Verification · Not marketing

Every tuning rule, verified against textbook references.

Savi LoopIQ ships a 64-case regression corpus that runs on every commit across three independent implementations (Python, Dart, TypeScript). Every rule must produce identical Kc, Ti, Td within a relative tolerance of 1e-6. If the math ever drifts, CI fails and the deploy is blocked.

CI runs on every commitcorpus 64 casestolerance ±1e-6parity Python · Dart · TypeScript

Cases

Rules covered

Model kinds

FOPDT · SOPDT · IPDT

Verticals

Rel. tolerance

1e-6

Abs. tolerance

1e-9

How verification runs

The reference implementation is Python (libloopiq_control_py). Expected Kc, Ti, Td for every case are machine-generated by regression/build_corpus.py and committed to regression/corpus.json. Every push to main and every pull request runs the same corpus through three separate rule engines — Python, Dart, and TypeScript — and asserts each output is within ±1e-6 (relative) or ±1e-9 (absolute) of the reference. If any implementation drifts, CI blocks the merge. The Python job additionally regenerates the corpus and diffs it against the committed file, so a silent rule change cannot slip in without a matching expected-value update.

Rules and academic references

SIMC

Skogestad, S. (2003). Simple analytic rules for model reduction and PID controller tuning. Journal of Process Control, 13(4), 291–309.

https://folk.ntnu.no/skoge/publications/2003/tuningPID/more/skogestad_pid.pdf

IMC

Rivera, D. E., Morari, M., & Skogestad, S. (1986). Internal Model Control: PID Controller Design. I&EC Process Design and Development, 25(1), 252–265.

Lambda

Seborg, D. E., Edgar, T. F., Mellichamp, D. A., & Doyle, F. J. (2016). Process Dynamics and Control (4th ed.), Chapter 12 — Direct Synthesis / Lambda Tuning.

Cohen-Coon

Cohen, G. H., & Coon, G. A. (1953). Theoretical consideration of retarded control. Transactions of the ASME, 75, 827–834.

ZN-OL

Ziegler, J. G., & Nichols, N. B. (1942). Optimum settings for automatic controllers (open-loop / reaction curve). Transactions of the ASME, 64, 759–768.

ZN-CL

Ziegler, J. G., & Nichols, N. B. (1942). Optimum settings for automatic controllers (closed-loop / ultimate cycle). Transactions of the ASME, 64, 759–768.

