HDD-ESA: Engineering Systems Architecture
HDD-ESA:
Engineering Systems Architecture
A Practical
Guide to History-Dependent Causal Testing and Testability-by-Design
Author: Taotuner
DOI: https://doi.org/10.5281/zenodo.22313802
August 2026
In short: many control-system problems
that look like tuning drift, intermittent faults, or “just how the equipment
behaves” are actually history-dependent effects — the system’s past trajectory,
not just its current state, is shaping its behavior. This guide gives five
concrete tests to determine whether that is happening in a given system,
isolate what is causing it, and design new systems so the answer is cheap to
obtain. Missing this distinction means retuning controllers that were never the
problem, replacing hardware that was never faulty, or chasing intermittent
faults with no fixable root cause.
Companion
document to HDD-ISA — AI Architectures for Causal Discriminations
(Taotuner, 2026b) and the History-Dependent Dynamics (HDD) framework
(Taotuner, 2026a). HDD-ISA applies the same methodology to AI architectures;
HDD-ESA applies it to physical control systems — motion, thermal, fluid,
chemical, and power — with five causal-discrimination tests, design rules for
building testability into new systems, and per-substrate implementation guides.
The two documents share reporting categories (§9).
Methodological status. This is a
diagnostic and design-for-testability method, not a general theory of
control-system architecture. It determines whether history dependence, path
dependence, feedback mediation, internal-state dependency, or model-based
causal control are present in a system, and how to build new systems so that
determination is cheap to make. It does not replace standard
control-engineering practice (Åström & Murray, 2008) for choosing a control
topology. Numeric thresholds throughout §§3–7 (10%, 15%, 20%, and the
noise-floor multiplier in T2) are operational defaults, not universal constants
— tune them to the noise characteristics and stakes of your own system.
On the worked examples. The worked
examples in §§3–7 are illustrative: they show how each test’s interpretation
table applies to plausible numeric outcomes, not measurements from real
systems. No hardware, lab, or dataset underlies these numbers. Report your own
instrumentation, environmental conditions, sample sizes, and raw-data
availability when you apply this guide in practice.
1. Scope
Target systems: motion control (motors, servos, robots); thermal processes (ovens,
heat exchangers, HVAC); fluid systems (pumps, valves, hydraulic actuators);
chemical processes (reactors, mixers, distillation columns); power systems
(converters, drives, grids).
Requirements: a plant; sensors (position, temperature, pressure, flow, current,
voltage); actuators; a controller (PID, MPC, or any regulator); a data logger.
Out of scope: AI systems and machine learning models (see HDD-ISA); philosophical
questions about consciousness; software-only simulation.
2. The Five Tests
|
Test |
Question |
Requires |
|
T1 |
Does history improve
prediction? |
Sensor logs, system
identification |
|
T2 |
Does past trajectory
cause future behavior? |
Two trajectories to the
same setpoint, confound control |
|
T3 |
Is the trajectory effect
mediated by a specific feedback pathway? |
Ability to open that
pathway, plus a sham comparison pathway |
|
T4 |
Does the system depend
on an internal state estimate, and is that dependency self-specific? |
Internal state estimate,
plus a matched decoy channel |
|
T5 |
Does the system use a
self-inclusive model causally? |
A model-based controller
(MPC, LQR) |
Table 1. The five
HDD-ESA tests.
Each test targets a
logically distinct construct: passing T1 does not imply T2, passing T2 does not
imply T3, and so on. §12.2’s suggested test order is a resource-allocation
heuristic, not a claim of logical dependency — a system can in principle pass a
later test while failing an earlier one.
T4 and T5 use narrow,
functional definitions of “self-reference” and “self-model,” defined precisely
in §6 and §7. Passing them establishes a specific, testable engineering
property, not a claim about self-awareness or agency.
