What is the structure that generates signals controlling the basic heartbeat rate?

simple, pacemaker. Also called the intrinsic cardiac conduction system. The SA node (sinoatrial node, the pacemaker) is located in the right atrial wall, just inferior to the entrance of the the superior vena cave. from the SA node, the depolarization wave spreads via the gap junctions thorough the atria and via the internodal pathway to the AV node (also called atrioventricular node), located in the inferior portion of the interatrial septum immediately above the tricuspid valve. Then to the AV bundle in the superior part of the interventricular septum. Then to the Right and Left bundle branches which course along the interventricular septum toward the apex of the heart until eventually curving up each side of the ventricles of the heart as the purkinje fibers, which are essentially long strands of barrel shaped cells with few myofibrils.