Feedforward Controller

Disturbance-based feedforward with lead-lag compensation

Overview

The Feedforward Controller anticipates process disturbances and adjusts the manipulated variable proactively. Combined with optional feedback PID, it provides excellent disturbance rejection by acting before the disturbance affects the controlled variable.

When to Use

• Measurable disturbances: Flow, load, composition changes
• Fast disturbance rejection: When feedback alone is too slow
• Known process relationships: Static gain can be determined
• Predictable upsets: Diurnal patterns, batch operations

Common Applications

Disturbance	Compensated Variable	Application
Influent flow	Chemical dose	Flow-paced dosing
Load change	Aeration rate	DO control
Temperature	Reaction rate	Digester heating
pH upset	Lime dose	pH control

Control Theory

Concept

graph TB
    D[Disturbance] --> FF[Feedforward]
    D --> Process[Process]
    FF --> Sum((+))
    FB[Feedback PID] --> Sum
    Sum --> MV[Manipulated Variable]
    MV --> Process
    Process --> PV[Process Variable]
    PV --> FB
    SP[Setpoint] --> FB

Mathematical Model

Feedforward output: $$FF = K_{FF} \cdot G_{LL}(s) \cdot d$$

Lead-lag compensator: $$G_{LL}(s) = K_{LL} \cdot \frac{1 + \tau_{lead} \cdot s}{1 + \tau_{lag} \cdot s}$$

Combined output: $$output = FF + FB + bias$$

Where:

• $d$ = Disturbance variable
• $K_{FF}$ = Static feedforward gain
• $\tau_{lead}$ = Lead time constant
• $\tau_{lag}$ = Lag time constant
• $FB$ = Feedback PID output

Lead-Lag Compensation

Without Lead-Lag:
Disturbance ────┐
                │          Output change instant
Output     ─────┴──────────

With Lead-Lag:
Disturbance ────┐
                │          Output leads then lags
Output     ───╮ ╭─────────
              ╰─╯
              ↑
         Lead spike

Parameters

Feedforward Parameters

Parameter	Unit	Range	Default	Description
Static Gain	-	0.1-10	1.0	Process gain (output/disturbance)
Lead Time	days	0-0.1	0.01	Lead time constant
Lag Time	days	0-0.1	0.02	Lag time constant
Bias	%	0-100	50	Base output level
Output Min	%	0-100	0	Minimum output
Output Max	%	0-100	100	Maximum output

Optional Feedback PID

Parameter	Unit	Range	Default	Description
FB Enabled	-	true/false	false	Enable feedback trim
FB Kp	-	0.1-10	1.0	Feedback proportional
FB Ki	-	0.01-2	0.1	Feedback integral
FB Kd	-	0-1	0	Feedback derivative
FB Setpoint	varies	-	-	Feedback target

Tuning Guidelines

Static Gain Calculation

$$K_{FF} = -\frac{K_{process,d}}{K_{process,m}}$$

Where:

• $K_{process,d}$ = Process gain from disturbance to PV
• $K_{process,m}$ = Process gain from MV to PV

Example: Flow-paced chemical dosing

• If flow increases 10%, pH drops 0.2
• If chemical increases 10%, pH rises 0.2
• K_FF = 0.2/0.2 = 1.0 (1:1 flow pacing)

Lead-Lag Tuning

1. Lead time: Match process dead time
2. Lag time: Match process time constant
3. Lead/Lag ratio: Lead ≤ Lag typically

Recommended Settings

Application	Static Gain	Lead Time	Lag Time
Flow pacing	1.0	0.005	0.01
Load compensation	0.5-2.0	0.01	0.02
Temperature FF	0.8	0.02	0.05

