# Physiological Control Law for Rotary Blood Pumps with Full-State Feedback Method
## 1 Introduction  
Chronic heart failure (HF) has been gradually increasing each year, and it is believed to be one of the most important causes of morbidity and mortality worldwide. Epidemiological studies of most new cases of heart failure in the United Kingdom (UK) have succeeded in clarifying some of the key features of the occurrence [1]. In the late 1990s, it was identified that the occurrence of heart failure was higher in men than in women, probably because of the more probable onset of coronary artery diseases in males rather than females. Moreover, the average age of diagnosis was identified to be in the late 70s [2]. The risk of heart failure in both genders increases by at least 10% each year [3]. The American Heart Association reported that 85.6 million people in the United States suffer from cardiovascular diseases, of which 5.7 million live with HF. In contrast, HF patients can often be left in the hospital, unable to undergo or await heart transplantation, and wishing for a decent quality of life. Also, according to the annual reports of Interagency Registry for Mechanically Assisted Circulatory Support (INTERMACS), more than 13,000 patients received left ventricular assist device (IVAD) in 2014 in the United States [4]. Cardiac assistance technology is now evolving in order to enable these patients to achieve a high standard of living. The advancement of the artificial heart from the original roller pumps to the new revolving blood pumps on today's drawing panels is a continuous worldwide effort to build a permanently implantable artificial heart that maximizes patients' quality of life. More than forty ventricular assist device (VAD) brands are now available, in thefollowing three different categories: (1) membrane or volume displacement products, (2) rotary pumps with mechanical contact bearings (axial- and center-level), and (3) rotary pumps, which are free of mechanical contact bearings (axial and central). Hydrodynamic and/or magnetic suspension systems in the third-generation VADs cause the impeller to fail, to produce a device with no mechanical parts and a life expectancy of 10 to 15 years. The magnetic systems are generally larger than the hydrodynamic bearing pumps, resulting in lower shear levels of blood-washed bearings, which reduces the risk of a blood injury. This new generation of VADs is available in axial and centrifugal versions without mechanical touch coils [5]. As also stated above, the introduction of rotary control pumps dates to the earlier period of the 1990s [6]. Rotary blood pumps (RBPs) were started at a steady rotational speed, particularly as left ventricular assist devices (LVADs), according to the patient's need. Early clinical observations after development showed that the technique had serious health hazards attached to it, including a probable ventricular collapse, and, occasionally, excessive and uncontrolled suction [7]. In this field, several control methods have been identified as being useful for cardiac assist devices [8; 9]. These control methods can be designed according to the control variable. Such variables include pressure difference, afterload, preload, and flow [10]. Of all of these variables, only those dealing with preload control have been clinically tested and implemented. Moreover, it is important to note that the flow rate, pulsatility index (PI), and current signal for the motor had been suggested [11; 12]. Therefore, these control methods are being clinically practiced in many available RBPs. In the early periods of operation, RBPs as the LVADs are often needed in order to perform at the maximum flow rate. Several methods tend to meet the criteria by inserting and running the pump at the area closest to the left ventricle, where the most damage tends to occur [13]. However, it should also be noted that the additional unloading of the left ventricle may have an impact on the pumping performance of the right ventricle. This could be the case because of the occurrence of the septum shift.