PID Controller Tuning on a Thermal System: Manual vs Ziegler-Nichols vs Autotuner

Thermal systems combine large time constants (30–120 s) with pure dead time from sensor placement (5–15 s)—Ziegler-Nichols tuned on this plant overshot 12 °C and oscillated for an hour. What worked: manual bump test for FOPDT model, conservative PI with derivative on PV only, and a 30-minute soak validation protocol instead of trusting autotuner defaults from a $200 PID module.

Plant under test

• Heater: 500 W cartridge, SSR driven PWM 1 Hz (time-proportional)
• Sensor: PT100 → MAX31865, 10 cm from heater, 40 cm from load chamber center
• Setpoint: 85 °C operating point, ambient 22 °C
• Controller: STM32G431 @ 170 MHz, control loop 1 Hz
• Disturbance: door open 10 s releases ~15 °C

Goal: ±1 °C at setpoint within 20 min of cold start, no sustained oscillation.

Ziegler-Nichols (ultimate gain method) — failed

Procedure: disable I and D, increase Kp until sustained oscillation (Pu, Ku).

Result: Ku occurred near heater duty 78% with Pu ≈ 180 s—uncomfortably close to SSR max cycling. ZN table (classic PID) gave Kp=0.6Ku, Ti=Pu/2, Td=Pu/8.

Step response: 12 °C overshoot, slow decay over 40 min. Thermal mass absorbed energy; D term on error amplified sensor noise from 50 Hz mains pickup (see ADC noise floor on STM32—we filtered PT100 before PID).

ZN assumes linear first-order plant. Our dead time / time constant ratio θ/τ ≈ 0.35—borderline where ZN overshoots badly per literature.

Autotuner (commercial PID module) — mixed

Autotuner in a $189 Eurotherm-style module identified model and suggested PI. Faster than manual—15 min relay test. Still overshot 6 °C because autotuner optimized for step response time, not our overshoot constraint.

Useful data: estimated τ=95 s, θ=12 s. We kept estimates, discarded gains.

Manual FOPDT + conservative PI — winner

Bump test: 40% → 60% duty step, log PV, fit FOPDT with Python script (scipy.optimize, not on-device).

Initial PI from IMC tuning (λ = 3θ):

Kp = τ / (K * (λ + θ))
Ti = τ

With K=0.42 °C/%, τ=95 s, θ=12 s, λ=36 s → Kp≈4.8, Ti=95 s.

Implementation (velocity form, anti-windup):

typedef struct {
    float kp, ti, td;
    float integral, prev_pv;
    float out_min, out_max;
} pid_t;

float pid_step(pid_t *p, float sp, float pv, float dt) {
    float err = sp - pv;
    p->integral += err * dt;
    p->integral = clampf(p->integral, p->out_min, p->out_max);
    float d_pv = (pv - p->prev_pv) / dt;
    p->prev_pv = pv;
    float out = p->kp * (err + p->integral / p->ti - p->td * d_pv);
    return clampf(out, p->out_min, p->out_max);
}

Derivative on process variable only—avoids setpoint kick when SP steps.

Final gains after one conservative tweak: Kp=3.2, Ti=110 s, Td=0 (no D needed after PT100 filtering).

Results: 2.1 °C overshoot, settle within ±1 °C in 18 min, door disturbance recovery 4 min.

Validation without industrial tools

• CSV log: {t, sp, pv, duty, integral} at 1 Hz to UART → Python matplotlib
• Criteria checklist signed before ship: max overshoot, settling time, IAE metric
• 3 cold starts, 3 hot restarts, 1 door event—minimum sample

Bench PSU logging correlated heater power with reported duty—bench PSU autobiography part 3 style sanity check.

Comparison summary

Method	Overshoot	Time to ±1 °C	Engineer time
Ziegler-Nichols	12 °C	35 min	2 h
Module autotune	6 °C	22 min	30 min
Manual FOPDT PI	2.1 °C	18 min	4 h

Manual took longest calendar time but met spec without hardware cycle limit.

What I'd do next

1. Feed-forward from known door state (magnetic reed)—trim integral windup during known disturbances.
2. Gain schedule for setpoints above 120 °C where radiation losses nonlinear.
3. Log tuning constants in NVM with version field—support can diff field units.

Integrator windup on saturations

Heater saturated at 100% duty during ramp—integral term accumulated assuming output could go higher. Anti-windup clamped integral but conditional integration (pause I when saturated) reduced overshoot another 0.8 °C without retuning Kp/Ti.

Sensor filter interaction

PT100 PT1 filter with τ=2 s added effective delay—PID saw stale PV. Either account delay in θ estimate or filter less aggressively; we reduced filter to τ=0.5 s after identifying phase lag in Bode plot from step test data.

Relay tuning vs PID

Door open disturbance dominated loop—not fixable by PID alone without feed-forward. Magnetic reed on door triggered temporary output cap reduction; manual tweak beat autotuner because disturbance was discrete event, not step response metric.

Logging rate for tuning sessions

UART CSV at 1 Hz filled flash during week-long soak—switched to log only step changes >0.5 °C or duty delta >5%. Enough for post-mortem, not drowning in points.

For thermal plants, skip textbook ZN unless you enjoy oscillation. Model dead time, tune PI conservatively, validate with soak tests longer than your QA shift.