# 🏭 Real Industrial Case Scenarios
## S7-1500 Advanced Signal Filtering — Where Theory Meets the Shop Floor

> *"Every filter exists because someone, somewhere, had a bad day with a noisy sensor."*

---

## 📋 Quick Navigation

| Filter | Industry Focus | Go To |
|--------|---------------|-------|
| 🔵 Simple Moving Average | Food, Steel, Energy, Packaging | [→ Jump](#-simple-moving-average-sma) |
| 🟢 Exponential Moving Average | Pharma, Chemicals, Robotics | [→ Jump](#-exponential-moving-average-ema) |
| 🟡 Weighted Moving Average | Automotive, AGV, Batch | [→ Jump](#-weighted-moving-average-wma) |
| 🔴 Median Filter | Mining, Oil & Gas, Filling Lines | [→ Jump](#-median-filter) |
| ⚪ Rate Limiter | Valves, Drives, HVAC, Robotics | [→ Jump](#-rate-limiter) |
| 🔗 Stacked Combinations | Advanced multi-filter chains | [→ Jump](#-stacking-filters--real-combinations) |

---

## 🔵 Simple Moving Average (SMA)

> **Best when:** Response speed is not critical, noise is continuous and random, and accuracy over time matters more than tracking every fluctuation.

---

### Case 1 — Agitated Chemical Reactor | Tank Level

**Industry:** Chemical / Pharma
**Signal:** Ultrasonic level sensor, 0–100%

```
Plant: 10,000L reactor vessel, bottom-mounted agitator, 60 RPM
Problem: Agitator creates surface turbulence → level signal bouncing ±3–5%
         The level is used for batch recipe decisions, NOT fast control
Decision threshold: "Add ingredient B when level < 40%"
```

**Without filter:**
```
Raw signal:  38.2 → 42.7 → 37.9 → 43.1 → 38.5 → 41.9 → 37.4
Result:      Ingredient B added and stopped repeatedly every few seconds
             → Recipe out of spec, batch rejected, €12,000 loss
```

**With SMA (window = 30):**
```
Filtered:    40.1 → 40.0 → 39.9 → 39.8 → 39.7 → 39.6 → 39.5
Result:      One clean crossing of 40% threshold, ingredient added once
             → Batch in spec ✓
```

**Configuration:**
```pascal
arAlarmDefs[0].iWindowSize := 30;   // 30 × 100ms = 3 second averaging window
// At 100ms cycle, window of 30 covers 3 full agitator revolutions (60RPM)
// One revolution = 1 second → three full cycles averaged out
```

---

### Case 2 — Multi-Zone Furnace | Temperature Averaging

**Industry:** Steel / Heat Treatment
**Signal:** 8× Type-K thermocouples, 0–1200°C

```
Plant: Roller hearth furnace, 12 meters long, 8 thermocouples in roof
Problem: Natural hot/cold spots exist between burner zones
         Single sensor reading causes burner to hunt unnecessarily
         Parts exit furnace under-soaked (hardness out of spec)
```

**Signal architecture with SMA:**
```
TC_1 (820°C) ──→ SMA(20) ──→ 819.4°C ──┐
TC_2 (835°C) ──→ SMA(20) ──→ 834.1°C ──┤
TC_3 (811°C) ──→ SMA(20) ──→ 812.3°C ──┤→ AVERAGE → 822.1°C → PID
TC_4 (828°C) ──→ SMA(20) ──→ 827.8°C ──┤
...                                      ┘
```

**Result:** PID controls to true chamber average, not a single sensor's local reading. Part hardness variation dropped from ±4 HRC to ±1.2 HRC.

