A high speed centrifugal compressor for compressing fluids includes a permanent magnet synchronous motor (PMSM) having a hollow shaft, the being supported on its ends by ball bearing supports. A permanent magnet core is embedded inside the shaft. A stator with a winding is located radially outward of the shaft. The PMSM includes a rotor including at least one impeller secured to the shaft or integrated with the shaft as a single piece. The rotor is a high rigidity rotor providing a bending mode speed of at least 100,000 RPM which advantageously permits implementation of relatively low-cost ball bearing supports.