Feedforward Control Notes

Instrument Technician - Feedforward Control

Objective One: Control Strategies

Feedforward control is a control strategy that prevents disturbances from affecting the controlled variable, unlike feedback control which reacts after the disturbance has already occurred.

Control Strategies

Control strategies are methods used to bring the controlled variable back to the desired value. A steam heat exchanger is often used as an example, where the control strategy aims to supply enough steam to heat the fluid to the desired temperature.

Process Variables and Disturbances

• Manipulated Variable: Steam flow, controlled by a valve.

• Controlled Variable: Temperature of the hot fluid leaving the exchanger.

• Disturbances:

  • Cold fluid inlet temperature.

  • Cold fluid flow rate.

  • Outside temperature.

Control strategies change the manipulated variable to maintain the desired value of the controlled variable. These strategies can be:

1. Feedback control

2. Pure feedforward control

3. Feedforward and feedback control

Feedback Control

Feedback control compares the process variable (PV) to the setpoint (SP) and responds when a disturbance causes the PV to deviate from the SP. The controller changes its output signal (CO) to the manipulated variable to reduce the error between the SP and PV.

Feedback Control System

A temperature controller (TIC-100) maintains the temperature at the SP. A temperature transmitter (TT-100) sends a signal for the exit temperature of the fluid (PV) to TIC-100. The controller compares the PV to its SP and adjusts the steam flow accordingly.

Feedback Response to a Disturbance

Feedback control cannot react until the PV starts to deviate from its SP. The controller then changes its output to bring the PV back to the SP. The speed of reaction depends on the controller's tuning settings. Incorrect tuning may lead to instability.

Characteristics of Feedback Control

• Determines the necessary signal to reduce the error between the PV and the SP.

• Uses standard off-the-shelf devices/software.

• Does not require detailed plant/process information.

• Corrective action occurs only after an error.

• Responds to changes in the outlet temperature, not the inlet.

• May cause substantial deviation from the setpoint for slow processes.

• Load disturbances may require new tuning settings.

• Loops can become unstable.

Pure Feedforward Control

Pure feedforward control measures disturbances and uses them to determine the value of the manipulated variable. The controlled variable is not measured. Perfect pure feedforward control requires perfect knowledge of the process.

Feedforward Control System

The feedforward control strategy measures disturbances like product mass flow ($q<em>{mp}$) and product inlet temperature ($T</em>{in}$). It determines the steam mass flow ($q_{ms}$) required to achieve the desired exit temperature.

Feedforward Response to a Disturbance

The feedforward control strategy immediately changes its output signal (FF) to adjust the steam flow. However, the PV may not reach the exact SP because the feedforward calculation is not perfect.

Characteristics of Pure Feedforward Control

• Requires detailed plant/process information.

• Cannot cause loop instability because there is no feedback.

• Requires measurement of all disturbances, which is often impossible.

• Compensates for disturbances before they affect the process variable.

Feedforward and Feedback Control

This strategy combines both feedforward and feedback control to manipulate the final control element. Feedforward addresses disturbances, while feedback ensures the controlled variable reaches the desired value.

Feedforward and Feedback Control System

The output of the feedback controller (TIC-100) is added to the feedforward signal (FF). The combined signal is sent to the steam flow controller (FIC-300).

Response to a Disturbance

The feedforward control strategy adjusts its output, and the feedback controller corrects any deviation from the setpoint.

Characteristics of Feedforward and Feedback Control

• The feedback controller reduces the error between the PV and the SP.

• The feedforward control strategy minimizes PV deviations.

• Requires detailed plant/process information.

• Can become unstable due to the feedback controller.

Objective Two: Feedforward Control Advantages and Applications

Feedforward control compensates for disturbances before their effect is felt in the output. It is always used with feedback control in industry.

Development of Feedforward Control Strategies

Feedforward control strategies can be developed from transfer functions (feedforward compensation) or from mass and energy balance equations (model predictive feedforward). These strategies can be static or dynamic.

Static vs. Dynamic Feedforward Control

• Static: Calculates the required steam flow and steps its output immediately. The CO value does not change after the initial response.

• Dynamic: Calculates how to change the steam flow over time. The CO value changes with time, and response may not be immediate.

