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The left ventricular assist device (LVAD) is a mechanical device that can assist an ailing heart in performing its functions. The latest generation of such devices is comprised of rotary pumps which are generally much smaller, lighter, and quieter than the conventional pulsatile pumps. The rotary pumps are controlled by varying the rotor (impeller) speed. If the patient is in a health care facility, the pump speed can be adjusted manually by a trained clinician to meet the patient's blood needs. However, an important challenge facing the increased use of these LVADs is the desire to allow the patient to return home. The development of an appropriate feedback controller for the pump speed is therefore crucial to meet this challenge. In addition to being able to adapt to changes in the patient's daily activities by automatically regulating the pump speed, the controller must also be able to prevent the occurrence of excessive pumping (known as suction) which may cause collapse of the ventricle. In this paper we will discuss some theoretical and practical issues associated with the development of such a controller. As a first step, we present and validate a state-space mathematical model, based on a nonlinear equivalent circuit flow model, which represents the interaction of the pump with the left ventricle of the heart. The associated model is a six-dimensional vector of time varying nonlinear differential equations. The time variation occurs over four consecutive intervals representing the contraction, ejection, relaxation, and filling phases of the left ventricle. The pump in the model is represented by a nonlinear differential equation which relates the pump rotational speed and the pump flow to the pressure difference across the pump. Using this model, we discuss a feedback controller which adjusts the pump speed based on the slope of the minimum pump flow signal, which is one of the model state variables that can be measured. The objective of the controller is - - to increase the speed until the envelope of the minimum pump flow signal reaches an extreme point and maintain it afterwards. Simulation results using the model equipped with this feedback controller are presented for two different scenarios of patient activities. Performance of the controller when measurement noise is added to the pump flow signal is also investigated.