The cable-driven hyper-redundant continuum robot possesses a highly slender and flexible body, rendering it particularly well-suited for operations in confined spaces. However, developing mathematical models and control strategies for ensuring the safe traversal of hyper-redundant continuum robots through such narrow and confined spaces poses significant challenges. This paper presents a cable-driven hyper-redundant continuum robot intended for diverse applications such as aviation engines, aircraft fuel tanks, and pipelines in nuclear power plants. Firstly, a cable-driven hyper-redundant continuum robot equipped with internal angle sensors was developed. Simultaneously, a kinematic model for the cable-driven hyper-redundant continuum robot was established. Subsequently, utilizing the derived kinematic equations and signals obtained from angle sensors, we further deduced the velocity-level kinematics for the cable-driven hyper-redundant continuum robot. Furthermore, we proposed methods for pose perception and closed-loop control suitable for the cable-driven hyper-redundant continuum robot. Finally, experimental verification is performed to demonstrate the effectiveness and accuracy of the control method. The results reveal a positioning error of the end-effector within 1.5 mm, highlighting the outstanding performance of the proposed method.