This paper presents a force control based on the observer without taking any force or torque measurement from the robot which allows realizing more stable and robust human robot interaction for the developed multi-functional upper limb rehabilitation robot. The robot has four functional training modes which can be classified by the human robot interaction types: passive, active, assistive, and resistive mode. The proposed observer consists of internal disturbance observer and external force observer for distinctive performance evaluation. Since four training modes can be quantitatively identified as impedance variation, position-based impedance control with feedback and feedforward controller was applied to the assistive training mode. The results showed that the proposed sensorless observer estimated cleaner and more accurate force compared to the force sensor and the impedance controller embedded with the proposed observer completed the assistive training mode safely and properly.