---

### Case 3 — Energy Metering | Power Consumption Dashboard

**Industry:** Automotive Assembly
**Signal:** Power transducer, 0–500 kW

```
Plant: Body shop production line, 47 servo drives, 12 robots
Problem: Motor inrush currents cause 50–200ms spikes on power reading
         Every robot start = false spike in energy log
         Monthly energy report showing 15% higher consumption than reality
         Triggering false demand charge penalties from utility
```

**Raw vs filtered at robot start:**
```
Time(ms):    0    50   100  150  200  250  300  350
Raw (kW):   120  340  280  380  150  125  122  121   ← inrush spikes
SMA (kW):   120  128  138  152  158  154  148  140   ← smooth energy trend
```

**SMA window sizing:**
```pascal
// Robot start inrush lasts ~200ms
// At 50ms OB cycle → window of 10 covers 500ms (absorbs full inrush + settle)
iWindowSize := 10;

// Result: SCADA energy logging uses SMA value
//         Inrush events invisible to billing system
//         Annual saving: €18,000 in false demand charges
```

---

### Case 4 — Dynamic Checkweigher | Food Packaging Line

**Industry:** Food & Beverage
**Signal:** Load cell, 0–500g

```
Plant: Biscuit packaging line, 120 packs/minute
Problem: Belt vibration, product impact, conveyor joints all corrupt load cell
         Products weigh ~250g, tolerance ±5g (legal requirement)
         False rejects running at 8% — should be <1%
         Each false reject = wasted product + manual check labor
```

**Timing-matched window:**
```
Belt speed:          0.8 m/s
Product length:      160mm
Transit time:        160mm / 800mm/s = 200ms
OB cycle:            10ms
Window size:         200ms / 10ms = 20 samples

→ SMA window of 20 averages exactly one product transit
→ Output at end of transit = stable weight of that product
→ False reject rate dropped from 8.1% to 0.7%
```

---

## 🟢 Exponential Moving Average (EMA)

> **Best when:** You need noise reduction AND fast response, memory is constrained, or you need to track a slowly drifting baseline.

---

### Case 1 — Pneumatic Pressure Control | Fast PID Loop

**Industry:** Semiconductor / Precision Manufacturing
**Signal:** Pressure transducer, 0–10 bar

```
Plant: Nitrogen blanket pressure control on lithography chamber
PID loop sample time: 50ms
Required response to setpoint change: < 300ms
Problem: High-frequency noise from N₂ flow turbulence = ±0.08 bar peak
         SMA with any useful window adds 150–400ms of lag → PID unstable
         Bare signal used directly → PID output oscillates at 8Hz
```

**EMA vs SMA lag comparison at alpha=0.2:**
```
Signal step at t=0:

Time (scans):    1    2    3    4    5    6    7    8    9   10
True signal:   100  100  100  100  100  100  100  100  100  100
SMA (N=10):     10   20   30   40   50   60   70   80   90  100   ← 10 scan lag
EMA (α=0.2):    20   36   49   59   67   74   79   83   87   89   ← tracks faster
```

**Result:** EMA with α=0.2 reduces noise by 73% while adding only ~2 scan lag vs SMA's 5 scan lag. PID loop stable, pressure held to ±0.015 bar.

---

### Case 2 — Adaptive Motor Current Baseline | Predictive Maintenance

**Industry:** Pulp & Paper
**Signal:** Current transformer on main drive, 0–500A

```
Plant: Paper machine main drive, 315kW motor, running 24/7
Problem: Fixed overcurrent alarm at 420A generates 3–5 false alarms/week
         Actual load varies with paper grade: 280A (light) to 380A (heavy)
         Maintenance ignores alarms → real fault missed → €240,000 motor burnout
```

**EMA-based adaptive alarm:**
```pascal
// Slow EMA tracks normal operating baseline (τ ≈ 10 minutes)
rAlpha_baseline := 0.0003;    // Very slow: tracks grade changes, not transients
fbEMA_baseline(rInput := rMotorCurrent, rAlpha := rAlpha_baseline);

// Alarm threshold = 20% above current baseline
rAdaptiveAlarmLimit := fbEMA_baseline.rOutput * 1.20;

// Result:
//   Light paper grade:  baseline=285A → alarm at 342A
//   Heavy paper grade:  baseline=372A → alarm at 446A
//   Genuine bearing fault: current rises 35% over 2 hours → caught at 20% mark
//   False alarms: reduced from 4/week to 0.2/week
```

---

### Case 3 — Spray Dryer Outlet Humidity | Moisture Control

**Industry:** Dairy / Food Processing
**Signal:** Capacitive humidity sensor, 0–100% RH

```
Plant: Milk powder spray dryer, 8-meter drying chamber
Problem: Humidity sensor has two noise sources:
         1. Electrical: High-frequency noise from steam injection solenoids (50Hz)
         2. Physical: Sensor membrane response is naturally slow (τ = 8 seconds)
         Goal: Filter electrical noise without making control slower than sensor itself
```

