This paper presents a comparative analysis of model-based control strategies for a Bionic Ankle Tensegrity Exoskeleton (BATE), designed to emulate the self-stress equilibrium and self-supporting characteristics of the human ankle biotensegrity structure. Model-based control strategies are conventional methods that can discover the principles of the BATE exoskeleton. The high dimensions and non-linearity of the BATE pose challenges for theoretical modeling and model-based control strategies. To address this, we propose a modeling method based on the force density that accounts for interaction forces. We evaluated the trajectory tracking performance and robustness of BATE under three power-assisted control methods: position control (PC), force control (FC) and hybrid force-position control (FPC). Experimental results demonstrate that the PC method offers superior performance in both trajectory tracking and robustness, making it suitable for early rehabilitation training to enhance flexibility. Our findings highlight the advantages of tensegrity exoskeletons over current wearable exoskeletons and introduce novel concepts for developing high-performance exoskeletons.