Configuration

Example: Flow-Paced Chemical Dosing

{
  "id": "flow-paced-dosing-1",
  "type": "Feedforward",
  "enabled": true,
  "targetNodeId": "dosing-pump-1",
  "disturbanceNodeId": "influent-1",
  "disturbanceVariable": "flow",
  "manipulatedVariable": "doseRate",
  "staticGain": 0.005,
  "leadLag": {
    "leadTime": 0.005,
    "lagTime": 0.01,
    "gain": 1.0
  },
  "outputMin": 0,
  "outputMax": 100,
  "bias": 0,
  "feedbackPID": {
    "enabled": true,
    "pvNodeId": "reactor-1",
    "pvVariable": "pH",
    "setpoint": 7.0,
    "kp": 2.0,
    "ki": 0.5,
    "kd": 0
  },
  "mode": "auto"
}

Example: Load-Based Aeration

{
  "id": "load-aeration-1",
  "type": "Feedforward",
  "enabled": true,
  "targetNodeId": "blower-1",
  "disturbanceNodeId": "influent-1",
  "disturbanceVariable": "flow",
  "manipulatedVariable": "airflow",
  "staticGain": 50,
  "leadLag": {
    "leadTime": 0.01,
    "lagTime": 0.02,
    "gain": 1.0
  },
  "outputMin": 100,
  "outputMax": 1000,
  "bias": 200,
  "feedbackPID": {
    "enabled": true,
    "pvNodeId": "aerobic-reactor-1",
    "pvVariable": "DO",
    "setpoint": 2.0,
    "kp": 50,
    "ki": 10,
    "kd": 5
  },
  "mode": "auto"
}

Integration Example

Chemical Dosing with Flow Compensation

Scenario: Maintain pH 7.0 with flow-paced lime dosing

Flow Increase: 10,000 → 12,000 m³/d (+20%)

Without Feedforward:
- pH drops from 7.0 to 6.8
- Feedback slowly increases dose
- Recovery takes 30+ minutes

With Feedforward:
- Flow increase detected immediately
- Dose increased by 20% proactively
- pH dip limited to 6.95
- Feedback provides fine trim

Response Comparison

Flow (m³/d)
12000 ───────────────────────────
           ┌─────────────────────
10000 ─────┘

pH
7.0  ─────┐   ╭─────────────────  With FF+FB
           ╲╱                      (small dip)
6.8  ───────╲──────────╭─────────  FB only
             ╲────────╯            (large dip)

Dose
120% ──────────────────────────────  FF+FB
           ┌─────────╭───────────
100% ─────────────────╯               FB only
           ┌─────────────────────

Best Practices

1. Accurate disturbance measurement

   • Good flow meters essential
   • Filter noisy signals

2. Correct static gain

   • Determine from process tests
   • Adjust based on performance

3. Lead-lag tuning

   • Start with lead = lag
   • Adjust for response timing

4. Combine with feedback

   • Feedforward handles load
   • Feedback handles errors

5. Monitor both components

   • Track FF and FB contributions
   • Verify FF is helping

Troubleshooting

Issue	Cause	Solution
Overcorrection	Gain too high	Reduce static gain
Undercorrection	Gain too low	Increase static gain
Phase mismatch	Lead/lag wrong	Adjust time constants
Oscillation	Lead too high	Reduce lead time
Drift	No feedback	Enable feedback PID

Advanced Topics

Dynamic Compensation

The lead-lag compensator handles timing mismatch:

• Lead: Anticipates slow process response
• Lag: Smooths rapid changes
• Ratio: Lead/Lag < 1 for most cases

Discrete Implementation

// Lead term
const disturbanceRate = (disturbance - previousDisturbance) / dt;
const leadOutput = disturbance + leadTime * disturbanceRate;

// Lag term (first-order filter)
const lagAlpha = dt / (lagTime + dt);
lagState = lagAlpha * leadOutput + (1 - lagAlpha) * lagState;

// Final FF output
ffOutput = staticGain * lagGain * lagState;

Related Controllers

• Ratio-Controller - For ratio-based feedforward
• Cascade-Controller - Alternative disturbance rejection
• PID-Controller - Feedback component

References

1. Shinskey, F.G. "Feedforward Control Applied" (ISA, 1977)
2. Seborg, D.E. "Process Dynamics and Control" (4th Edition)
3. Smith, C.L. "Practical Process Control" (2009)