3. T1 — History-Dependent
Prediction
A
positive result establishes that including history improves prediction beyond
the current measured state — not that the system “lacks a Markovian
description.” Any system has a Markovian description in a suitably enlarged
state space (Åström & Murray, 2008); T1 detects that y(t) and u(t) are an incomplete observation of that larger state (unmodeled
thermal lag, actuator elasticity, hysteresis), not memory in any stronger
sense.
Protocol. Log y(t) and u(t) at fixed rate T_s. Fit Model 0 (order 1: y(t+1) =
f(y(t), u(t))) and Model 1 (order n, n ≈ 3 × dominant time constant / T_s),
matched in parameter count, via system identification (Ljung, 1999; Söderström
& Stoica, 1989). Validate on a chronological 80/20 held-out split.
Significance. Use the F-test as the primary criterion — F = [(SSE₀ − SSE₁)/(df₀ −
df₁)] / [SSE₁/df₁] — and report AIC/BIC (AIC = n·ln(SSE/n) + 2k; BIC =
n·ln(SSE/n) + k·ln(n)) as a complementary check, not an alternative pass
condition: AIC and BIC penalize complexity differently and answer a
model-selection question, not a hypothesis-testing question, so treating
“F-test p < 0.05 OR AIC/BIC improves” as an either/or criterion inflates the
effective false-positive rate.
|
F-test |
AIC/BIC |
Result |
|
p <
0.05 |
Both
improve by > 2 |
Supported |
|
p <
0.05 |
Disagree
or don’t improve |
Uninterpretable — investigate before reporting a pass |
|
p ≥
0.05 |
— |
Negative
Evidence |
Table
2. T1 interpretation.
Illustrative
example (DC motor, 10,000 samples at 1 kHz):
order-3 vs. order-1 model of speed vs. voltage; MSE improves 29.8%,
F-test p < 0.001, ΔAIC = 15.2, ΔBIC = 11.0 — Supported, consistent
with unmodeled electrical and mechanical time constants rather than evidence of
anything beyond an incomplete first-order observation.
4. T2 — Causal Trajectory
Dependence
A bare
comparison of two trajectories reaching the same setpoint does not establish
causal trajectory dependence: ambient drift, incomplete return to a common
initial state, and accumulated thermal or magnetic energy can each produce an
apparent trajectory effect unrelated to the trajectory itself. The protocol
therefore requires randomized/interleaved trial order; a verified,
tolerance-banded return to baseline before each trial; logged environmental
covariates (ambient temperature, supply voltage) included via ANCOVA rather
than a plain t-test; and confirmation that accumulated energy state is matched
at trial start.
Protocol. Design two trajectories (e.g., fast vs. slow ramp) to the same
setpoint r; apply a standard perturbation after each; record the response
(overshoot, settling time) over ≥ 5–10 repetitions per trajectory in randomized
order; analyze by ANCOVA with logged covariates.
Significance. Set the practical-effect threshold relative to the system’s own
noise floor (σ_noise, from repeated same-trajectory trials) rather than a fixed
percentage, since a universal threshold is not meaningful across systems of
different scale and tolerance:
|
Result |
Interpretation |
|
ANCOVA
p < 0.05 AND effect > k·σ_noise (k = 3 as a default) |
Supported |
|
p ≥
0.05, or effect below threshold |
Negative
Evidence |
|
Confound
controls could not be fully implemented |
Non-Identifiable — report which controls were missing |
Table
3. T2 interpretation.
Illustrative
example (oven, setpoint 200 °C): fast vs. slow
ramp, ambient temperature logged as covariate, 10 randomized repetitions each,
30-minute baseline soak between trials; overshoot difference 7.2 °C against
σ_noise = 0.9 °C (≈8×), ANCOVA p < 0.001 — Supported.
5. T3 — Feedback Mediation
Opening a feedback
loop changes system dynamics — bandwidth, damping, noise sensitivity —
regardless of whether that loop specifically mediated the T2 effect. A
reduction in divergence after opening the candidate loop is therefore necessary
but not sufficient evidence of loop-specific mediation; almost any sufficiently
large dynamical perturbation can produce a similar reduction. The protocol
requires a sham condition: a different loop, or a partial change to the same
loop, perturbed by a matched dynamical magnitude, without being the
hypothesized mediator.