**Matching EMA to sensor physics:**
```pascal
// Sensor time constant τ = 8 seconds, OB cycle = 500ms
// EMA equivalent time constant: τ_EMA = CycleTime × (1-α)/α
// Solve for α: α = CycleTime / (τ + CycleTime) = 0.5 / (8 + 0.5) = 0.059

rAlpha := 0.06;    // Matches sensor's own response — adds no extra lag
                   // Removes electrical noise completely
                   // Moisture controller now operates at sensor's natural limit
```

**Outcome:** Powder moisture content variation reduced from ±0.8% to ±0.3%. Shelf life of product increased. No additional hardware needed.

---

### Case 4 — HMI Live OEE Display | Operator Feedback

**Industry:** Automotive / Discrete Manufacturing
**Signal:** Calculated OEE%, updated every 60 seconds

```
Plant: Engine assembly line, 3 shifts, OEE target 85%
Problem: OEE calculated per minute swings wildly: 91%, 68%, 95%, 72%, 88%...
         Operators cannot read trend from bouncing number
         Shift supervisors arguing about whether line is improving or declining
         HMI trending chart looks like noise, not a signal
```

**EMA on the HMI trend calculation:**
```pascal
// Every 60-second OEE update feeds into EMA
// α = 0.15 → approximately 12-minute smoothing window
// Fast enough to show real shifts within 30 minutes
// Slow enough to remove single-cycle statistical noise

fbOEE_EMA(rInput := rOEE_Raw, rAlpha := 0.15);
rHMI_OEE_Trend := fbOEE_EMA.rOutput;

// HMI shows both: raw minute value (small) and EMA trend (large bold number)
// Operators now clearly see: "We've been declining for 45 minutes" vs noise
```

---

## 🟡 Weighted Moving Average (WMA)

> **Best when:** Recent measurements are more physically relevant than older ones — acceleration, reaction peaks, or directional motion.

---

### Case 1 — Robotic Laser Seam Tracker | Welding

**Industry:** Heavy Equipment / Off-Highway Vehicles
**Signal:** Laser line sensor position offset, ±15mm

```
Plant: Robotic MIG welding of excavator boom arms
Weld speed: 600mm/min, joint can change direction every 80mm
Problem: Laser speckle noise = ±0.3mm random error each scan
         SMA(6) at 50ms cycle = 300ms averaging → robot lags 3mm behind joint
         WMA(6) at 50ms cycle → recent samples dominate → lag reduced to 1mm
```

**Weight distribution comparison:**

| Sample Age | SMA Weight | WMA Weight | Effect |
|------------|-----------|-----------|--------|
| Current (n) | 16.7% | 28.6% | WMA reacts faster |
| n-1 | 16.7% | 23.8% | |
| n-2 | 16.7% | 19.0% | |
| n-3 | 16.7% | 14.3% | |
| n-4 | 16.7% | 9.5% | |
| n-5 (oldest) | 16.7% | 4.8% | WMA forgets faster |

**Result:** Seam tracking error reduced from ±1.8mm (SMA) to ±0.9mm (WMA). Weld quality went from requiring 60% repair rate to 8% repair rate.

---

### Case 2 — AGV Speed Estimation | Intralogistics

**Industry:** Warehouse / E-Commerce Fulfillment
**Signal:** Encoder pulse interval → calculated speed, 0–2.5 m/s

```
Plant: 48 AGVs in a fulfilment centre, path includes tight 90° turns
Problem: AGV decelerates from 2.5 m/s to 0.3 m/s for turns
         Speed estimated from encoder interval averaging
         SMA reports average of deceleration journey → thinks AGV is faster than reality
         Collision avoidance allows insufficient braking distance
         Result: 3 AGV collisions in 6 months, €85,000 in damage
```

**Why WMA solves this:**
```
Decelerating: 2.5 → 2.1 → 1.7 → 1.2 → 0.8 → 0.5 m/s

SMA(6) estimate:  (2.5+2.1+1.7+1.2+0.8+0.5)/6 = 1.47 m/s  ← overestimates!
WMA(6) estimate:  weighted toward recent 0.5, 0.8, 1.2 m/s  = 0.92 m/s  ← accurate

Stopping distance at 1.47 m/s → collision
Stopping distance at 0.92 m/s → safe stop ✓
```

