This article explains how to design an observer-based feedback controller for multi-rate systems where sensors and actuators operate at different sampling periods. The key idea is to convert the multi-rate system into a periodically time-v…

A system identification framework that turns measurement noise into a structured uncertainty description. Cyclic reformulation with period N is applied to LTI systems to construct polytopes from a single experiment, then used for robust H∞…

A tutorial on kernel-based regularized system identification. Explains stable spline, tuned-correlated, and diagonal-correlated kernels, hyperparameter tuning via empirical Bayes, and MATLAB implementation with impulseest.

Compare IMC, Smith Predictor, Disturbance Observer, 2-DOF control, and Model Error Compensator (MEC). Structural comparison, selection guidelines, and connections to robust control engineering.

A comprehensive tutorial on state feedback control and state-space design for control systems. Covers pole placement, LQR optimal regulators, integral-type servo systems, LMI-based design, observer-based feedback with the separation princi…

The 2-DOF conditional feedback structure is the structural origin of MEC. Setting T = P_M yields MEC, which is equivalent to 2-DOF control for linear systems with feedforward input. MEC extends further to non-minimum-phase and nonlinear sy…

Structural comparison of Internal Model Control (IMC) and Model Error Compensator (MEC). Both use the plant-model output difference, but IMC designs the controller while MEC adds robustness to existing systems.

A survey of Model Error Compensator (MEC) research by independent groups worldwide. Covers applications to quadcopters, teleoperation, underwater robots, power electronics, data-driven tuning with FRIT and Smart MBD, and theoretical analys…

Apply the Model Error Compensator (MEC) to nonlinear systems for robust feedback linearization. Unlike standard feedback linearization, MEC does not require exact model knowledge or full state measurement. The output-feedback structure ach…

How to apply the Model Error Compensator (MEC) to non-minimum phase systems using a parallel feedforward compensator. Non-minimum phase plants have unstable zeros that prevent standard high-gain compensation. The PFC approach resolves this…

Learn how to add robustness to existing PID control systems using the Model Error Compensator (MEC). MEC is a simple add-on compensator that suppresses the effect of model uncertainty and parameter variations without modifying the PID cont…

A tutorial on classical parametric system identification. Explains ARX, ARMAX, Output-Error, and Box-Jenkins model structures, the prediction error method (PEM) for parameter estimation, model order selection, and MATLAB implementation. In…

A tutorial on subspace identification methods for control systems. Explains N4SID, MOESP, and CVA algorithms, model order selection via SVD, and MATLAB implementation. Includes connections to multirate and LPTV system identification resear…

A comprehensive guide to system identification in control engineering. Covers parametric methods, subspace identification (N4SID), kernel-based estimation, multirate systems, and data-driven control. With MATLAB code and links to research …

A detailed comparison between Model Error Compensator (MEC) and Disturbance Observer (DOB) for robust control. Covers structural differences, inverse model requirements, applicability to non-minimum phase and nonlinear systems, and practic…

A comprehensive guide to the H-infinity filter for robust state estimation. Covers the worst-case optimization formulation, LMI-based design with Bounded Real Lemma, comparison with Kalman filter, pole placement constraints, and extensions…

A comprehensive guide to the Kalman filter for state estimation. Covers the prediction-update algorithm, steady-state Kalman filter, Kalman-Bucy filter, tuning of Q and R, Extended and Unscented Kalman filters, and multi-rate Kalman filter…

A comprehensive guide to state observers and state estimation in control systems. Covers Luenberger observers, Kalman filters, H-infinity filters with LMI design, multi-rate state estimation, and outlier-robust MCV observers. Includes link…

Comprehensive guide to the Model Error Compensator (MEC), a general-purpose method for adding robustness to control systems against model errors and disturbances. Compatible with PID, MPC, nonlinear, and non-minimum phase systems. Includes…

This follow-up explores some advanced LMI techniques including Schur's lemma, variable elimination methods, and practical implementation with MATLAB code examples.

Stability Analysis of Discrete-Time Systems In control system design, system stability is the most fundamental and important characteristic. While in continuous-time systems, stability is determined by whether the roots (poles) of the char…

Linear matrix inequalities (LMIs) and controller design The method using Linear Matrix Inequality (LMI) is one of the most powerful controller design methods in the field of control engineering. The usefulness of controller design using LM…

Discretization of Continuous-Time Control Systems When expressing the characteristics of a control target based on physical laws, it is often represented in the form of differential equations, which are treated within the framework of cont…

This blog is about state estimation method unaffected by sensor outliers. For the overview of state estimation methods including Kalman filters and robust observers, see: State Observer and State Estimation: A Comprehensive Guide The state…

Optimal Velocity Control Method in Path Following Control Problem IFAC World Congress 2008 youtu.be Conference paper link: Optimal Velocity Control Method in Path Following Control Problem - ScienceDirect

Unified Form of Performance Limitations in Reference Tracking Control Problem for Discrete-Time Systems Hiroshi Okajima, Toru Asai, Shigeyasu Kawaji the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese …

Optimal quantization interval design of dynamic quantizers which satisfy the communication rate constraints Hiroshi Okajima, Kenji Sawada, Nobutomo Matsunaga 49th IEEE Conference on Decision and Control (CDC) youtu.be Conference paper link…

Model Error Compensator for adding robustness for existing systems IFAC world congress 2023, Yokohama, Japan youtu.be Conference paper link: Model Error Compensator for adding Robustness toward Existing Control Systems⋆ - ScienceDirect Add…

Direct Yaw-moment Control method for electric vehicles to follow the desired path by driver Hiroshi Okajima; Shouhei Yonaha; Nobutomo Matsunaga; Shigeyasu Kawaji Proceedings of SICE Annual Conference 2010 youtu.be Proceedings link: Direct …

A Design Method of Delta-Sigma Data Conversion System with Pre-Filter Hiroshi Okajima; Maho Honda; Rei Yoshino; Nobutomo Matsunaga SICE Journal of Control, Measurement, and System Integration Volume 8, 2015 - Issue 2: Special Issue on SICE…