制御工学を学ぶ方向けの教育用GPTを公開しました。 このGPTでは，伝達関数，状態方程式，PID制御，安定性，オブザーバ，最適制御，ロバスト制御，非線形制御，システム同定，MPC などについて，日本語で段階的に説明するようにしています。初学者にはできるだけ直感的に，学部上級生や大学院レベルの内容には仮定や設計意図も含めて答えることを意識しています。 今回のGPTでは，単に質問に答えるだけでなく，関連するブログ記事，動画，コード，インタラクティブ教材への導線も示せるようにしました。制御工学では，その場の説明だけでなく，「次に何を見ればよいか」が分かることも大事だと感じているためです。 伝達関数やボード線図，状態方程式，可制御性，オブザーバ，LMI，MPC などについては，できるだけ個別の教材につながるように整理しました。授業や演習の補助として使うこともできますし，学習の入口として使うこともで

In many control and signal processing applications, state estimation must be performed using measurements from multiple sensors operating at different sampling rates. GPS updates at 1 Hz while inertial sensors run at 100 Hz — how do you optimally fuse these measurements? The standard Kalman filter assumes uniform sampling, but real-world multirate systems exhibit periodic time-varying dynamics in

This blog covers control engineering — from fundamental tutorials to research-level topics — with MATLAB code examples and video lectures. It also provides guides on LaTeX writing, presentation skills, and lab information for students. Run by a university researcher with 20+ years of experience. 本ブログでは、制御工学の基礎から専門的な研究トピックまで、MATLABコードや動画付きで解説しています。また、LaTeXによる論文執筆やプレゼンテーション技術、研究室紹介の記事も掲載しています。 Conte

This article provides a comprehensive overview of model-based compensation methods in control engineering — control structures that place a plant model inside the feedback loop and use the difference between the model output and the actual plant output as a feedback signal. These methods share a common principle but differ in their architecture, assumptions, and applicability. This article explain

This article is a comprehensive guide to system identification — the process of building mathematical models of dynamical systems from measured input-output data. It covers the fundamental concepts and workflow of system identification, classical parametric methods, subspace identification, kernel-based regularized approaches, identification for periodically time-varying and multirate systems, pol

This article provides a comprehensive explanation of the Kalman filter for state estimation in control systems. Starting from the basic discrete-time formulation, it covers the prediction-update algorithm, steady-state Kalman filter, continuous-time Kalman-Bucy filter, and extensions to multi-rate sensing environments using LMI optimization. Related articles, research papers, and MATLAB links are

This article is a comprehensive guide to state observers and state estimation in control systems. It covers the fundamental theory of Luenberger observers in both continuous-time and discrete-time settings, Kalman filters for stochastic estimation, robust H∞ filters using LMI-based design, and advanced topics including multi-rate state estimation and outlier-robust observers. Links to detailed art

This article provides a detailed explanation of a state observer that eliminates the influence of outliers in sensor outputs using a median-based selection from multiple estimation candidates. Related articles, related papers, and MATLAB links are placed at the bottom. Author: Hiroshi Okajima, Associate Professor, Kumamoto University, Japan — 20 years of control engineering research This article i

This article provides a detailed explanation of tracking performance limitations for one-degree-of-freedom (1DOF) control systems, extending the achievable-output-set approach to systems where unstable poles also affect the fundamental limit. Related articles, related papers, and links are placed at the bottom. Author: Hiroshi Okajima, Associate Professor, Kumamoto University, Japan — 20 years of

This article provides a detailed explanation of a compensator design method that minimizes the modeling gap between a nominal model and the actual plant. This paper is the foundational work that later developed into a broader research program known as the Model Error Compensator (MEC). Related articles, related papers, and MATLAB links are placed at the bottom. Author: Hiroshi Okajima, Associate P

This article provides a detailed explanation of system identification for control systems with multiple sensors operating at different sampling rates, using cyclic reformulation and subspace identification methods. Related articles, related papers, and MATLAB links are placed at the bottom. Author: Hiroshi Okajima, Associate Professor, Kumamoto University, Japan — 20 years of control engineering r

This article provides a detailed explanation of system identification for linear periodically time-varying (LPTV) systems using cyclic reformulation and subspace identification. Related articles, related papers, and MATLAB links are placed at the bottom. Author: Hiroshi Okajima, Associate Professor, Kumamoto University, Japan — 20 years of control engineering research This article is based on the

This article provides a detailed explanation of an extended Model Error Compensator (MEC) that uses a parallel feed-forward filter (PFF) to handle non-minimum-phase plants. The standard MEC achieves high model error suppression for minimum-phase plants but faces difficulty when the plant has unstable zeros or time delays. This paper proposes a new structure that overcomes these limitations. Relate

This article provides a detailed explanation of a design method for the Model Error Compensator (MEC) that handles polytopic-type uncertainty and disturbances. While the MEC was originally designed using frequency-domain methods (e.g., synthesis), this paper proposes a new state-space approach combining LMI-based performance analysis with particle swarm optimization (PSO), enabling flexible design

This article provides a detailed explanation of a design method for the Model Error Compensator (MEC) with a parallel feedforward compensator (PFC) for non-minimum phase MIMO systems with polytopic-type uncertainties. This work unifies two previous developments — the PFC-based approach for non-minimum-phase systems and the LMI/PSO-based design for polytopic uncertainties — into a single state-spac

This article provides a detailed explanation of robust invariant set estimation for discrete-time switched linear systems with peak-bounded disturbances. Related articles, related papers, and MATLAB links are placed at the bottom. Author: Hiroshi Okajima, Associate Professor, Kumamoto University, Japan — 20 years of control engineering research This article is based on the following paper. Okajima

マルチレートカルマンフィルタのArXiv マルチレートカルマンフィルタの論文を投稿し，投稿前にArXivに原稿提出しました。 LMI Optimization Based Multirate Steady-State Kalman Filter Design https://arxiv.org/abs/2602.01537 概要： 本論文では，異なるサンプリング周期で動作する複数のセンサを有するシステムに対し，マルチレート定常カルマンフィルタのための LMI に基づく設計手法を提案する．マルチレートシステムは周期時変システムとして定式化され，カルマンゲインはフレーム周期ごとに繰り返される周期定常値へと収束する．この周期系に対してサイクリング（cyclic reformulation）を施すことで，問題は時不変系として表現できるが，その結果として得られる観測雑音共分散行列は正定ではなく半正定

この記事では、MATLABによる制御シミュレーションのアニメーション実装について紹介します。制御工学の理論を視覚的に理解するためには、シミュレーション結果をアニメーションとして表現することが非常に効果的です。ここでは、MATLAB File Exchangeで公開している6つの制御シミュレーションとアニメーション実装について解説します。 なお、状態フィードバック制御やオブザーバ設計の基礎については次の記事でまとめています。 状態フィードバック制御・状態方程式に基づく制御のまとめ MATLABによる制御シミュレーション アニメーション実装の基本手順 公開しているシミュレーションの紹介 1. 倒立振子のシミュレーションとアニメーション 倒立振子シミュレーションの動画 2. 最適レギュレータのアニメーション（重みと性能の関係） 最適レギュレータアニメーションの動画 3. 車両モデルを用いたアダプ

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This article provides a detailed summary of the Model Error Compensator (MEC). Videos, related articles, related papers, and MATLAB links related to the Model Error Compensator are placed at the bottom. The "Model Error Compensator" is a general-purpose method for enhancing the robustness (resilience to disturbances and model errors) of control systems. It can be used to improve the robustness of