An interesting alternative for today's high efficiency variable speed drives is the Permanent Magnet-Assisted Synchronous Reluctance Motor drive, which belongs to the family of brushless synchronous AC motor drives. Generally, the reluctance torque of this motor is significant compared to the Permanent Magnet electrical torque. The advantage of increased reluctance torque is the decreased need of expensive permanent magnet (PM) material, which makes this solution thus cheaper than the respective permanent magnet motor. Also due to its synchronous operation, sensorless rotational control is possible along with higher power factor and better efficiency compared to the induction motor (IM). Therefore, this thesis first deals with the implementation of a vector control strategy for speed control of the PMa-synRM motor that can be applied to a washing machine application. The machine is supplied by a current controlled voltage source PWM inverter to control the instantaneous stator currents which are decided by the reference speed. Secondly, the thesis focuses on the sensorless speed operation of the PMa-SynRM to take advantage of the lower costs as well as increased system reliability which otherwise is not possible using the delicate speed or position sensors. The concept involves estimation of the rotor speed and/or position. There are several speed estimation techniques proposed by researchers and among them the observer based technique is proven and commonly used in the industry. The only requirements of the observer system are a very fast signal processor, specialized and optimized to perform complex mathematical calculations. The feasibility and effectiveness of the control techniques are verified using the experimental results, implemented using the Texas Instruments TMS320F2812 eZDSP controller board and the overall motor drive system in the laboratory.