Design of PI^λ D^δ-Heart Rate Controllers for Cardiac Pacemaker

An arrhythmia is any disorder of your heart rate or rhythm. It means that the heartbeats too quickly, too slowly, or with an irregular pattern. Most arrhythmias result from problems in the electrical system of the heart. A cardiac pacemaker is a medical device that invented for those reasons. It helps the suffering patient to control abnormal heart rhythms. Several proportional-integral-derivative (PID) controllers have been proposed for improving the performance of such device, but it was shown that each of them has some limitations in facing the dynamic challenge of regulating heart rate. In this paper, we propose a robust fractional-order PID (PI^λ D^δ) controller to improve that performance. This controller has been designed based on Particle Swarm Optimization (PSO) algorithm via El-Khazali's approach. To illustrate the proposed design method, the objective function of the model under consideration is presented as well as the results of using the PI^λ D^δ-controller are compared with the results of using the conventional PID-controller to minimize several error functions; ITAE, IAE, ISE and ITSE. These results of such comparisons that are related to step response specifications, allow us to see the effectiveness of the best controller. Among of all these performance indices, the ITAE in case of the PI^λ D^δ-controller, shows more capability than others in providing closed-loop response with minimal overshoot, fast rise time and fast settling time. Further, to illustrate the influence and the efficiency of the proposed design method, the PSO-PI^λ D^δ-controller via El-Khazali's approach is compared with that of the same using two well-known approximations for s^±α; i.e., the Continued Fractional Expansion (CFE) and Oustaloup's approximations. The main results of this work are verified via numerical simulations.