In this paper, a novel framework to investigate the effect of external electrical signals on cardiac rhythm dynamics using the extended state observer-based control (ESOBC) is proposed. Heterogeneous coupled oscillator model (HCOM) is adopted for the generation of P, Ta, QRS, and T waves, and the realistic synthetic electrocardiogram (ECG) due to its capacity for simulating cardiac muscles response. Sinoatrial (SA) and atrioventricular (AV) nodes and His–Purkinje system are described by modified Van der Pol-type (MVDP) equations connected with time-delay velocity coupling. The electrical responses resulted from depolarization (De) and repolarization (Re) of cardiac muscles are separately presented by modified FitzHugh–Nagumo (MFHN) model. The SA and HP pacemakers are coupled with atrial (AT) and ventricles (VT) muscles, respectively, through the stimulation currents. To satisfy the integral chain form of ESO, and deal with the complex structure of the model, including the large number of parameters, and the coupling between the oscillators and interdependent states, three steps are considered. Firstly, a coordinate transformation is proposed for AT and VT responses described by MFHN model to handle mismatched condition. Following this, the nonlinearity of MFHN and the coupling between cardiac muscles and pacemakers are considered as lumped disturbances. Lastly, an extended state observer is designed to compensate the nonlinearity and estimate the unmeasured system states and handle the lumped disturbances. The stability of the closed-loop system is proved, and the effectiveness of the proposed framework for suppressing well-known rhythm disorder, i.e., sinus tachycardia is demonstrated. The framework presented in this work can be easily extended for a wide range of arrhythmia, and serve as an approach to investigate the effect of external stimulation to the heart muscles.

在本文中，提出了一种新的框架，该框架使用扩展状态基于观察者的控件（ESOBC）来研究外部电信号对心律动力学的影响。异质耦合振荡器模型（HCOM）被用于生成P，Ta，QRS和T波，并且由于其具有模拟心肌反应的能力，因此还可以使用逼真的合成心电图（ECG）。窦房（SA）和房室（AV）节点以及His-Purkinje系统通过与时滞速度耦合相关的改进的范德波尔型（MVDP）方程进行描述。修改后的FitzHugh-Nagumo（MFHN）模型分别显示了由心肌去极化（De）和复极化（Re）引起的电响应。SA和HP起搏器分别与心房（AT）和心室（VT）肌肉相连，通过刺激电流。为了满足ESO的整体链形式，并处理模型的复杂结构（包括大量参数）以及振荡器与相互依存状态之间的耦合，需要考虑三个步骤。首先，针对MFHN模型描述的AT和VT响应提出了坐标变换，以处理不匹配的情况。在此之后，MFHN的非线性以及心肌与起搏器之间的耦合被视为集总干扰。最后，设计了扩展状态观察器以补偿非线性并估计未测系统状态并处理集总干扰。证明了闭环系统的稳定性，并且所提出的框架对于抑制众所周知的节奏紊乱的有效性，即 表现出窦性心动过速。在这项工作中提出的框架可以很容易地扩展到广泛的心律失常，并且可以作为一种方法来研究外部刺激对心肌的影响。