---

### Case 3 — Exothermic Batch Reactor | Reaction Peak Detection

**Industry:** Specialty Chemicals
**Signal:** Reactor core temperature, 20–180°C

```
Plant: Polymerisation reactor, batch cycle 4 hours
Critical event: Exothermic peak at ~120 minutes into batch
                Temperature rises 2–4°C/minute near peak
                Cooling water must be added within 2 minutes of peak detection
Problem: SMA lags behind rising temperature → peak detection delayed → runaway risk
         Raw signal → too noisy for reliable derivative calculation
```

**WMA tracking the peak better:**
```
At peak approach (rising fast):
  Raw temps:     148, 151, 154, 158, 162°C

  SMA(5) output: 154.6°C  (reports average, underestimates current)
  WMA(5) output: 157.1°C  (weights recent high values → closer to true current)

  Rate of change from WMA: (157.1-153.2)/scan = higher rate → earlier alarm
  Cooling water triggered 90 seconds earlier than SMA-based system
  Runaway prevented ✓
```

---

### Case 4 — Port Crane Wind Safety | Gust Detection

**Industry:** Port / Logistics
**Signal:** Anemometer, 0–40 m/s wind speed

```
Plant: Ship-to-shore gantry crane, 65-meter height, 50-ton SWL
Safety rule: Suspend operations above 15 m/s sustained wind
Problem with SMA: A 20 m/s gust brings 10-sample SMA to only 13.5 m/s
                  Crane keeps operating → safety violation
Problem with raw signal: Brief 16 m/s spike stops crane unnecessarily mid-lift
                         Dangerous suspended load situation
```

**WMA asymmetric behavior:**
```
Gust event — wind 8→22 m/s over 5 samples:
Samples:  8, 10, 14, 19, 22

SMA(5):   14.6 m/s  → misses danger threshold
WMA(5):   17.4 m/s  → correctly triggers stop ✓

Lull event — wind 18→12 m/s over 5 samples:
Samples:  18, 16, 15, 13, 12

SMA(5):   14.8 m/s  → keeps crane stopped unnecessarily
WMA(5):   13.3 m/s  → allows restart sooner (recent calm dominant) ✓
```

**Result:** WMA naturally creates faster response to danger (rising winds dominate quickly) and faster recovery from false stops (falling winds dominate quickly). 23% reduction in unnecessary crane stoppages.

---

## 🔴 Median Filter

> **Best when:** Noise is not random but impulsive — single-scan or multi-scan spikes of large magnitude. Median is the only filter immune to outliers regardless of their size.

---

### Case 1 — Cement Silo Radar Level | Bulk Solids

**Industry:** Building Materials / Cement
**Signal:** Radar level transmitter, 0–100%

```
Plant: 4 × 500-tonne cement silos, radar mounted in silo roof
Problem: Bulk loading — cement dropped from 8-meter height
         Falling dust cloud reflects radar → false reading of 0–5% (apparent empty)
         Each false event lasts 2–4 scans (200–400ms at 100ms cycle)
         False empty alarm triggers emergency fill order
         Cost of unnecessary delivery: €2,800 per incident
         Incidents per month: 12–18 before filter installed
```

**Why only median works here:**
```
Spike magnitude: 95% → 3% → 4% → 97%  (two false samples in 4-sample window)

SMA(7):   (95+95+95+3+4+97+97)/7  = 69.4%  ← pulled dramatically toward zero
EMA:      Previous 95% → α×3% + (1-α)×95% = still dragged toward false value
Median(7): Sort [3, 4, 95, 95, 95, 97, 97] → middle value = 95% ✓

The false readings cannot become median of 7 values.
They just don't matter, regardless of magnitude.
```

