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Manufacturing Equipment Reference

Look up your equipment → get the pattern, equation, and starting parameters.

This table maps common manufacturing equipment to Odibi simulation patterns. Instead of deriving equations from textbooks, find your equipment, copy the expression, and tune the 1–2 numbers that matter.

Not listed?

Ask one question: what does the output do when I change the input?

  • Settles to a new value → first_order
  • Keeps ramping → integrator
  • Bounces before settling → second_order
  • Nothing, then responds → dead_time
  • Changes instantly → gain

Find the closest equipment below and copy its equation. The pattern is what matters, not the exact equipment name.

Quick Reference: Key Terms

Before reading the table, here's what each column means:

  • gain = max output ÷ 100 (when input is 0–100%). It converts input units to output units. Example: a valve with max flow 15 m³/hr → gain = 15 ÷ 100 = 0.15
  • alpha = how fast it responds. Each timestep, alpha × the remaining gap gets closed. Only applies to first_order. Low (0.02) = sluggish. High (0.3) = snappy
  • dt = timestep unit conversion so rates accumulate correctly. Example: flow in m³/hr with a 5-min timestep → dt = 5/60

See Parameter Intuition Guide for the full breakdown of alpha, gain, and dt.

Valves

Equipment Pattern Equation Gain Alpha Notes
Globe valve (throttling) first_order prev(flow) + alpha × (gain × valve_pct - prev(flow)) Max flow ÷ 100. Example: 15 m³/hr max → 0.15 0.05–0.15 Slow — designed for precise flow control
Ball valve (on/off) first_order prev(flow) + alpha × (gain × valve_pct - prev(flow)) Max flow ÷ 100 0.2–0.5 Fast — quarter-turn, snaps open/closed
Butterfly valve first_order prev(flow) + alpha × (gain × valve_pct - prev(flow)) Max flow ÷ 100 0.1–0.3 Moderate speed. Nonlinear at low openings
Relief / safety valve gain max_flow if pressure > setpoint else 0 Binary — fully open or closed — Threshold behavior, not proportional

Pumps

Equipment Pattern Equation Gain Alpha Notes
Centrifugal pump first_order prev(flow) + alpha × (gain × speed_pct - prev(flow)) Max flow ÷ 100. Example: 20 m³/hr → 0.20 0.2–0.5 Fast response. Flow varies with speed² at extremes, but linear enough for simulation
Positive displacement pump gain gain × speed_pct Max flow ÷ 100 — Flow is directly proportional to speed. Nearly instant response
Peristaltic / diaphragm pump gain gain × speed_pct Max flow ÷ 100 — Like PD pumps — flow tracks speed with very little lag

Vessels & Tanks

Equipment Pattern Equation Gain Alpha Notes
Storage tank (liquid level) integrator max(0, min(cap, prev(level) + (inflow - outflow) × dt)) — — Always clamp to [0, capacity]. Get dt units right
Tank with gravity drain integrator (self-regulating) Level: max(0, min(cap, prev(level) + (inflow - drain_coeff × prev(level)) × dt)) — — Self-regulates — outflow increases with level. No controller needed
Pressure vessel (gas) second_order Velocity: prev(vel) + beta × (target - prev(pressure)) - damping × prev(vel) then Pressure: prev(pressure) + velocity — — Gas compresses/expands with overshoot. Use beta=0.04, damping=0.3 as starting point
Mixing tank (concentration) first_order prev(conc) + alpha × (inlet_conc - prev(conc)) — 0.05–0.2 Alpha depends on tank volume vs flow rate. Bigger tank = lower alpha
Reactor (CSTR) first_order prev(conc) + alpha × (feed_conc - prev(conc)) — 0.02–0.1 Similar to mixing tank but slower. Reaction kinetics add complexity — start simple