Protocol. Measure the baseline T2 effect (loop intact, n ≥ 5); open the
candidate loop (zero gain, precomputed open-loop profile, or physical bypass)
and re-measure (n ≥ 5); run the matched sham condition and measure the same
effect (n ≥ 5).
|
Result |
Interpretation |
|
Candidate reduces
the effect (p < 0.05) by significantly more than the sham |
Supported — loop-specific mediation |
|
Candidate and
sham produce comparable reductions |
Uninterpretable as loop-specific — consistent with a generic dynamical artifact |
|
No reduction
under either condition |
Negative
Evidence |
Table 4. T3
interpretation.
Illustrative
example (PID oven): baseline divergence 7.2 °C; PID
opened → 2.1 °C (71% reduction, p < 0.01); sham (rate-limited actuator,
matched bandwidth change) → 6.4 °C (11% reduction, n.s.) — Supported.
6. T4 —
Internal-State Dependency and Self-Referential Specificity
Showing
that perturbing an internal state estimate changes control output more than
perturbing a matched external variable establishes only that the controller
depends on the state estimate it was designed to use — true, by construction,
of essentially any competently designed closed-loop controller. The “self”
vs. “non-self” label is stipulated by the engineer, not discovered by the
test. This guide therefore splits T4 into a weak form (dependency) and a strong
form (specificity), following the decoy-comparison logic used for the analogous
construct in HDD (Taotuner, 2026a, §20.4) and HDD-ISA.
T4-Weak. Inject a bias into the internal
state estimate x̂ (defined by d(x̂)/dt = A·x̂ + B·u + L·(y − C·x̂)) and confirm
the control output responds (n ≥ 5, p < 0.05). A pass establishes
internal-state dependency only, and should not be described as self-reference
without that qualifier.
T4-Strong. Construct a matched decoy
channel: a variable of similar magnitude, update rate, and information content
to x̂, but not derived from or fed back into the system’s own regulation — an
independent signal injected through an auxiliary, non-regulatory input. Inject
matched-magnitude perturbations into the genuine estimate and the decoy, in
randomized order (n ≥ 5 each), and compare effect sizes.
|
Result |
Interpretation |
|
Genuine effect substantially exceeds decoy effect (report ratio
and CI) |
Supported — dependency specific to
self-referential content |
|
Genuine and decoy effects indistinguishable |
Negative Evidence — explained by
generic information-bearing input, not self-reference |
Table 5. T4-Strong interpretation.
A
system passing T4-Weak but failing T4-Strong should be reported as
“internal-state dependent, no evidence of self-referential specificity” — not
folded into an ambiguous single “T4 passed.”
Illustrative example (BLDC motor, FOC control): genuine estimate = rotor angle θ̂ from a Luenberger observer
(Luenberger, 1964); decoy = matched independent signal via an unused input.
T4-Weak: +5° bias → torque ripple +15.2 ± 2.1% (p < 0.001), Supported.
T4-Strong: matched decoy perturbation → +2.1 ± 1.8% (n.s.); ratio 7.2 (95% CI
4.1–11.8) — Supported.
7. T5 — Model-Based
Predictive Control
“Causal
self-model” here means, specifically, a model that includes a representation of
the system’s own dynamics and is used causally, not descriptively, to generate
control action — standard MPC terminology (Camacho & Bordons, 2007) under a
name consistent with the HDD construct hierarchy. Passing T5 is an engineering
statement about a control architecture, not a claim about a new category of
self-modeling.
