【Control】🧪 19. Applicability Limits of Adaptive Control

― Quantitative Results and Decision Criteria for A-Type / B-Type

topics: [“control”, “adaptive control”, “PID”, “FSM”]

🎯 Purpose of This Article

This article summarizes verification results from Articles 01–16
to define where adaptive control may be used and where it must not be used,
based strictly on numerical indicators and decision criteria.

Philosophy or ideology: ❌
Optimistic expectations: ❌

👉 The goal is immediate operational decision-making.

🧱 Common Verification Conditions

Target system: V–I control loop (PID-based)
Degradation model: friction / resistance increase (up to 1000 days equivalent)
Disturbances: step disturbance + noise
Compared controllers:
- Fixed PID
- A-Type (always-on adaptation)
- B-Type (FSM-permitted adaptation)

🗺️ Applicability Decision Flow

flowchart LR
    Start[Operation Start]

    Start -->|Mild degradation| BType[B-Type<br/>Conditional Adaptation]
    BType -->|Metrics OK| BType
    BType -->|Threshold exceeded| Stop[Adaptation Stop]

    Start -->|Moderate degradation| Stop
    Stop --> PIDonly[Fixed PID]

    Start -->|Experimental use| AType[A-Type<br/>Always-on Adaptation]
    AType -->|Limit measured| Stop

🧪 A-Type Results (Observed Facts)

✅ What Was Confirmed

Temporary tracking improvement in early degradation
Gain retuning feasibility
Short-term response improvement

❌ What Could Not Be Guaranteed

Δt (time reliability)
Long-term stability
Reproducibility

📊 Common Quantitative Trends

Metric	Trend with Degradation	Notes
Δt	Monotonic increase	All controllers
Kp	Increase → saturation	Over-compensation risk
Amplitude A	Decrease	Loss of controllability

👉 A-Type improves short-term response but provides no long-term guarantees.

🛡️ B-Type Results (Observed Facts)

✅ What Became Possible

Stopping adaptation
Immediate fallback to fixed PID
Maintaining a reliability lower bound

🔐 Stop Conditions (Examples)

Δt / Δt₀ > threshold
Kp / Kp₀ > threshold
A / A₀ < threshold

if metric exceeds threshold:
    ADAPT_STOP
    FALLBACK_TO_PID

🧭 Applicability Matrix (Final)

Degradation Level	Recommended Method	Reason
Mild	B-Type	Conditional adaptation acceptable
Moderate	B-Type → Stop	Metric degradation detected
Severe	Fixed PID	Adaptation becomes harmful
Experimental	A-Type	Limit exploration only

🚫 Disallowed Operations (Immediate Failure)

❌ Using A-Type in real operation
❌ Always-on adaptive control
❌ No numerical stop criteria
❌ No fallback to fixed PID

✅ Conclusion (Fact-Based)

Adaptive control does not function as the primary controller
Designs assuming continuous adaptation are not suitable for operation
Stop logic is a mandatory design requirement
Operational configurations are based on B-Type with fixed PID fallback

📌 Final Summary

Experimental use: 🧪 A-Type
Operational use: 🛡️ B-Type
Final defense line: ⚙️ Fixed PID

With this summary,
the applicability boundaries and operational criteria for adaptive control are considered finalized.