Feedforward Compensation

Uses experimentally determined transfer functions of the process and disturbances to develop the control strategy. It enhances the performance of a feedback control loop by minimizing the effect of a measured disturbance.

Implementation

A transmitter measures the disturbance, and its output changes the feedback controller's output signal to the final control element (FCE). The disturbance transmitter output is modified as it passes through function blocks, using the equation: $-\frac{G<em>L}{G</em>p}$

Where:

• $G_L$ is the transfer function of the load disturbance.

• $G_p$ is the transfer function of the plant.

Transfer Function

For self-regulating processes, the transfer function is modeled as a first-order plus dead time process in the Laplace domain:

$G = \frac{Ke^{-T_D s}}{1 + \tau s}$

Where:

• K is the gain of the process.

• $T_D$ is process dead time.

• $\tau$ is the process first-order time constant.

Experimental Determination of Transfer Functions

1. Plant Transfer Function ($G_p$): Step the feedback controller output in manual and record the PV response:

   $G<em>p = \frac{K</em>p e^{-T<em>{DP} s}}{1 + \tau</em>p s}$

2. Disturbance Transfer Function ($G_L$): Step the disturbance with the feedback controller in manual and record the PV response:

   $G<em>L = \frac{K</em>L e^{-T<em>{DL} s}}{1 + \tau</em>L s}$

Static Feedforward Control Strategy

Uses the ratio of the two static gains:

$K = -\frac{K<em>L}{K</em>p}$

Where:

• K is a unitless static gain value.

$ΔCO = ΔU × K$

Dynamic Feedforward Control Strategy

Adds a dead time function block and a lead/lag function block to the static feedforward strategy to provide a timed response. The required timed response is calculated from the disturbance/plant transfer function: $-\frac{G<em>L}{G</em>P}$

$(\frac{1 + \tau<em>p s}{1 + \tau</em>L s})$ is the ratio of the two first-order time constants and can use a lead/lag function block where $T<em>{ip}$ is the lead time and $T</em>{iL}$ is the lag time.

$(e^{-(T<em>{DL} - T</em>{DP})s})$ is the difference between the two dead time constants and can use a dead time function block.

Example: Heat Exchanger Parameters

Determine the parameters in the feedforward compensation control strategy for a heat exchanger.

Plant Transfer Function:

• $K_p = 1.9$

• $T_{DP} = 3 \text{ min}$

• $\tau_p = 8 \text{ min}$

• $G_p = \frac{1.9e^{-3s}}{1 + 8s}$

Disturbance Transfer Function:

• $K_L = -0.8$

• $T_{DL} = 3.8 \text{ min}$

• $\tau_L = 10 \text{ min}$

• $G_L = \frac{-0.8e^{-3.8s}}{1 + 10s}$

Feedforward Parameters:

• Static gain: $K = \frac{-K<em>L}{K</em>p} = \frac{-(-0.8)}{1.9} = 0.42$

• Lead time: $T_{ip} = 8 \text{ min}$

• Lag time: $T_{iL} = 10 \text{ min}$

• Dead time: $e^{-(T<em>{DL} - T</em>{DP})s} = e^{-(3.8 - 3.0)s} = e^{-0.8s}$

Nonlinear Process Considerations

A nonlinear process affects the performance of a feedforward compensation control strategy because it is based on experimentally derived transfer functions for one set of load conditions.

Model Predictive Feedforward

Model predictive feedforward uses a mathematical model developed from mass or energy balance equations to develop the control strategy. This control strategy enhances the performance of a feedback control loop by minimizing the effect of a measured disturbance.

Static Model Predictive Feedforward

Uses a mathematical model of the process to calculate the required value of the manipulated variable, which is then added to the feedback controller output signal to the final control element.

Dynamic Model Predictive Feedforward

For a dynamic model, predictive feedforward lead/lag and dead time function blocks are necessary.

Model Predictive Feedforward Example: Steam Heat Exchanger

Mathematical Model:

Energy loss by the steam = Energy gain by the product.
$q<em>{ms} h</em>{fg} n = C<em>p q</em>{mp} (T<em>{SP} - T</em>{in})$

Where:

• $q_{ms}$ is the steam flow (kg/min).

