Contents
1. Objective...2 2. Summary of Results...2 3. Discussion...4 4. Conclusion...6 5. References...6List of Figures
Figure 1: Controller output vs set point value, for PB=200, I=3 and D=0...2Figure 2: Controller output vs set point value for PB=200, I=3 and D=5...2
Figure 3: Controller output vs set point value for PB=200, I=3 and D=20...3
Figure 4: Controller output vs set point value for PB=200, I=3 and D=20...3
Figure 5: Controller output vs set point value for PB=100, I=1500 and D=0...3
Figure 6: Controller output vs set point value for PB=6 and PB=5...4
1. Objective
The objective of this experiment was to use a proportional controller to control the pressure of a process by automatically manipulating a pneumatic valve. Pressure disturbances that may appear in processes were investigated by changing the set point, integral time and derivative time of the controllers and measuring the response.
The responses to the changes in the system were investigated firstly using a P and I and a PI and D controllers and secondly investigating the effect of proportional band.
The experiment also focused on the tuning of a controller and observing the improved response.
2. Summary of Results
Figure 1: Controller output vs set point value, for PB=200, I=3 and D=0
Figure 2: Controller output vs set point value for PB=200, I=3 and D=5
In section 1 of the experiment a PI controller and a PID controller were investigated by comparing different values for each. In figures 1 and 2 in can be seen that a PID controller leads to a reduction in overshoot in the present of a disturbance, in comparison to a PI
controller. This is indicated by a decline in amplitude of the spike seen in figures 2 when compared to that of figure 1.
Figure 3: Controller output vs set point value for PB=200, I=3 and D=20
In figure 3 it can be seen that when the derivative time is increased from 5s to 20s, while the integral time is held constant, that the controller displays an improved response with the amplitude of the spike seen in this figure being smaller than that of the spikes seen in both figure 1 and 2.
Figure 4: Controller output vs set point value for PB=200, I=3 and D=20.
Figure 6: Controller output vs set point value for PB=6, I=1500 and D=0 and PB=5, I=1500 and D=0
In section 2 of the experiment the proportion bad was manipulated to see the effects of this parameter on the process. It was observed in figure 6 that a lower PB value, had a better response time and less offset. This is reflected in the results shown for that of the PB values PB=6 and PB=5. However it should also be noted that a low PB value increases oscillation which can result in the system becoming unstable. The results above reflect this with oscillation increasing from PB=100 (see figure 4) to PB = 5 (see figure 5).
Figure 7: Controller output vs set point value for PB=10, I=5 and D=1 after applying control loop tuning.
In section 3 investigated a loop tuning procedure called the Nicholas method. It can be seen in the above figure (figure 7), that the tunned loop has a very quick response time, little overshoot and oscillation and little to no offset.
3. Discussion
In this experiment both PI and PID controllers were compared. The integral term gives a sum of accumulated error over a set period of time and corrects any error in the system
accordingly. This allowing the controller to optimise process control outputs and almost completely eliminates offset. If the I time is too long the correction in any offsets would take a much longer duration and would result in a larger quantity of error within the system. If the I term were too short the set point value will be exceeded resulting in the process becoming unsteady, as the I term reacts to the accumulation of previous errors in order to correct the system. In reference to the set of data in figure 1, the controller output (green) is observed to be relatively stable as oscillations are kept to a minimum. The offset between the controller output and set point is also low and almost completely eliminated. However it can
also be observed that the response time of this controller is relatively slow in the presence of pressure disturbances placed onto in the system or set point changes. When a derivative term (D=5s) is introduced to the systems as can be seen in figure 2 the controller response is improved. This is depicted by the amplitude of the spike resulting from the introduction of a disturbance, as seen in this figure, being smaller than that of the spikes seen in figure 1. When the derivative is increased to 20s it can be observed that the response time and overshoot is reduced further and it can be seen that the amplitude of the disturbance spike seen in figure 3 is significantly smaller than that of the spikes in figures 1 and 2.It can also be observed that the offset has been completely eliminated in both figures 2 and 3 due to the introduction of said derivative term.
In section 2 of this experiment it can be observed that a relatively low proportional band percentage is needed to minimise error within the system. This is shown by figure 6 in which PB =6% and 5% respectively. In this figure it can be seen that these PB values have a better convergence time in comparison to the data shown in figure 5 and lower offset. This is because reducing the proportional band will increase the proportional gain and decrease the steady-state off set.
A relatively low proportional band will allow the system to minimise error at the output as error ∝ Kp =
100
PB , where Kp is the proportional gain and PB is the the proportional
band %. However if the proportional band is too the low the process will become unstable and major oscillation will occur. It can be seen that when the PB value is equal to 100% (see figure 5) no oscillation occurs
suggesting a stable system, but a relatively high proportional band will result in a slow response to disturbances and will lead to an increase in offsets. This can be seen in figure 5 when the proportional band equals 100%. Whilst it can be observed that the graph shows a relatively smoother line through this section (relatively minimal oscillation), it can also be observed that the time taken for the process to settle back at the set point is drastically larger than that of the when the proportional band is set to 6% or 5% (figure 6).
Once the controller output pattern began to exhibit constant amplitude cycling as can be seen in figures 6 and 7,tunning using the Ziegler and Nicholas method was instigated.. The purpose of control loop tuning is to find the optimal balance between the P, I and D terms of the PID controller which will consequently result in a faster and more accurate controller response in the presence of any disturbances or set point changes. The Ziegler and Nicholas PB, I and D terms were calculated using the formulae below:
PB=2
(
P B')
; I= τ01.2; D=
τ0
8 ;
Where PB’ is the proportion band setting at which constant amplitude cycling is exhibited. And τ0 is the natural period and the time between two successive peaks.
In this experiment it was found that PB’=5 and τ0 =5.
Using the above formulae it was calculated that the appropriate PID terms were PB=10%, I=5s and D=1s. The data obtained in figure 7 is that in which the Ziegler and Nicholas terms are portrayed. This is figure it can be observed that the response of the controller significantly improved. It can be seen that the offset was entirely eliminated, overshoot was dramatically reduced and the controller was very quick to respond to any disturbances or set point
changes. It can also be observed that the system is only exhibiting small oscillation and is therefore stable.
4. Conclusion
In this experiment it was found that a PID controller is more successful at maintaining better regulated pressure process than a PI controller. This is because the PID controller maintains a good response time and completely eliminates offset, with little oscillation. It can also be concluded that a smaller PB value is best as it has a relatively good convergence time with only a small amount of offset. However if the PB value is too small major oscillation will occur resulting in the system becoming unstable.
It was also demonstrated that the tunning of a controller is very effective in achieving desired control conditions. With appropriate tunning offset can be completely eliminated and the controller response time becomes extremely fast with little to no oscillation.
5. References
June 2009. Process Lab Projects, Pressure Control: Laboratory Manual.(1).Chemical Engineering Department, Curtin University.
June 2012. Essentials of Process Control, Level Control Process: Instruction Manual.(2). Armfield Limited.
