Output to main control and trim control final elements

I have a loop in a plant that involves two split range outputs. One to a small trim valve, the other to a variable speed drive on a pump. The
pump and the trim valve both add a particular dense material to a tank of water in a density loop that measures the density of the solution leaving the tank. The flow from the tank is variable. The variable speed pump on the dense additive cannot change speed fast, so the trim valve is used for rapid changes based on measured density changes (due to discharge flow changes).
Both outputs are from the same controller, using a split range output. It is an old, analog controller. That controller will be replaced with a loop added to an existing DCS. Basically, the loop does not work and nobody has been able to tune it. It stays in manual, the discharge from the tank is not constant. This variation in density causes problems downstream.
Is there a better way of controlling the density? We would like to keep the trim valve about 50% open on average, going further open or closed to control short term variations in the density. Larger changes, resulting from more significant changes in the flow from the tank, will be handled by the variable speed pump, although it is slow to react.
Both the dense material from the trim valve and the material from the variable speed pump are the same material, but from different supply tanks. The trim valve does not have the rangeability to cover the necessary change in addition of the dense material.
Has anyone worked with a loop like this before?
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Anita Richards wrote:

You can link control of the pump to the trim valve with a second, slow response controller, commonly referred to as a valve position controller. It watches the position of the trim valve and adjusts it output as the valve position changes from the setpoint value (50%, in this case). In effect, the valve reacts first, and the valve position controller forces it back to 50% after an excursion, by adjusting the pump speed. You can also use the pump speed as a feed forward to the density (valve) controller to undo most of the pump flow changes at the valve, instead of waiting for the density measurement to discover them.
A bigger question, is, do you have a measurement or inference of the mixed outflow (by level controller output, for instance)? That value would make a very useful feed forward variable for the valve controller that would predict the change in valve position required before the density measurement even reacted to flow changes.
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The control of gross and fine final control elements is a classic problem. I see it most in situations such as the let down of steam through a turbine and through a let down valve, or control of feed water by changing pump speed and by changing trim valve position.
I would not expect a split range output from one controller to work.
There are several methods of control. The one I have found useful in most situations is to (based on your case) control the trim valve by a faster acting controller with the density as input. Then a second controller would take the trim valve (or the controller output) as an input, and manipulate the speed of the pump to hold the trim valve at a certain position.
Anita Richards wrote:

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