What Have I Learned? – Ratio Control (Part 2)

So the question on the minds of automation engineers for process control and even the members of congress for the banks and the economy is how do you fix your model? Will feedback correction be enough? Will the correction arrive too late? How do you deal with a response that is not self-regulating but is integrating or a possibly a runaway?

If you want the bottom line and don’t have time for technical jibber-jabber: “The most universal but not well known solution for feedback correction of the flow feedforward model for ratio control uses a Ratio block in tandem with a Bias/Gain block as shown in slide 7 of RatioControl.pdf. The Ratio block operates in the AUTO mode and has its local setpoint adjusted by the operator. The Bias/Gain block runs in the CAS mode and has its CAS setpoint (bias) connected to the output of the process controller used for rapid feedback correction.” Of course, you need to checkout and test this solution like any other.

Ratio control is basically a very simple flow feedforward model that involves a simple bias and gain applied to independent flow to compute the dependent flow. On a plot of dependent flow (Y-axis) versus independent flow (X-axis), the gain is the slope and the bias is the intercept. The feedforward multiplier and summer in a process controller for feedback correction of the ratio control would change the slope and bias, respectively. The slope is the ratio factor (delta dependent flow/ delta independent flow).

Nearly all PID blocks have internal feedforward functionality. Some PID blocks have feedforward multipliers besides feedforward summers but the internal structure is fixed and often difficult to understand and maintain. For ratio control, the feedback correction by multiplication or summation is best done outside of the PID block. The use of the Ratio block and Bias/Gain block provide the flexibility and visibility needed through its BKCAL and built-in features and options such as bumpless transfer to the existing ratio. In either case, the independent flow is the IN_1 input and the dependent flow is the IN input to the Ratio (RTO) block as shown in Slide 7 of RatioControl.pdf. The setpoint of the RTO block is the desired flow ratio and the PV is the actual flow ratio.

For a feedback correction by multiplication, the output of the process controller manipulates the ratio factor used in the multiplication of the independent flow. The RTO block is put in the CAS mode and the output of process feedback PID is connected to the CAS_IN of the RTO block. The output of the RTO block becomes the CAS_IN setpoint of the dependent flow loop.

For a feedback correction by summation, the output of the process controller directly manipulates a bias after the multiplication of the independent flow by an operator set ratio factor. The RTO block is put in the AUTO mode and the operator adjusts the local setpoint (SP). The output of the RTO block becomes the input (IN) and the process feedback controller becomes the setpoint (SP) of a Bias/Gain (BG) block. The output of the BG block becomes the CAS_IN setpoint of the dependent flow loop.

A straightforward feedforward explanation can be found on pages 73-83 of the E-book posted on this site on April 3 titled Continuous Control Techniques for Distributed Control Systems. Just ignore the antiquated Figures 5-1a and 5-1b that offered a solution to the missing adjustable filter and time delay blocks back in the early days of the DCS. For more on the nuances of feedforward, check out the May 2008 Control Talk Column “Feeding on Feedforward:” http://www.controlglobal.com/articles/2008/171.html

To visualize and quantify the correction you can use Excel to plot on the Y axis the dependent flow and on the X axis the independent flow for various operating conditions (e.g. compositions and temperatures) so you have a family of lines. If the lines all intercept close to zero, then the slope or ratio factor is mostly changing and a feedforward multiplier would be the apparent choice as shown in Figure 5-2a on page 77 for a ratio of reagent to feed flow. This relationship holds for most blend, composition, pH, % solids, and temperature control systems in continuous (self-regulating) processes. In other words, if the feed flow goes to zero, the reagent, reactant, blend, or coolant flow should go to zero.

On the other hand, if the intercept varies and the slope is relatively constant, then a feedforward summer is the first choice as shown in Figure 5-2b on page 78 for a ratio of feed water flow to steam flow where the blow down flow shifts the operating line.

