Feedforward and Ratio Control

In process control, waiting for a disturbance to affect your key output variable before taking action is often too slow. Feedforward control and ratio control are proactive strategies designed to act on measurable disturbances before they can degrade process performance. By using a model of the process, these methods anticipate the necessary corrective action, leading to faster response times, reduced variability, and improved product quality, especially in industries like chemical manufacturing where disturbances are frequent and predictable.

The Foundation of Feedforward Control

Pure feedback control reacts to an error—the difference between a setpoint and the measured process variable. While robust, it is inherently reactive. If a major disturbance enters the process, the controller cannot act until the error has already developed. Feedforward control, in contrast, measures the disturbance directly and uses a process model to calculate and apply a corrective action before the disturbance can influence the controlled variable.

The core principle is the feedforward control law, derived from a steady-state model of the process. Consider a process where the controlled variable $y$ is affected by a manipulated variable $u$ and a measurable disturbance variable $d$. The goal is to keep $y$ at its setpoint. The feedforward controller solves for the required change in $u$ to perfectly cancel out the effect of a change in $d$. If the process model is perfect and instantaneous, the disturbance is compensated for exactly, and no error ever occurs. The design starts with the combined process relationships: $\Delta y=K_p\Delta u+K_d\Delta d$. For perfect rejection, we set $\Delta y=0$, yielding the feedforward control law: $\Delta u=-(K_d/K_p)\Delta d$. Here, $K_p$ is the process gain and $K_d$ is the disturbance gain.

Dynamic Compensation: Lead-Lag Units

The simple steady-state feedforward law assumes the effects of $u$ and $d$ on $y$ have identical dynamics—they take the same amount of time to manifest. In reality, this is almost never true. Applying the steady-state correction will lead to a temporary error because the corrective action from $u$ and the disturbance effect from $d$ will misalign in time.

This is where dynamic compensation, typically in the form of a lead-lag unit, becomes essential. Its transfer function is $G_{ff}(s)=K({\tau }_{lead}s+1)/({\tau }_{lag}s+1)$. The steady-state gain $K$ is the ratio $-K_d/K_p$ from the steady-state law. The time constants ${\tau }_{lead}$ and ${\tau }_{lag}$ are tuned to match the dynamic responses. If the disturbance path is slower than the manipulated variable path, a lead component (${\tau }_{lead}>{\tau }_{lag}$) is used to "speed up" the controller's response. If the disturbance path is faster, a lag component (${\tau }_{lag}>{\tau }_{lead}$) is used to "slow down" the controller's action. Proper tuning of this compensator is critical for effective dynamic rejection of the disturbance.

Combined Feedforward-Feedback Control

While powerful, feedforward control has a major weakness: it relies on the accuracy of its process model. Any unmeasured disturbance, model inaccuracy, or calibration drift will result in a persistent offset that the feedforward controller cannot correct. Therefore, feedforward is almost always implemented in combination with a feedback loop.

In a combined feedforward-feedback system, the two strategies complement each other perfectly. The feedforward component provides immediate, proactive compensation for the major, measurable disturbance. The feedback component then handles everything else: it corrects for any residual error caused by model mismatch, accounts for all other unmeasured disturbances, and ensures long-term setpoint tracking. The output of the feedforward controller and the feedback controller (e.g., a PID) are summed to form the final command to the control valve. This architecture leverages the speed of feedforward with the robustness and accuracy of feedback, offering superior performance to either strategy alone.

Ratio Control for Stream Composition

A specialized and extremely common application of the feedforward principle is ratio control. Its objective is to maintain the ratio of two process streams, rather than the absolute value of one. This is essential in operations like blending, combustion, and reactor feed systems, where maintaining a correct proportion (e.g., fuel-to-air, acid-to-water, monomer-to-catalyst) is critical for safety, quality, and efficiency.

In a standard ratio control scheme, one stream is designated the wild flow (or uncontrolled flow), $F_{wild}$. The other is the controlled flow, $F_{controlled}$. The system must maintain $F_{controlled}/F_{wild}=R$, where $R$ is the desired ratio. The measured wild flow acts as the measurable disturbance. The ratio controller is, in essence, a feedforward controller that calculates the setpoint for the controlled flow loop: $S{P}_{controlled}=R\times F_{wild}$. This setpoint is dynamically updated as the wild flow changes, proactively adjusting the controlled flow to maintain the ratio. A secondary feedback loop on the controlled flow valve ensures this flow setpoint is achieved.

Common Pitfalls

1. Neglecting Dynamic Compensation: Implementing only the steady-state feedforward gain is a frequent error. Without a lead-lag unit to align dynamic responses, the controller can actually make performance worse by introducing inverse responses, causing larger temporary deviations than if no feedforward was used at all.
2. Over-Reliance on Feedforward: Using feedforward without a feedback companion is risky. As process equipment wears or operating conditions drift, the model will become inaccurate. The feedback loop is necessary to provide the ongoing correction and adaptation that a static feedforward model cannot.
3. Incorrect Sensor Placement for Ratio Control: In a ratio loop, the flow measurement for the wild stream must be taken before any mixing point. If it is measured after blending, the disturbance (change in wild flow) is detected too late, and the feedforward action becomes ineffective. Sensor location is critical for measurable disturbance variables.
4. Ignoring Implementation Limits: Feedforward calculations assume the final control element (e.g., a valve) has sufficient rangeability to deliver the computed correction. If a disturbance drives the calculated valve signal to 100% or 0%, the feedforward action saturates and becomes ineffective. Always analyze the expected range of disturbances during design.

Summary

• Feedforward control is a proactive strategy that uses a process model to calculate control action based on measured disturbances, providing faster rejection than reactive feedback alone.
• Dynamic compensation via a lead-lag unit is essential to align the timing of the corrective action with the disturbance's effect, preventing temporary errors caused by differing process dynamics.
• Combined feedforward-feedback control is the standard implementation, leveraging the speed of feedforward for known disturbances and the robustness of feedback for model errors and unmeasured upsets.
• Ratio control is a vital feedforward application that maintains a specified proportion between two flows, widely used in blending, combustion, and reactor feed systems.
• Successful implementation requires an accurate and measurable disturbance, a reasonably good process model, and careful consideration of sensor placement and actuator limits.