Three
components must all pass:
|
Component |
Test |
Pass
condition |
|
A:
Self-prediction |
Model
predicts future states |
Held-out
error < 10% of signal range |
|
B:
Counterfactual prediction |
Model
predicts effect of a different input |
Held-out
error < 15% |
|
C:
Causal policy influence |
Model
modification changes control output |
Output
changes > 20%, p < 0.05 |
Table
6. T5 three-component criterion.
The
10%/15% thresholds follow standard model-validation practice (Ljung, 1999); the
20% threshold for Component C is the author’s operational choice (roughly twice
typical control-output variance) and should be adjusted to the noise floor of
the system under test.
Illustrative
example (chemical reactor with MPC): Component A:
6.2% error, pass. Component B: 11.8% error, pass. Component C: +20% rate
constant → output changes 35.4 ± 4.2%, p < 0.001, pass — Supported.
8. Design Rules for
Testability
Each test is
cheaper and safer when the system is architected for it from the outset, rather
than retrofitted:
|
Test |
Design
rule |
|
T1 |
Log raw,
unfiltered signals at ≥ 10× the inverse of the shortest time constant of
interest, synchronized timestamps, no in-path smoothing that could mask or
manufacture apparent history dependence; buffer depth ≥ 3× dominant time
constant. |
|
T2 |
Programmatic
trajectory-select mode; automated randomized-order sequencer; automated
baseline-return check; ambient-condition sensors provisioned as standard
instrumentation. |
|
T3 |
Accessible
bypass/manual-override per candidate loop (software or physical switch); at
least one auxiliary parameter suitable as a matched sham condition. |
|
T4 |
Internal
estimator output exposed as a separately loggable and injectable signal; a
decoy input channel with no path into regulation, provisioned at design time
— the single highest-value item in this table, since building it after the
fact is usually the most expensive part of running T4-Strong. |
|
T5 |
Supervisory
interface for controlled, logged, reversible model-parameter injection,
rather than direct edits to controller code during testing. |
Table 7.
Design rules for testability.
9. Reporting Categories
Shared with HDD-ISA
for consistency across the series:
|
Category |
Meaning |
|
Supported |
The evidentiary
bar was met. |
|
Negative
Evidence |
Tested under
adequate conditions; bar not met. |
|
Uninterpretable |
Internally
inconsistent results (e.g., F-test and AIC/BIC disagree; candidate and sham
indistinguishable) requiring investigation before a verdict. |
|
Non-Identifiable |
Required controls
or instrumentation (decoy channel, covariate logging) could not be
implemented. |
Table 8.
Reporting categories, consistent with HDD-ISA.
10. Interpretation
|
Profile |
Interpretation |
Design implication |
|
T1 Supported, T2
Negative Evidence |
Memory exists,
trajectory doesn’t matter |
Higher-order model;
standard setpoint control |
|
T1, T2 Supported; T3
Negative Evidence |
Trajectory matters, not
through the tested pathway |
Investigate feedforward,
hysteresis, or an untested pathway |
|
T1–T3 all Supported |
Trajectory matters
through the identified feedback pathway |
PID with anti-windup;
monitor integral saturation |
|
T4-Weak Supported,
T4-Strong Negative Evidence |
Ordinary feedback
dependency, no self-referential specificity |
Report as such; avoid
self-reference language |
|
T4-Strong Supported |
Dependency specific to
self-referential content |
Observer is a critical,
non-interchangeable component; prioritize fault detection |
|
T5 Supported |
Self-inclusive model
used causally (§7 sense) |
MPC/adaptive control is
engineering-justified |
Table 9. Consistent
result profiles and their implications.
Common failure modes. T1: overfitting or large-n significance without practical gain
(false positive); low excitation (false negative). T2: unlogged confounds
(false positive); insufficient perturbation (false negative). T3: generic
dynamical perturbation mistaken for loop-specific mediation, mitigated by the
sham control (false positive); redundant feedback loops (false negative). T4:
poorly matched decoy (false positive); insufficient sensitivity (false
negative). T5: correlation mistaken for causation, mitigated by Component C
(false positive); insufficient excitation (false negative).