**Annual saving after installation:** €480,000 in avoided false deliveries.

---

### Case 2 — Engine Exhaust Thermocouple | Vibration Environment

**Industry:** Power Generation / Diesel Gensets
**Signal:** Type-K thermocouple, 0–900°C

```
Plant: 2MW standby diesel generator, data centre backup power
Problem: Engine vibration causes intermittent micro-disconnect in TC extension cable
         Disconnected thermocouple reads 1372°C (open-circuit limit value)
         These spikes last 1–2 scans (50–100ms at 50ms cycle)
         Before filter: High-temp alarm fires → generator shuts down
                        Data centre loses power for 8 seconds until UPS takes over
                        Estimated cost per incident: €45,000 (SLA penalties)
```

**Median neutralises open-circuit spikes perfectly:**
```
Window = 5 samples, OB cycle = 50ms:

Reading sequence:  520, 522, 1372, 521, 523°C

Sorted:            [520, 521, 522, 523, 1372]
Median (pos 3):    522°C  ← correct exhaust temperature

The 1372°C spike ends up in position 5 every time.
Alarm system never sees it.
Generator stays online ✓
```

---

### Case 3 — Bottle Presence Sensor | Filling Line

**Industry:** Beverage / Bottling
**Signal:** Ultrasonic proximity, BOOL-level thresholded from REAL, 0–500mm

```
Plant: Beer bottling line, 36,000 bottles/hour (10 bottles/second)
Problem: Label on bottle creates bad angle reflection → false absence reading
         Duration of false absence: exactly 1 scan (10ms at 10ms cycle)
         Without filter: False absence during filling → nozzle lifts → beer spray
                         Line stop, cleanup, 15 minutes lost = 9,000 bottles lost
```

**Minimum median window for 1-scan rejection:**
```pascal
// Median(3) requires false reading to appear in ≥2 of 3 consecutive scans
// A genuine absence appears in ALL scans
// A 1-scan label reflection appears in 1 of 3 scans → median = present ✓

iWindowSize := 3;   // Smallest effective window, lowest latency

// Genuine absence detection latency: 2 scans = 20ms
// 1-scan false absence: completely invisible ✓
// Line stops due to false absence sensor: 3/month → 0/month
```

---

### Case 4 — Wastewater pH Control | Biological Treatment

**Industry:** Municipal Wastewater Treatment
**Signal:** pH electrode, 0–14 pH

```
Plant: Activated sludge aeration tank, 2.5 million litre capacity
Problem: Biological process produces CO₂ bubbles
         Bubbles contact pH membrane → 1–3 second false readings (±2–3 pH units)
         Acid/base dosing pump reacts to false readings
         Over-dosing of H₂SO₄ kills biological culture → treatment failure
         Rebuilding biological culture: 3 weeks, €95,000 in penalties
```

**Bubble immunity via median:**
```
OB cycle: 500ms
Bubble duration: 1–3 seconds → 2–6 false samples

pH readings over 10 scans:
[7.1, 7.1, 7.2, 4.3, 4.1, 7.1, 4.8, 7.2, 7.1, 7.2]
                  ↑         ↑         ↑
               3 bubble-affected readings (30% of window)

Median(9):  Sort → [4.1, 4.3, 4.8, 7.1, 7.1, 7.1, 7.2, 7.2, 7.2]
            Median = 7.1  ← correct pH ✓

For median to fail, bubbles must corrupt >50% of window samples
At current bubble frequency: essentially impossible
```

**Dosing pump overdose events:** 8/month → 0/month. Biological culture preserved continuously for 14 months.

---

## ⚪ Rate Limiter

> **Best when:** The problem is not sensor noise but command discontinuities — sudden jumps in setpoints, references, or outputs that would mechanically shock the equipment downstream.

---

### Case 1 — DN200 Steam Control Valve | Water Hammer

**Industry:** Petrochemical / Refining
**Signal:** PID output → valve position command, 0–100%

```
Plant: Steam supply to distillation column reboiler, 12 bar saturated steam
Valve: Pneumatic butterfly, DN200 (200mm bore), actuated in 4 seconds full stroke
Problem: PID integral windup during startup → output jumps from 15% to 90% in one scan
         Valve opens full in 4 seconds
         Steam condensate slug accelerated to 40 m/s in main header
         Water hammer peak pressure: 28 bar (design pressure: 16 bar)
         Result: 3 pipe flange failures in 18 months, 2 injuries
```

