Ratio Control

In some processes, it is a common requirement for two flows to be kept in precise ratio to each other for example, a gas or oil and air in combustion control, and reagents being fed to a chemical reactor hence the need for ratio control.

In simple ratio control, one flow is declared to be the primary. This flow is set to meet higher level requirements such as plant throughput or furnace temperature. The second flow is the secondary and is manipulated to maintain the set flow ratio.

The controlled variable in this case is the ratio, and not the flow hence an intuitive solution might look similar to figure 1(a)

As illustrated in figure 1(a) the actual ratio A/B is calculated by a divider module and is used as the process variable for controller which manipulates the secondary control valve.

This arrangement has a hidden problem. The secondary loop includes the divider module and hence the term A. The loop gain varies directly with the flow A, leading to a sluggish response at low flows and possible instability at high flow. If we were to use the inverse ratio B/A as the controller variable, the saturation becomes worse as the term 1/A now appears in the secondary loop giving a loop gain which varies inversely with A, becoming very high at low flows. Any system based on figure 1(a) would be impossible to tune for anything other than constant flow rates.

Ratio control systems are so often, based on figure 1(b) as illustrated below:

In this second arrangement, the primary flow is multiplied by the ratio R to produce the setpoint for the secondary flow controller. The secondary flow therefore follows the primary flow. Note that, in the event of failure in the primary loop for example a stuck valve, the secondary controller will still maintain the correct ratio.

The secondary flow will tend to lag behind the primary flow. On gas/air burner, the air flow could be the primary and the gas flow the secondary. Such a system would run lean on increasing heat and run rich on decreasing heat. To some extent this can be overcome by making the primary loop slower acting than the secondary loop, perhaps by tuning.

In ratio control, a choice has to be made for primary and secondary loops. The first consideration is normally safety. For example in a gas/air burner, air primary/gas secondary (called gas follows air) is usually chosen as most failures in the air loop cause the gas to shut down. If there are no safety considerations, the slowest loop should be the primary and the fastest loop should be the secondary to overcome the lag described above.

The ratio block is a simple multiplier. The ratio is simply set by an operator; this can be a simple potentiometer acting as a voltage divider (for ratios less than the unity) or an amplifier with variable gain (for ratios greater than unity). In digital control systems, this is done by a simple multiply instruction.

If the ratio is to be changed remotely (for example a trim control from an automatic sampler on a chemical blending system) a single quadrant analog multiplier is required.

Ratio blocks in general are easier to deal with in digital control working in real engineering units. True ratios e.g. air/gas ratio of 10/1 can be used. In analog systems the range of the flow meters need to considered. Assume we have primary flow with full scale deflection (FSD) of 12000 liters/min, and a secondary flow of FSD 2000 liters/min and the required ratio (primary/secondary) of 10/1. The required setting of R on figure 1(b) would be 0.6.

In a well-designed plant with correctly sized pipes, control valves and flow rates, analog ratios are usually close to unity. If this is not the case, the plant design should be examined.

You can also read: Cascade Control

Problems may arise with ratio control, if the secondary loop saturates before the primary. A typical scenario on a gas follow air burner control would go like this: the temperature loop calls for a large increase in heat (because of some outside influence). The air valve (primary) opens fully, and the gas valve follows correctly but cannot match the requested flow. The end result is a flame that is lean and cold (flame temperature falls off rapidly with too lean a ratio) and the temperature does not rise. The system is now locked with temperature loop demanding more heat and the air/gas loops saturated, delivering full flow but no temperature rise. The lesson here is that, the primary loop must saturate before the secondary. If this is not achieved by the pipe sizing, the output of the primary controller should be limited.