The corpus — every case

View source on GitHub

ID	Vertical	Loop	Rule	Model	Kc	Ti	Td
ref-01	refining	crude tower reflux flow	SIMC	FOPDT(Kp=1.2, τ=8, θ=1)	3.3333	8	0
ref-02	refining	crude tower bottom temp	Lambda	SOPDT(Kp=0.9, τ₁=45, τ₂=6, θ=8)	1.2821	45	0
ref-03	refining	vac tower pressure	IMC	FOPDT(Kp=1.7, τ=15, θ=3)	1.7647	16.5	1.3636
ref-04	refining	reformer feed flow	SIMC	FOPDT(Kp=1, τ=4, θ=0.3)	6.6667	2.4	0
ref-05	refining	FCC riser temperature	Lambda	SOPDT(Kp=1.4, τ₁=30, τ₂=8, θ=12)	0.4286	30	0
ref-06	refining	alkylation acid ratio	IMC	SOPDT(Kp=0.8, τ₁=20, τ₂=4, θ=5)	3.8971	26.5	3.0189
ref-07	refining	hydrogen makeup pressure	SIMC	IPDT(Kp=0.05, θ=2.5)	4	20	0
ref-08	refining	gasoline blender ratio	Cohen-Coon	FOPDT(Kp=1, τ=6, θ=1.5)	5.5833	3.35	0.5217
ref-09	refining	coker drum level	Lambda	IPDT(Kp=0.02, θ=4)	4.7091	34	0
ref-10	refining	sulfur recovery temp	SIMC	SOPDT(Kp=1.6, τ₁=25, τ₂=5, θ=6)	1.3021	25	5
chm-01	chemicals	jacket flow	SIMC	FOPDT(Kp=0.9, τ=3, θ=0.4)	4.1667	3	0
chm-02	chemicals	reactor temperature	IMC	SOPDT(Kp=1.2, τ₁=18, τ₂=3.5, θ=2.5)	3.6111	22.75	2.7692
chm-03	chemicals	reactor pressure	Lambda	FOPDT(Kp=1.5, τ=6, θ=0.8)	1.0526	6	0
chm-04	chemicals	polymer viscosity	IMC	SOPDT(Kp=2.1, τ₁=40, τ₂=8, θ=10)	1.2619	53	6.0377
chm-05	chemicals	cascade slave flow	SIMC	FOPDT(Kp=1, τ=2, θ=0.15)	6.6667	1.2	0
chm-06	chemicals	analyser composition	Lambda	SOPDT(Kp=1.3, τ₁=25, τ₂=6, θ=15)	0.469	25	0
chm-07	chemicals	pH neutralisation	Cohen-Coon	FOPDT(Kp=2.5, τ=8, θ=1.5)	2.9444	3.4267	0.5275
chm-08	chemicals	reactor level (integrating)	Lambda	IPDT(Kp=0.03, θ=1.5)	9.073	11.5	0
chm-09	chemicals	distillation reboiler duty	SIMC	SOPDT(Kp=1.1, τ₁=15, τ₂=3, θ=3)	2.2727	15	3
chm-10	chemicals	cooling water temp	IMC	FOPDT(Kp=0.7, τ=12, θ=2)	4.6429	13	0.9231
wtr-01	water_ww	aeration DO	Lambda	FOPDT(Kp=0.4, τ=180, θ=30)	5	180	0
wtr-02	water_ww	chlorine dose (integrating)	Lambda	IPDT(Kp=0.008, θ=8)	7.6531	48	0
wtr-03	water_ww	filter influent flow	SIMC	FOPDT(Kp=1, τ=6, θ=0.5)	6	4	0
wtr-04	water_ww	clarifier level (integrating)	Lambda	IPDT(Kp=0.005, θ=12)	6.8047	92	0
wtr-05	water_ww	pH adjustment	Cohen-Coon	FOPDT(Kp=3.5, τ=10, θ=2.5)	1.5952	5.5833	0.8696
wtr-06	water_ww	raw water intake pressure	SIMC	FOPDT(Kp=0.6, τ=4, θ=0.3)	11.1111	2.4	0
wtr-07	water_ww	sludge blanket depth	Lambda	SOPDT(Kp=0.9, τ₁=90, τ₂=15, θ=20)	1.0526	90	0
wtr-08	water_ww	polymer feed	IMC	FOPDT(Kp=1.8, τ=6, θ=1)	1.2037	6.5	0.4615
wtr-09	water_ww	UV lamp intensity	SIMC	FOPDT(Kp=1, τ=8, θ=0.4)	10	3.2	0
wtr-10	water_ww	digester temperature	Lambda	SOPDT(Kp=0.7, τ₁=120, τ₂=25, θ=15)	1.4286	120	0
pp-01	pulp_paper	stock consistency	Lambda	FOPDT(Kp=1.1, τ=25, θ=4)	1.4205	25	0
pp-02	pulp_paper	headbox pressure	SIMC	FOPDT(Kp=0.8, τ=3, θ=0.2)	9.375	1.6	0
pp-03	pulp_paper	brightness (scanner)	Lambda	SOPDT(Kp=1.5, τ₁=35, τ₂=8, θ=18)	0.4167	35	0
pp-04	pulp_paper	basis weight (scanner)	IMC	SOPDT(Kp=1.3, τ₁=30, τ₂=6, θ=20)	1.011	46	3.913
pp-05	pulp_paper	dryer steam pressure	SIMC	SOPDT(Kp=1, τ₁=15, τ₂=3, θ=2)	3.75	15	3
pp-06	pulp_paper	digester Kappa number	Lambda	FOPDT(Kp=2, τ=90, θ=25)	0.5294	90	0
pp-07	pulp_paper	white water level	Lambda	IPDT(Kp=0.015, θ=3)	9.073	23	0
pp-08	pulp_paper	chip conveyor flow	SIMC	FOPDT(Kp=1, τ=5, θ=0.6)	4.1667	4.8	0
pp-09	pulp_paper	bleach plant pH	Cohen-Coon	FOPDT(Kp=1.8, τ=6, θ=1.2)	3.8426	2.7288	0.4211
