ICS / RICS Control

MIMO System Identification · Iterative Control · Online Adaptation

Synthetic MIMO control portfolio covering:

• offline iterative correction with ICS,
• frame-to-frame online model adaptation with RICS,
• coherence-based model correction,
• confidence-weighted continuous model blending.

Full MATLAB implementation is maintained privately.
This public repository presents the methodology, experimental design, and validated synthetic results.

All results are synthetic MIMO experiments validated by the project author, not physical industrial tests.

Control Architecture

Multichannel broadband excitation → MIMO identification → identified model
                                                        ↓
ICS:  trial response → tracking error → next-trial input correction
RICS: frame input/output → online identification → model correction → next-frame input

ICS — Offline Iterative Control

ICS corrects tracking error from one trial to the next:

$$E_j = Y_d - Y_j$$ $$U_{j+1} = U_j + G_d \hat{H}^{-1} G_r E_j$$

Here, $U_j$ and $Y_j$ denote the trial input and output, $Y_d$ the desired output, and $\hat H$ the identified MIMO frequency-response model. $G_d$ and $G_r$ are the update weighting operators.

For the corresponding linear error-propagation model:

$$E_{j+1}=ME_j$$ $$M=I-H_{\mathrm{true}}G_d\hat H^{-1}G_r$$

Synthetic result

Validated synthetic result: RMSE 0.5849 → 0.0165 over 10 iterations. The observed iteration-to-iteration error ratio is approximately 0.70, consistent with the spectral radius ρ(M) ≈ 0.70 < 1. MIMO identification relative error is approximately 0.2%–0.5% within the effective frequency band.

These are synthetic results, not industrial or customer measurements.

ICS Tracking

Tracking response before and after 10 ICS iterations. The final response closely follows the desired trajectory.

ICS Convergence

Tracking RMSE decreases from 0.5849 to 0.0165 over 10 iterations.

ICS Convergence Analysis

The frequency-dependent spectral radius remains approximately 0.70, consistent with the observed iteration-to-iteration error reduction.

RICS — Online Model Adaptation

$$(U_m,Y_m)\rightarrow H_m\rightarrow\bar H_m\rightarrow U_{m+1}$$

Each frame supplies input/output data for a new model estimate. Coherence-based model correction uses identification confidence to select or blend model information before computing the next input.

• ICS: trial-to-trial error correction.
• RICS: frame-to-frame online model adaptation.

Paper-inspired / reproduced methods

• Online Only
• Frame + Weighted Coherence
• Point + Coherence
• Point + Response PSD

These methods are presented as reproductions or paper-inspired implementations, without claiming authorship of the original HRICS method or paper.

Experimental extensions

• Frame + Coherence Blend
• Point + Coherence Blend

These extensions apply confidence-weighted continuous model updates at frame and frequency-point levels, respectively.

Scenario A — Corrupted Identification Data

Scenario A Tracking Performance

Under locally corrupted identification data, hard frequency-wise coherence gating provides the lowest average tracking error.

Method	Average RMSE
Fixed Model	0.25161
Online Only	0.19876
Frame + Weighted Coherence	0.19326
Frame + Coherence Blend	0.19635
Point + Coherence	0.16430
Point + Coherence Blend	0.18533
Point + Response PSD	0.20978

Scenario B — Genuine Local Plant Change + Medium-Confidence Identification

The plant change occurs within the synthetic experiment.

Scenario B Tracking Performance

When the plant itself changes under medium-confidence identification, continuous point-wise confidence blending achieves the lowest average tracking error.

Method	Average RMSE
Fixed Model	0.16475
Online Only	0.08862
Frame + Weighted Coherence	0.09856
Frame + Coherence Blend	0.08748
Point + Coherence	0.09192
Point + Coherence Blend	0.08443
Point + Response PSD	0.10563

Scenario B Model Adaptation

Continuous confidence weighting incorporates useful new model information instead of fully rejecting medium-confidence estimates, enabling faster adaptation after genuine plant changes.

Key Insight

Hard rejection is effective when new model information is unreliable; continuous confidence weighting becomes advantageous when uncertain measurements still contain useful information about genuine plant changes.

These conclusions apply to the designed synthetic scenarios and do not establish universal superiority.

Detailed Documentation

• ICS: identification, control law, and convergence
• RICS: online identification and coherence correction
• Experimental confidence-blend extensions
• Results: ICS figures · RICS figures

References

Zhang, F., Zhou, H., Zhang, B., Song, W., & Wang, T. (2024). “Real-Time Iterative Control Method Research of Shaking Table.” Engineering Mechanics, 41(3), 187–198, 240. DOI: 10.6052/j.issn.1000-4750.2022.03.0265.

Privacy / IP

This repository is an independent synthetic implementation for technical study and portfolio demonstration. It does not contain proprietary SERVOTEST/BBK code, customer data, or internal engineering documents.

Full MATLAB implementation is maintained privately.

MATLAB source, proprietary employer material, customer data, BUAA/client-sensitive material, tutor nonpublic code, and private job-search material are excluded.