Heat Transfer

Equipment Pattern Equation Gain Alpha Notes
Shell & tube heat exchanger first_order prev(t_out) + alpha × (gain × t_in - prev(t_out)) 0.6–0.9 (efficiency) 0.02–0.08 Large thermal mass = slow. Gain < 1.0 because heat transfer isn't perfect
Plate heat exchanger first_order prev(t_out) + alpha × (gain × t_in - prev(t_out)) 0.7–0.95 0.1–0.3 Much faster than shell & tube — less thermal mass, more surface area
Jacketed vessel first_order prev(t_vessel) + alpha × (gain × t_jacket - prev(t_vessel)) 0.3–0.7 0.01–0.05 Very slow — heating/cooling a large batch through a wall
Cooling tower first_order prev(t_out) + alpha × (t_wet_bulb - prev(t_out)) — 0.02–0.1 Target is wet-bulb temp. Gain ≈ 1.0 in ideal conditions
Electric heater first_order prev(temp) + alpha × (gain × heater_pct - prev(temp)) Max temp rise ÷ 100 0.05–0.2 Gain = max temp above ambient per % power
Boiler / steam generator first_order prev(steam_pressure) + alpha × (gain × fuel_rate - prev(steam_pressure)) System-specific 0.01–0.05 Very slow, large thermal mass. Steam drum adds lag

Conveyors & Transport

Equipment Pattern Equation Gain Alpha Notes
Belt conveyor dead_time delay(input, steps, default) — — steps = belt length ÷ belt speed ÷ timestep. Pure transport delay
Screw conveyor dead_time delay(input, steps, default) — — Shorter delay than belt. steps = screw length ÷ feed rate ÷ timestep
Pipeline (liquid) dead_time + first_order prev(output) + alpha × (delay(input, steps, default) × gain - prev(output)) Flow gain 0.1–0.3 Dead time = pipe volume ÷ flow rate. First-order for pressure dynamics
Pneumatic transport dead_time delay(input, steps, default) — — Air velocity is fast, so fewer delay steps than liquid pipeline

Motors & Drives

Equipment Pattern Equation Gain Alpha Notes
VFD motor (variable frequency drive) first_order prev(speed) + alpha × (command_pct - prev(speed)) 1.0 (command = speed in %) 0.2–0.5 Fast response. VFD ramp rate determines alpha
Direct-on-line motor gain rated_speed if running else 0 — — On/off — no speed control. Full speed or stopped
Compressor first_order prev(pressure) + alpha × (gain × speed_pct - prev(pressure)) Max pressure ÷ 100 0.05–0.15 Slow — compressed gas has thermal mass

Instruments & Sensors

Equipment Pattern Equation Gain Alpha Notes
Thermocouple first_order prev(reading) + alpha × (true_temp - prev(reading)) 1.0 (reads what it sees) 0.1–0.3 Sensor lag — doesn't read instantly. Add noise: + (random() - 0.5) * band
RTD (resistance temp detector) first_order prev(reading) + alpha × (true_temp - prev(reading)) 1.0 0.05–0.15 Slower than thermocouple — larger thermal mass in the sensor
Pressure transmitter first_order prev(reading) + alpha × (true_pressure - prev(reading)) 1.0 0.3–0.5 Very fast — nearly instant. Often modeled as gain
Flow meter (magnetic / Coriolis) gain true_flow + (random() - 0.5) * noise_band 1.0 — Essentially instant. Main imperfection is noise, not lag
Level sensor (ultrasonic) first_order prev(reading) + alpha × (true_level - prev(reading)) 1.0 0.2–0.4 Moderate lag. Surface turbulence adds noise
pH probe first_order prev(reading) + alpha × (true_ph - prev(reading)) 1.0 0.02–0.1 Slow — electrochemical response time. Gets slower as probe ages

How to Use This Table

Step 1: Find your equipment (or the closest match).

Step 2: Copy the equation into your YAML expression: field. Replace variable names with your column names.

Step 3: Pick a gain and alpha from the ranges shown. Use the middle of the range to start.

Step 4: Run the simulation and look at the chart. Does it respond too fast? Lower alpha. Too slow? Raise alpha. Wrong magnitude? Adjust gain.

Example — Globe valve controlling cooling water flow:

columns:
  - name: valve_position_pct
    data_type: float
    generator:
      type: random_walk
      start: 50.0
      min: 0.0
      max: 100.0
      step_size: 3.0

  - name: cooling_flow_m3_hr
    data_type: float
    generator:
      type: derived
      expression: "max(0, prev('cooling_flow_m3_hr', 7.5) + 0.1 * (0.15 * valve_position_pct - prev('cooling_flow_m3_hr', 7.5)))"
      # gain = 0.15 → 100% valve = 15 m³/hr max flow
      # alpha = 0.1 → globe valve, moderate speed
      # default = 7.5 → starts at 50% valve = 7.5 m³/hr