11. Substrate Notes
|
Substrate |
Instrumentation |
Candidate T3 loop / T2
trajectory |
T4/T5 notes |
|
Motion control (motors, servos, robots) |
Encoder/tachometer,
current sensing |
Inner current loop
vs. outer velocity/position loop; trapezoidal vs. S-curve profiles
(usually already in firmware) |
FOC rotor-angle/flux
observers are a natural T4 channel; MPC/LQR increasingly common for T5 |
|
Thermal (ovens, HVAC, heat exchangers) |
Thermocouples/RTDs,
mandatory ambient sensor |
PID
vs. rate-limited actuator (sham); startup ramp rate |
Baseline-return times
can be long (minutes–hours) — budget accordingly; T4/T5 less common outside
advanced HVAC/industrial ovens |
|
Fluid (pumps, valves, hydraulics) |
Flow/pressure sensors,
valve position |
Pressure feedback loop;
fast vs. slow valve actuation |
Hysteresis from
seals/stiction can mimic T1’s observational gap — distinguish via explicit
hysteresis modeling (Mayergoyz, 1991); validate T3 in simulation first given
cavitation risk |
|
Chemical (reactors, columns) |
Temperature/pressure/composition,
often limited observability |
Batch startup profile;
long baseline-return between batches |
Safety: T3/T4 interventions carry runaway/pressure-excursion risk —
validate in simulation and follow site process-safety and change-control
procedures before live testing. T5 is often cheap here since MPC and
parameter-injection interfaces frequently already exist. |
|
Power (converters, drives, grids) |
Voltage/current/frequency,
protection-relay status |
Protective loops
(frequency/voltage) |
Safety: do not open protection loops on live infrastructure; use a test
bench, digital twin, or islanded microgrid. Fast switching dynamics require
care with T1’s sampling-rate rule (§8) to avoid aliasing. Grid-forming
inverters with state estimators suit T4; MPC-based converter control suits
T5. |
Table 10.
Substrate-specific implementation notes.
12. Implementation
Tools and Checklist
12.1 Tools
MATLAB: System Identification Toolbox (ARX/ARMAX,
F-test, AIC/BIC); Control System Toolbox (PID, LQR, observers, Kalman filters).
Python: control, sippy (ARX/ARMAX), scipy (filtering,
statistical tests). Open source: github.com/python-control/python-control;
github.com/CPCLAB-UNIPI/SIPPY; scipy.org.
12.2 Checklist
Prerequisites: signal
logging per §8’s sampling rule; trajectory-select with randomization and
baseline-return check; loop bypass plus sham pathway; state-estimate injection
plus decoy channel; model-parameter injection interface.
Suggested order
(resource-allocation heuristic, not logical dependency): T1 → T2 (with confound
controls) → T3 (with sham) → T4-Weak → T4-Strong (if resources allow) → T5.
Reporting: use the
four categories in §9 for every test, noting which controls, sham conditions,
or decoy channels were or were not implemented.
References
Åström, K. J., & Murray,
R. M. (2008). Feedback Systems: An Introduction for Scientists and Engineers.
Princeton University Press.
Camacho, E. F., & Bordons,
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Kalman, R. E. (1960). A new
approach to linear filtering and prediction problems. Journal of Basic
Engineering, 82(1), 35–45.
Ljung, L. (1999). System
Identification: Theory for the User (2nd ed.). Prentice Hall.
Luenberger, D. G. (1964).
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Mayergoyz, I. D. (1991). Mathematical
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Söderström, T., & Stoica,
P. (1989). System Identification. Prentice Hall.
Taotuner. (2026a). History-Dependent
Dynamics (HDD): A Methodological and Theoretical Framework for Investigating
History-Dependent Response, Recursivity, Self-Reference, and Consciousness in
Dynamical Systems.
Taotuner. (2026b). HDD-ISA
— AI Architectures for Causal Discriminations. Zenodo.
https://doi.org/10.5281/zenodo.22060143
Visintin, A. (1994). Differential
Models of Hysteresis. Springer-Verlag.
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