3 it is good. (For details see the supplemented CD.)
1.10E-01 1.20E-01 1.30E-01 1.40E-01 1.50E-01 1.60E-01 1.70E-01 1.80E-01
22:30 23:30 0:30 1:30 2:30 3:30 4:30 5:30
1.50E-01 1.70E-01 1.90E-01 2.10E-01 2.30E-01 2.50E-01 2.70E-01 2.90E-01 3.10E-01 3.30E-01 3.50E-01
CV1*10^3 (left axis) CV1 SETPOINT (left axis) CV2*10^7 (right axis) CV3*10^3 (right axis) CV3 SETPOINT (right axis) CV2 SETPOINT (right axis)
Figure 4.34: Simulation results with PID controllers, controlled variables (CV1=crystal size, CV2=crystal size-distribution, CV3=delivery of the crystalliser)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
22:30 23:30 0:30 1:30 2:30 3:30 4:30 5:30
1.00E+03 1.02E+03 1.04E+03 1.06E+03 1.08E+03 1.10E+03 1.12E+03 1.14E+03 1.16E+03 1.18E+03 1.20E+03
1000*MV1 (left axis) MV2 (left axis) MV3 (right axis)
Figure 4.35: Simulation results with PID controllers, manipulated variables (MV1=pressure, MV2=temperature, MV3=residence time)
Comparison of the control results
It is clearly shown from Figure 4.23 and Figure 4.34 that MPC can control the crystalliser better, but to compare the simulation results with a number in a simple way, G average deviation was calculated from the time of the change of the setpoint of the first controlled variable:
samples of
number
setpoint CV
G CV
h steptime steptime 3 2
) _
1 1
∑
+ ( −=
The results can be founded in the Table 4.2.
Controller G MPC with the high order models 7.02*10-6
MPC with the simplified models 4.85*10-6
PID controllers 1.23*10-5
Table 4.2. The comparison of the controllers
The difference of the MPCs with high and low order models would be bigger with real model errors.
With the PID controllers the new setpoint was not really reached. The reason can be that the operating points coming from the MPC simulation study are unreachable with PIDs or the tuning can be the problem.