**Rate limiter configuration:**
```pascal
// Valve full stroke = 4 seconds for 100% travel = 25%/second max mechanical
// Safety margin: limit to 5%/second for steam service (industry standard)
// Asymmetric: allow faster close (emergency) than open (process safety)

rMaxRiseRate := 5.0;    // %/second opening  — slow, controlled steam admission
rMaxFallRate := 15.0;   // %/second closing  — faster emergency closure allowed
rCycleTimeS  := 0.1;    // 100ms OB cycle

// PID can demand whatever it wants — valve command never exceeds 0.5%/scan
// Water hammer peak pressure: 28 bar → 13.2 bar (within design limit) ✓
// Zero flange failures in 30 months since installation
```

---

### Case 2 — Frequency Inverter Speed Reference | Conveyor Anti-Jerk

**Industry:** Logistics / Distribution Centre
**Signal:** Speed reference from master PLC → drive, 0–50 Hz

```
Plant: 800-metre main sortation conveyor, 23 drive sections
Problem: PROFINET communication glitch every 2–3 weeks causes reference reset
         Drive section receives 0 Hz command → reapplies last valid setpoint next scan
         Effective command: 45 Hz → 0 Hz → 45 Hz in two scan cycles (4ms)
         Conveyor belt jerks violently
         Result: Parcels thrown off belt, belt tracking lost, 4-hour shutdown per event
```

**Rate limiter as communication fault protection:**
```pascal
rMaxRiseRate := 8.0;    // Hz/second — matches drive's own acceleration ramp
rMaxFallRate := 12.0;   // Hz/second — matched to deceleration ramp
rCycleTimeS  := 0.004;  // 4ms PROFINET cycle time

// Communication glitch: reference drops to 0 Hz for 1-2 cycles
// Rate limiter maximum drop in 2 cycles:
// MaxDrop = 12.0 Hz/s × 0.004s × 2 cycles = 0.096 Hz
// Belt barely notices a 0.096 Hz dip ✓

// Recovery: rises back at 8 Hz/s — smooth, no jerk
// Sortation conveyor uptime improved from 97.1% to 99.6%
```

---

### Case 3 — Plastic Extruder Barrel Heating | Element Life

**Industry:** Plastics / Injection Moulding
**Signal:** Temperature setpoint to PID, 0–300°C

```
Plant: 80-tonne injection moulding machine, 5-zone barrel heating
Heater bands: Ceramic band heaters, 3kW each, €280 each, 12 on machine
Problem: Cold start — operator sets all zones to 220°C immediately
         PID demands 100% heater output from cold (20°C)
         Thermal shock: 20°C → 220°C at maximum power in 8 minutes
         Ceramic elements crack from thermal gradient (centre hot, shell cool)
         Heater replacement frequency: 2.3 elements/week = €840/week
         Downtime per replacement: 45 minutes (barrel must cool to 60°C first)
```

**Setpoint ramping via rate limiter:**
```pascal
// Industry standard for ceramic heater protection: max 2°C/second warmup
rMaxRiseRate := 2.0;    // °C/second — controlled warmup
rMaxFallRate := 99.0;   // °C/second — allow fast setpoint drops (unrestricted)
rCycleTimeS  := 0.1;    // 100ms OB

// Cold start: PID sees 20°C → 220°C ramp over 100 seconds (not 8 minutes!)
// Heater operates at 60–70% output during warmup instead of 100%
// Thermal gradient across ceramic: reduced by 65%

// After installation:
// Heater replacement: 0.2 elements/week (from 2.3/week)
// Annual saving: €88,000 in parts + €210,000 in avoided downtime
```

---

### Case 4 — Collaborative Robot Joint Command | Safety Fault Prevention

**Industry:** Automotive Final Assembly
**Signal:** Path planner position command → joint controller, degrees

```
Plant: Human-robot collaboration cell, door panel installation
Robot: KUKA LBR iiwa 7 R800, 7-axis
Problem: Path planning software occasionally produces waypoint calculation error
         Error causes instantaneous jump of 35° in joint 3 command
         Drive detects commanded velocity exceeds dynamic limit → E-STOP triggers
         Robot in middle of panel installation → panel dropped, damage €2,200/incident
         E-STOP recovery: 8 minutes (safety system reset + manual verification)
         Incidents per month: 4–6 (software team cannot reproduce reliably)
```

