Shape memory alloys (SMAs) have been used as actuators for applications in fields like artificial muscle in robotics, assistive devices, and surgical manipulators. SMA possesses attractive features like inherent stiffness varying property during phase transformation, high force to mass ratio, offer new mechanically simple and flexible designs, making them a potential alternative to conventional compliant/variable stiffness actuation technologies. This paper focuses on the performance analysis of active stiffness control of the synergistically operated translational compliant variable stiffness actuator (STCVSA), which comprises a compressive passive bias spring (coil spring/wave spring) and SMA wire(s) appropriately arranged between two discs and around a shaft. To control the stiffness of the compliant actuator, adaptive control (fuzzy PID and fuzzy SMC) algorithms are designed and implemented. The performances of the STCVSA with the controllers are compared with their conventional forms. It is observed that fuzzy SMC has a better ability to handle uncertainties, disturbances, and parameter variations.