• $h_{fg}$ is the steam enthalpy (kJ/kg).

• n is the exchanger efficiency (fraction).

• $C_p$ is the product's specific heat (kJ/kg °C).

• $q_{mp}$ is the product flow (kg/min).

• $T_{SP}$ is the required product outlet temperature (°C).

• $T_{in}$ is the product inlet temperature (°C).

Rearranging to solve for the steam flow ($q_{ms}$):

$q<em>{ms} = \frac{C</em>p q<em>{mp} (T</em>{SP} - T<em>{in})}{n h</em>{fg}}$

Static Model Predictive Feedforward Control Strategy

Calculates the required steam flow based on its model. However, because this calculation is not perfect, the feedback control signal adds or subtracts from the feedforward control calculation to ensure the PV reaches the setpoint.

Dynamic Model Predictive Feedforward Control Strategy

Lead/lag and dead time function blocks are added to the output of both load disturbances. These blocks provide the timed response required for dynamic feedforward control.

Control Applications

Feedforward control improves processes that are slow and subject to frequent and large disturbances and processes that have a dynamic inverse response.

Frequent and Large Disturbances

If the ratio of the dead time to the first-order time constant is close to one or greater, feedback control cannot prevent disturbances from causing substantial deviations of the PV from the SP.

Inverse Response

An inverse response is the dynamic characteristic of a process where its output responds to an input change by moving initially in one direction, but finally in the other.

Example: Liquid level in a steam drum has an inverse response to a change in the steam demand caused by shrink and swell.

Shrink and Swell

• Swell: A sudden rise in steam demand causes the steam header pressure to drop, which allows the vapor bubbles to expand and raise the fluid level in the steam drum temporarily.

• Shrink: A sudden decrease in steam demand causes the steam header pressure to rise, which causes the vapor bubbles to contract and lower the fluid level in the steam drum temporarily.

Control Advantages

• Minimizes the effect that disturbances have on the controlled variable.

• Feedback takes care of disturbances that are not important enough to be measured and compensated for.

• The feedforward portion of the strategy does not have to compensate exactly for disturbances, as any errors are looked after by the feedback loop.

Objective Three: Block Diagrams

A block diagram models each element of the control loop using transfer functions. This provides a model of the process that can determine how the process variable reacts to a change in controller output.

Feedback Control Loop

• AU: Load change

• GL: Load change effect on the PV

• ACO: Change in controller output

• Gp: Effect on the PV

Equation

$ΔPV = (ΔU(G<em>L) + ΔCO (G</em>P)) G_T$

Feedforward Compensation Control Strategy

• FF: Feedforward control strategy

Figure 25 shows how a load change AU and a change in the controller output ACO affects the process variable APV.

Equation:

$ΔPV = [ΔU(G<em>L) + ΔU(-\frac{G</em>L}{G<em>P}) + ΔCO (G</em>P )] G_T = 0$

Objective Four: Tuning Feedforward Control Systems

To tune a feedforward control system, adjust the feedforward parameters and the feedback tuning parameters for optimal performance.

Feedforward Compensation Tuning

Uses experimentally determined transfer functions of the process and disturbances to determine static and dynamic feedforward control parameters.

Tuning Steps

1. Adjust the feedback trim controllers tuning parameters with the feedforward control strategy enabled and the cascade loop in cascade mode, if used.

2. Tune the feedback trim control in a feedforward control strategy the same way you tune a standalone feedback controller.

Static Feedforward Compensation Tuning

1. Ensure the process is operating at normal conditions.

2. Put the feedback trim controller in manual and adjust its output to bring the PV to the normal operating SP.

3. If the feedforward control system uses a cascaded loop to control the manipulated variable, ensure it is tuned correctly and in cascade mode.

4. Disable dynamic compensation.

5. Program the feedforward static gain with the experimentally determined static gain.

6. Enable the feedforward control strategy.

   • if the PV decreases and recovers below its original value after a disturbance, then the static gain is too low.

Dynamic Feedforward Compensation Tuning

Tune the lead/lag function block before the dead time function block.
Lead < Lag. Lead > Lag. Lead =Lag 1m