**Rate limiter as hardware-level protection:**
```pascal
// Joint 3 mechanical limit: 85°/second at rated payload
// Software path planner should never command faster than 60°/second
// Rate limiter set to 60°/second → software fault cannot reach drive

rMaxRiseRate := 60.0;   // °/second
rMaxFallRate := 60.0;   // °/second
rCycleTimeS  := 0.004;  // 4ms robot controller cycle (250Hz)

// 35° jump in one 4ms cycle would require 8,750°/s
// Rate limiter allows maximum 0.24° per cycle
// Fault appears as smooth 0.24°/cycle motion → safe, imperceptible deviation
// Drive never sees over-speed command → E-STOP never triggered

// E-STOP events: 5/month → 0/month
// Software team still investigating root cause at their own pace
```

---

## 🔗 Stacking Filters — Real Combinations

The most demanding applications chain multiple filters. Each handles a different type of signal corruption.

---

### Combination 1 — Pump Pressure Signal for PID

```
Application: Centrifugal pump discharge pressure, variable speed drive
Environment: High vibration, nearby VFD causes EMI spikes

Chain:  Raw → Median(5) → EMA(α=0.2) → PID

Median removes:   EMI-induced single-scan spikes (±15 bar magnitude, 1 scan)
EMA removes:      Residual vibration noise (±0.3 bar, high frequency)
PID receives:     Clean, responsive pressure signal

Without chain:    PID oscillates at 4Hz, cavitation risk
With chain:       PID stable, pressure held ±0.08 bar
```

---

### Combination 2 — Operator Setpoint to Large Actuator

```
Application: District heating control valve, DN400, 16 bar hot water
Source of problems: Operator makes sudden large setpoint changes on SCADA

Chain:  SCADA setpoint → SMA(5) → RateLimiter(3%/s) → PID setpoint

SMA removes:      SCADA communication glitches and double-click entries
RateLimiter:      Prevents any mechanical shock regardless of SMA output
PID setpoint:     Always smooth, physically achievable trajectory

Result:           Valve seal lifetime: 3 years → 8+ years
                  Pipe stress incidents: 4/year → 0/year
```

---

### Combination 3 — Quality Inspection on High-Speed Line

```
Application: Inline optical thickness measurement, steel strip rolling mill
Line speed: 25 m/s, sensor samples every 2mm = 12,500 samples/second
Reported to control system: Every 100ms (subsampled)

Chain:  Raw(12500Hz) → Median(3) → WMA(8) → Thickness controller

Median removes:   Optical speckle, oil droplet occlusions (1–2 sample spikes)
WMA emphasizes:   Most recent measurements (strip just left the roll gap)
Controller sees:  True current thickness weighted toward exit, not entry

Thickness tolerance: ±12μm achieved vs ±28μm before filter chain
Customer rejection rate: 0.8% → 0.1%
```

---

## 📊 Filter Selection Decision Tree

```
Signal has SPIKES (single-scan large jumps)?
│
├─ YES → Use MEDIAN first
│         Then add EMA/SMA for residual noise
│
└─ NO → Signal changes too FAST for your filter?
         │
         ├─ YES (fast process, tight PID) → Use EMA (tune α carefully)
         │
         └─ NO → Response speed flexible?
                  │
                  ├─ Recent samples more RELEVANT? → Use WMA
                  │
                  ├─ All samples EQUAL importance? → Use SMA
                  │
                  └─ Problem is COMMAND JUMPS not noise? → Use RATE LIMITER
```

---

## 💡 Engineering Rules of Thumb

| Situation | Rule |
|-----------|------|
| Noise frequency >> process frequency | SMA or EMA work equally well |
| Noise duration = 1–3 scans, any magnitude | Always use Median first |
| PID loop with noise issues | EMA preferred over SMA (less lag) |
| Actuator protection | Rate Limiter on output, not input |
| Unknown noise character | Start with Median(5) + EMA(0.15) chain |
| Very large window needed (>50) | Use EMA — no array cost |
| Safety-critical setpoint path | Rate Limiter is mandatory, not optional |

---

*S7-1500 Advanced Signal Filtering Library — Real Industrial Case Studies*
*Companion document to `README.md` and SCL source code*