Conveyor Speed Control in Food Processing Cold Storage

Scenario

Project Type: Energy-efficient speed regulation retrofit for stainless-steel belt conveyor in frozen food packaging line Location Context: -25°C cold storage facility in Winnipeg, Canada; high humidity causing condensation on motor windings and encoder optics; frequent product jam events inducing transient load spikes. Constraints: Must operate continuously at 0.1–1.2 m/s; torque ripple <5% at low speeds; no integral windup during 3–5 s jams; ambient temperature drift causes ±15% variation in motor resistance and friction over 8-hour shifts.

Given Data

• Motor Inertia: 0.015 kg·m² (nameplate + rotor inertia measurement at -25°C)
• Load Inertia: 0.092 kg·m² (belt mass + rollers + accumulated frozen product load, worst-case)
• Viscous Friction: 0.42 N·m·s/rad (measured at -25°C — 4× higher than room-temp spec due to grease thickening)
• Gear Ratio: 5.0 (helical bevel gearbox, confirmed via maintenance log)
• Time Delay: 0.18 s (dominated by PLC scan time + analog I/O conversion lag in legacy control cabinet)

Calculation

Using the PID Tuner tool with inputs:

• motor_inertia = 0.015
• load_inertia = 0.092
• viscous_friction = 0.42
• gear_ratio = 5.0
• time_delay = 0.18

The tuner selects the Cohen-Coon method explicitly due to significant time delay (>0.1 s). It computes effective inertia (J_eff = motor_inertia + load_inertia / gear_ratio² = 0.015 + 0.092 / 25 = 0.0187 kg·m²) and estimates process time constant τ = J_eff / (viscous_friction / gear_ratio²) ≈ 0.0187 / (0.42 / 25) ≈ 1.11 s. With L = time_delay = 0.18 s, it applies Cohen-Coon formulas:

• Kp = (0.9·τ/L) / (1 + 0.05·τ/L) ≈ (0.9·1.11/0.18) / (1 + 0.05·1.11/0.18) ≈ 5.55 / 1.31 ≈ 4.24
• Ki = 0.27·Kp·τ/L² ≈ 0.27·4.24·1.11/(0.18)² ≈ 1.27 / 0.0324 ≈ 39.2
• Kd = 0.27·Kp·L ≈ 0.27·4.24·0.18 ≈ 0.206

Rounded to precision: Kp = 4.24, Ki = 39.20, Kd = 0.21

Result and Decision

Initial deployment caused oscillatory behavior during jam recovery due to aggressive integral action. Engineers implemented anti-windup via conditional integration (disabling Ki during torque saturation) and reduced Ki by 30% to 27.4. Kp was increased slightly to 4.6 to compensate for low-speed stiffness loss in cold. Final validated gains: Kp = 4.60, Ki = 27.40, Kd = 0.21. Achieved ±0.015 m/s speed deviation under jam transients and reduced motor heating by 18% vs. prior Ziegler-Nichols tuning.

Lesson

In thermally variable environments, friction and inertia change non-uniformly — always re-measure viscous friction at operating temperature, not at room temperature; neglecting this led to initial 4× underestimation of friction and unstable integral action.