pp-10	pulp_paper	calender roll temp	IMC	FOPDT(Kp=1.2, τ=20, θ=3)	2.3889	21.5	1.3953
pwr-01	power	drum level (integrating)	Lambda	IPDT(Kp=0.01, θ=5)	7.2	45	0
pwr-02	power	superheater outlet temp	IMC	SOPDT(Kp=1.5, τ₁=40, τ₂=10, θ=15)	1.3939	57.5	6.9565
pwr-03	power	fuel/air ratio slave	SIMC	FOPDT(Kp=1, τ=3, θ=0.5)	3	3	0
pwr-04	power	feedwater flow	SIMC	FOPDT(Kp=1, τ=2, θ=0.2)	5	1.6	0
pwr-05	power	condenser hotwell level	Lambda	IPDT(Kp=0.012, θ=6)	4.8561	56	0
pwr-06	power	gas turbine inlet temp	ZN-CL	FOPDT(Kp=1, τ=8, θ=2)	1.92	4.25	1.0625
pwr-07	power	deaerator level	Lambda	IPDT(Kp=0.008, θ=4)	11.7729	34	0
pwr-08	power	stack O2	Lambda	SOPDT(Kp=0.6, τ₁=25, τ₂=8, θ=10)	1.0965	25	0
pwr-09	power	turbine governor speed	ZN-OL	FOPDT(Kp=1, τ=2, θ=0.3)	8	0.6	0.15
pwr-10	power	cooling tower fan pitch	IMC	FOPDT(Kp=0.9, τ=15, θ=4)	2.3611	17	1.7647
gap-imc-fopdt-default	refining	IMC FOPDT default lambda	IMC	FOPDT(Kp=1.5, τ=12, θ=2)	1.9697	13	0.9231
gap-imc-sopdt-default	chemicals	IMC SOPDT default lambda	IMC	SOPDT(Kp=1.1, τ₁=20, τ₂=5, θ=3)	3.6501	26.5	3.7736
gap-imc-ipdt-default	power	IMC IPDT default lambda (M1 regression)	IMC	IPDT(Kp=0.02, θ=4)	5	20	0
gap-imc-ipdt-floor	power	IMC IPDT default lambda floored at 1.0	IMC	IPDT(Kp=0.05, θ=0.2)	18.1818	2.2	0
gap-simc-fopdt-default	refining	SIMC FOPDT default tauC	SIMC	FOPDT(Kp=1, τ=10, θ=2)	2.5	10	0
gap-simc-ipdt-default	power	SIMC IPDT default tauC	SIMC	IPDT(Kp=0.03, θ=3)	5.5556	24	0
gap-lambda-fopdt-default	chemicals	Lambda FOPDT default lambda	Lambda	FOPDT(Kp=1.2, τ=8, θ=1.5)	0.381	8	0
gap-lambda-ipdt-default	power	Lambda IPDT default lambda	Lambda	IPDT(Kp=0.01, θ=5)	11.1111	25	0
gap-imc-fopdt-theta0	refining	IMC FOPDT theta=0	IMC	FOPDT(Kp=1, τ=5, θ=0)	4	5	0
gap-simc-fopdt-theta0	refining	SIMC FOPDT theta=0 (found via a real crash: default tau_c=theta collapsed to 0)	SIMC	FOPDT(Kp=2, τ=10, θ=0)	50	0.4	0
gap-simc-ipdt-theta0	refining	SIMC IPDT theta=0	SIMC	IPDT(Kp=1, θ=0)	10	0.4	0
gap-simc-fopdt-negkp	chemicals	SIMC FOPDT reverse-acting (negative Kp)	SIMC	FOPDT(Kp=-1.4, τ=9, θ=1.5)	2.1429	9	0
gap-zn-ol-pi	power	ZN open-loop PI	ZN-OL	FOPDT(Kp=1, τ=6, θ=1)	5.4	3.33	0
gap-zn-cl-pi	power	ZN closed-loop PI	ZN-CL	FOPDT(Kp=1, τ=6, θ=1)	1.125	5	0

Verify it yourself

The corpus and the three rule engines are open in the public repository. Clone the repo, run any of the three implementations, and diff against the committed expected values. If a case disagrees by more than 1e-6 relative or 1e-9 absolute, we consider it a rule regression.

git clone https://github.com/Savage-4-Lyfe/loopiq
cd loopiq

# Python
pip install -e python/libloopiq_control_py
python regression/run_python_corpus.py

# TypeScript
cd webapp && npm ci && npm test

# Dart
cd ../dart/libloopiq_control && dart pub get && dart test

What this does not claim

Verification proves the tuning rules are implemented correctly against published references. It does not guarantee any particular tuning is safe for your plant, that your process model is accurate, or that your controller structure matches the assumptions of the rule. You are the engineer. Savi LoopIQ is a tool. Read the robustness metrics (Ms, Mt, GM, PM), inspect the Nyquist plot, bump-test conservatively, and stay in the control room during commissioning.

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