Ratio Controller

Maintain ratio between wild and controlled flows with PID trim

Overview

The Ratio Controller maintains a specified ratio between a "wild" (leader) variable and a "controlled" (follower) variable. Optional PID trim provides fine adjustment to correct for deviations from the target ratio.

When to Use

• Flow ratio control: RAS/Q ratio, chemical feed to flow
• Blend control: Multiple stream mixing
• Load following: Chemical dose proportional to load
• Feed-forward: Predictive adjustment based on flow

Common Applications

Wild Variable	Controlled Variable	Typical Ratio
Influent flow	RAS flow	0.5-1.5
Influent flow	Chemical dose	Variable
Primary effluent	Methanol dose	kg/m³
MLSS	WAS flow	% of inventory

Control Theory

Concept

graph LR
    Wild[Wild Flow] --> Ratio[Ratio Station]
    SP[Ratio SP] --> Ratio
    Ratio --> CV_SP[Controlled SP]
    CV_SP --> Sum((+/-))
    CV[Controlled PV] --> Sum
    Sum --> Trim[PID Trim]
    Trim --> Output[Final Output]

Mathematical Model

Base calculation: $$output_{base} = ratio \times wild$$

With PID trim: $$output = output_{base} \times (1 + trim)$$

$$trim = K_p \cdot e_r + K_i \int e_r , dt + K_d \frac{de_r}{dt}$$

Where:

• $e_r = ratio_{setpoint} - ratio_{actual}$
• $ratio_{actual} = \frac{controlled}{wild}$

Parameters

Parameter	Unit	Range	Default	Description
Ratio	-	0.1-10	1.0	Target ratio (controlled/wild)
Wild Lag	days	0-0.1	0	Delay compensation for wild
PID Trim Enabled	-	true/false	true	Enable feedback trim
Trim Kp	-	0.1-2	0.5	Trim proportional gain
Trim Ki	-	0.01-0.5	0.1	Trim integral gain
Trim Kd	-	0-0.1	0	Trim derivative gain
Max Trim	fraction	0.05-0.3	0.1	Maximum trim adjustment
Output Min	varies	-	0	Minimum output
Output Max	varies	-	10000	Maximum output

Tuning Guidelines

Ratio Selection

1. Steady-state requirement: Based on process stoichiometry
2. Dynamic requirement: May vary with load
3. Safety margin: Include buffer for upsets

PID Trim Tuning

The trim loop should be:

• Conservative: Small gains, slow response
• Secondary: Feedforward does most work
• Bounded: Max trim ±10-20%

Recommended Settings

Application	Ratio	Kp	Ki	Max Trim
RAS/Q ratio	1.0	0.3	0.05	0.15
Chemical/Flow	0.005	0.5	0.1	0.2
Blend ratio	0.5	0.4	0.08	0.1

Configuration

Example: RAS Ratio Control

{
  "id": "ras-ratio-1",
  "type": "Ratio",
  "enabled": true,
  "wildNodeId": "influent-1",
  "wildVariable": "flow",
  "controlledNodeId": "clarifier-1",
  "controlledVariable": "flow",
  "targetNodeId": "ras-pump-1",
  "manipulatedVariable": "flow",
  "ratio": 1.0,
  "pidTrim": {
    "enabled": true,
    "kp": 0.3,
    "ki": 0.05,
    "kd": 0,
    "maxTrim": 0.15
  },
  "outputMin": 0,
  "outputMax": 50000,
  "wildLag": 0,
  "mode": "auto"
}

Example: Flow-Paced Chemical Feed

{
  "id": "chemical-ratio-1",
  "type": "Ratio",
  "enabled": true,
  "wildNodeId": "influent-1",
  "wildVariable": "flow",
  "controlledNodeId": "chemical-tank-1",
  "controlledVariable": "flow",
  "targetNodeId": "dosing-pump-1",
  "manipulatedVariable": "flow",
  "ratio": 0.005,
  "pidTrim": {
    "enabled": true,
    "kp": 0.5,
    "ki": 0.1,
    "kd": 0,
    "maxTrim": 0.2
  },
  "outputMin": 0,
  "outputMax": 1000,
  "wildLag": 0.01,
  "mode": "auto"
}

Integration Example

RAS Flow Ratio Control

Scenario: Maintain RAS/Q ratio of 1.0

Influent (Wild)     10,000 m³/d
                         │
                         ▼
              ┌──────────────────────┐
              │    Ratio = 1.0       │
              │    Trim = +5%        │
              └──────────────────────┘
                         │
                         ▼
RAS Flow (Output)   10,500 m³/d

Calculation:

• Base output: 10,000 × 1.0 = 10,000 m³/d
• Trim: If actual ratio is 0.95, trim adds 5%
• Final output: 10,000 × 1.05 = 10,500 m³/d

Dynamic Response

Flow (m³/d)
15000 ─────────────────────────────
                  ┌────────────────  Wild (Influent)
10000 ────────────┘
                     ┌─────────────  Output (RAS)
                  ┌──┘                with trim tracking
10000 ────────────┘
      └─────────────────────────────

Time      0        1h       2h       3h

Best Practices

1. Measure both flows accurately

   • Wild and controlled need good meters
   • Flow totalizers help verify ratio

2. Keep trim bounded

   • Max trim ±10-20%
   • Large trim indicates ratio error

3. Consider transport lag

   • Use wild lag for distance
   • Prevents overshooting

4. Monitor actual ratio

   • Trend ratio over time
   • Alert on sustained deviation

5. Coordinate with other controls

   • RAS ratio affects clarifier
   • Chemical ratio affects pH

Troubleshooting

Issue	Cause	Solution
Ratio offset	Trim too conservative	Increase Ki
Oscillation	Trim too aggressive	Reduce Kp, Ki
Overcorrection	Max trim too high	Reduce max trim
Lag mismatch	Wild lag incorrect	Adjust wild lag
Ratio hunting	Measurement noise	Filter inputs

Advanced Features

Wild Variable Lag

Compensate for transport delay:

{
  "wildLag": 0.01
}

Uses delayed wild value to match when flow arrives at controlled point.

Bounded Trim

Prevents runaway:

{
  "maxTrim": 0.15
}

Output limited to ±15% of base calculation.

Comparison: Ratio vs Feedforward

Aspect	Ratio	Feedforward
Feedback	Yes (trim)	Optional
Complexity	Moderate	Higher
Response	Immediate	Lead-lag compensated
Best for	Flow ratios	Disturbance rejection

Related Controllers

• Feedforward-Controller - Disturbance-based control
• Cascade-Controller - Nested loops
• PID-Controller - Base trim algorithm

References

1. Shinskey, F.G. "Process Control Systems" (4th Edition)
2. Liptak, B.G. "Instrument Engineers' Handbook: Process Control"