Switch Controller

Smooth S-curve transition between discrete states

Overview

The Switch Controller provides smooth transitions between two discrete output states using a logistic (S-curve) function. This prevents process upsets from sudden step changes while still providing essentially on/off control behavior.

When to Use

• Smooth state transitions: When step changes cause process upsets
• Soft start/stop: Equipment that benefits from gradual changes
• Process sensitivity: When abrupt changes stress the process
• Hybrid control: Between on/off and continuous modulation

Common Applications

Application	Low State	High State	Transition Time
Blower ramp	0%	100%	5-15 min
Chemical feed	0 L/h	100 L/h	2-5 min
Valve position	Closed	Open	1-3 min
Recycle flow	Min	Max	5-10 min

Control Theory

Concept

The logistic function provides smooth S-curve transition:

Output
100% ─────────────────────────────────────
                           ╭──────────
                        ╭──╯
                     ╭──╯
                  ╭──╯
               ╭──╯
            ╭──╯
  0% ───────╯─────────────────────────────
         Low      Threshold      High
                      PV

Mathematical Model

Logistic Function:

$$output = L + \frac{H - L}{1 + e^{-k(PV - threshold)}}$$

Where:

• $L$ = Low output value
• $H$ = High output value
• $k$ = Steepness parameter (higher = sharper transition)
• $PV$ = Process variable
• $threshold$ = Switch point

Transition Characteristics

Steepness (k)	Transition Width	Behavior
1	~4.5 × threshold	Very gradual
5	~0.9 × threshold	Moderate
10	~0.45 × threshold	Sharp
20	~0.22 × threshold	Near step

Parameters

Parameter	Unit	Range	Default	Description
Threshold	same as PV	-	-	Switch point
Steepness	-	1-50	10	Transition sharpness
Low Output	%	0-100	0	Output when PV << threshold
High Output	%	0-100	100	Output when PV >> threshold
Hysteresis	same as PV	0-5% span	0.1	Dead zone around threshold
Transition Time	days	0-0.1	0.01	Rate limiting
Action	-	direct/reverse	direct	Control direction

Tuning Guidelines

Steepness Selection

1. Process sensitivity: More sensitive = lower steepness
2. Response speed: Faster needed = higher steepness
3. Noise immunity: Noisy signal = lower steepness

Recommended Settings

Application	Steepness	Transition Time	Hysteresis
Blower ramp	5-10	0.01 (15 min)	0.1 mg/L
Chemical feed	10-15	0.005 (7 min)	5%
Valve control	15-20	0.002 (3 min)	2%

Configuration

Example: Smooth Blower Control

{
  "id": "switch-blower-1",
  "type": "Switch",
  "enabled": true,
  "targetNodeId": "aerobic-reactor-1",
  "pvNodeId": "aerobic-reactor-1",
  "pvVariable": "DO",
  "manipulatedVariable": "blowerSpeed",
  "threshold": 2.0,
  "steepness": 10,
  "lowOutput": 30,
  "highOutput": 100,
  "hysteresis": 0.2,
  "action": "reverse",
  "transitionTime": 0.01,
  "mode": "auto"
}

Integration Example

Smooth Aeration Ramping

Scenario: Ramp blower between 30% and 100% based on DO

1. DO well above 2.0: Output near 30% (low)
2. DO approaching 2.0: Output begins rising
3. DO at threshold: Output at 65% (midpoint)
4. DO below 2.0: Output rises toward 100%
5. Rate limited: Cannot change faster than transition time allows

Response Curves

DO (mg/L)
3.0 ─────┐
         │
2.5      │
         │
2.0 ─ ─ ─│─ ─ ─ ─ ─ ─ ─ ─ threshold
         │
1.5      └────────────────

Output %
100 ─────────────────────┐
                      ╭──┘
                   ╭──╯
                ╭──╯
 30 ────────────╯

Comparison: Switch vs Deadband

Aspect	Switch	Deadband
Transition	Smooth curve	Instant step
Equipment stress	Low	Higher
Control precision	Continuous	Binary
Computation	More complex	Simple
Best for	VFDs, modulators	On/off actuators

Best Practices

1. Match steepness to process

   • Slower processes = lower steepness
   • Faster processes = higher steepness

2. Use hysteresis for noise

   • Prevents oscillation around threshold
   • Typically 5-10% of expected variation

3. Set appropriate transition time

   • Consider equipment ramp rates
   • Account for process dynamics

4. Choose correct action

   • Direct: Output increases as PV increases
   • Reverse: Output increases as PV decreases

Troubleshooting

Issue	Cause	Solution
Hunting	Steepness too high	Reduce steepness
Slow response	Steepness too low	Increase steepness
Oscillation at threshold	No hysteresis	Add hysteresis
Jerky transitions	No rate limit	Add transition time
Wrong direction	Action incorrect	Toggle action

Mathematical Details

Logistic Function Properties

• Symmetric: Around threshold point
• Bounded: Always between low and high outputs
• Smooth: Infinitely differentiable
• Monotonic: Always increasing (direct) or decreasing (reverse)

Effective Transition Zone

The PV range over which output transitions from 5% to 95% of range:

$$\Delta PV_{transition} \approx \frac{4.4}{k}$$

For k=10: $\Delta PV \approx 0.44$ units

Related Controllers

• Deadband-Controller - Step transitions
• TimeOnOff-Controller - Time-based operation
• ContinuousP-Controller - Proportional-only modulation

References

1. Verhulst, P.F. "Mathematical Researches into the Law of Population Growth Increase" (1845)
2. Smith, C.L. "Digital Computer Process Control" (1972)