Run a set of fluid level control simulations beginning with an empty process tank and using the following parameters. Ensure that the Auto Drain feature is turned off in each case. In order to turn off the integral action completely you can either remove the tick from the white box to the left of the I term or you can leave this in and set the I term to 100,000. (Note that the amount of integral action is inversely proportional to the integral action time as it is specified in PCUSIM and on the table below). You will need to allow the simulation to run for at least two minutes in the case where I = 100,000. Record the eventual ‘steady state’ level of the water in the process tank and your main observations as to the nature of the response in the table below.
SP PG I Steady State Observations
30% 5 100,000 30% 5 20,000 30% 5 10,000 30% 5 4,000 30% 5 2,000 30% 5 1,400 30% 5 1,000 30% 5 700 30% 5 500
What conclusions about the nature of these fluid level experiments may be drawn from your observations?
The best response was achieved by the proportional only controller (i.e. the one with I = 100,000) and this fact seems to militate against what you learned from studying flow rate control in the earlier exercises. Normally we might expect to see a ‘proportional offset’ when using a proportional only controller, so why is there no such offset seen in this particular example? Also, why is there apparently no need of an integral term within the algorithm that controls the pump being used to raise the liquid to the desired level?
These questions can lead us to an insight into the fundamental nature of level control when it is implemented by pumping liquid into a closed tank. (Incidentally the word ‘closed’ in this context simply means that the level set point is never specified to be above any overflows or other outlets, it does not imply that the tank should actually have a lid on top of it!).
This type of approach to level control is not unique to the Bytronic PCU of course! Many industrial and other processes including the ubiquitous toilet cistern regulate level by controlling the rate at which liquid flows into a closed container.
You can see the effectiveness of a simple proportional level controller at any time by lifting the cover off any convenient toilet cistern. The rate at which the water under mains pressure flows into the tank is determined by the choking action of the ball cock valve. The valve is progressively closed by the action of the rising water as the floating ball lifts the lever connected to it. The valve’s ‘degree of openness’ is proportional to the difference between the desired level and the actual level. No one would argue that once the inrush of water has come to an end the cistern is full to the desired level, (defined by the geometry of the ball/lever assembly) which should obviously be below the emergency overflow. This is similar to what you see with PCUSIM, the proportional controller brings the level up to the set point smoothly and then the pump cuts off altogether. (What is the effect of increasing PG in the proportional only controller?).
The graph above shows several fluid level responses taken from PCUSIM simulations (with PG = 5 in each case), drawn on the same axes.
It is clear that there is a progressive increase in what we might call an integral offset effect as the magnitude of the integral action is increased. How can we account for this phenomenon? The questions to answer then are: why is there no proportional offset, why is an integral term in the controller unnecessary and why do integral terms give rise to offsets in this kind of level control?
The explanation is that by its very nature the process itself provides an element of integral action due to the volumetric capacity of the tank. (It is said to have a ‘free integrator’ in transfer function parlance, i.e. a 1/s term in its Laplace Transform). Consider for a moment the case of flow control, here some output to the pump is required if there is to be any fluid flow at all, if the pump is off then there can definitely be no flow. With the level control however there is always a certain level of water when the pump is
off, and if the pump is running then the level will always be rising.
Integral action in a PI (or PID) controller takes account of the recent history of the error by adding up the errors for a fixed number of ‘recent’ samples and contributing a component of controller output which is proportional to this sum. With the level control situation the volumetric capacity of the tank continuously ‘integrates’ the incoming flow rate that results in an increasing depth of liquid. This intrinsic characteristic is analogous to the familiar integration of velocity to obtain displacement thus:
In the level control experiment the actual water level is the integral of the flow rate into the tank. Therefore even with a proportional only flow rate controller, both proportional and integrating actions are present within the closed loop formed by the controller and the process. As a result of this intrinsic integral effect there will never be a proportional offset and an explicit integral term in the control algorithm would be entirely redundant. Any integral term that is added either produces no visible effect (if it is very small) or the aforementioned integral offset effect because it keeps the control output to the pump higher for longer than is required.
There is one other point that needs to be borne in mind. This level control scenario is non-linear in that the water level may be increased by controlling the pump but, irrespective of the algorithm, the level cannot be
lowered through any use of the pump. Once a particular level has been
reached, even with the pump turned off completely it cannot be lowered. The only means of lowering the level is to open one of the drain valves. (If you think about it, this again is exactly true of the toilet cistern that was discussed above).