The steady state process gain for continuous processes is best seen on a plot of the controlled variable (temperature, composition, % solids, blend, and pH) on the Y-axis versus the ratio of manipulated flow (coolant, reactant, dilution, blend, and reagent flow) to the feed flow. These plots can be generated from the first principle equations in the Advanced Application Note 3 posted April 3 on this website or by simulation programs that use first principle equations. The result is a steady state process gain that is inversely proportional to the feed flow. By using a feedforward multiplier, you are effectively multiplying the controller output by the feed flow which cancels out the steady state gain.

So why are feed forward summers mostly used in industrial applications? The short answer is that they work well enough and are easy to implement and understand. You can do an awful lot with a bias correction. The feedback correction of nearly all advanced control tools such as model predictive control, neural network estimators, and partial least squares estimators use a simple bias that is a fraction of the error between the predicted value and the measured value.

There are also good technical reasons to use a summer if you dig deeper. The bias corrects for offset and drift, which is the largest error in most flow measurements. You don’t need to nail the ratio factor range for scaling the controller output. You can simply use a + and – % correction to the flow feedforward. In some older versions of the DCS you had to implement a bias of 50% so that we could get a “+ and – 50% correction. If the controller output was 50%, the flow feedforward was perfect. The deviation from 50% was a measure of the flow feedforward error. An integral only valve position controller (VPC) whose setpoint (SP) is 50% and whose process variable (PV) is the feedback controller output can then trim the ratio factor (RTO setpoint). If the VPC IDEADBAND option is employed so you get no integral action if the PV is within 10% of the SP, you get a gradual slope correction only if the fast bias correction is insufficient.

For well mixed vessels and distillation columns, the process time constant is inversely proportional to the feed flow. Since the maximum controller gain for load rejection is proportional to the process time constant divided by the process gain which itself is inversely proportional to flow, the net effect of feed flow on controller gain is cancelled out. The use of a feedforward multiplier now creates a nonlinearity where the controller tuned for low flow will tend to oscillate at a higher flow. This is often aggravated by an equal percentage flow characteristic whose slope (valve gain) is proportional to flow.

If you have an integrating process response, you need an overcorrection to get you back to set point. The correction is most readily visualized as a bias. The easiest to understand example of an integrating response is the level loop where the correct ratio of manipulated discharge flow to the feed flow is one. If the level is too high, keeping the discharge flow equal to the feed flow will not bring the level down. Batch temperature, pH, and composition control tend to have integrating responses. Continuous processes where the process output flow comes from vapor phase tend to have an integrating response in liquid phase. Conductivity (total dissolved solids) control of a boiler drum is an example because the only way to get solids out of the liquid is by blowdown. The ratio of blowdown flow to feedwater flow shifts based on the amount of unbalance in the integrated response. If the total dissolved solids is below the set point, the correct ratio of blowdown to feedwater flow is zero. Similarly, impurity concentration builds up in reactors with a vapor phase product or a significant recycle stream. Here the ratio of purge rate to fresh feed rate shifts due to the integrating response. The overcorrect requirements for a runaway response are even greater because the process is accelerating away from the setpoint. For some reactors, there is a point of no return where the best you can do is to implement the emergency and evacuation procedures. Let’s hope that is not the case for the economy. Mars doesn’t look terribly inviting and the Martians in the movies have bad attitudes

The main scope of applications where a feedforward multiplier provides a desirable compensation for a nonlinearity is when the feedback controller output goes to a linear installed characteristic or flow controller for blend, composition, % solids, and pH control at the outlet of a static mixer or for temperature control at the outlet of an exchanger because this process equipment has essentially plug flow (with very little backmixing) and hence a negligible process time constant.

This leaves us with the final question, why do oxygen controllers on a boiler stack correct the air flow rather than the ratio of air to fuel flow? Why go to the confusion of a calculated versus a real air flow? The main reason is to actively use the cross limits or lead-lag systems employed in a combustion control system to insure the air flow leads the fuel flow on an increase in firing demand and air lags fuel on a decrease in firing demand.

Regardless of whether a feedforward multiplier or summer is used, the desired ratio before feedback correction and the actual ratio after feedback correction should be displayed, historized, and trended along with the controller output and independent flow.