Tendon-sheath-driven manipulators (TSM) are widely used in minimally invasive surgical systems due to their long, thin shape, flexibility, and compliance making them easily steerable in narrow or tortuous environments. Many commercial TSM-based medical devices have non-linear phenomena resulting from their composition such as backlash hysteresis and dead zone, which lead to a considerable challenge for achieving precise control of the end effector pose. However, many recent works in the literature do not consider the combined effects and compensation of these phenomena, and less focus on practical ways to identify model parameters in realistic conditions. This paper proposes a simplified piecewise linear model to construct both backlash hysteresis and dead zone compensators together. Further, a practical method is introduced to identify model parameters using motor current from a robotic controller for the TSM. Our proposed methods are validated with multiple Intra-cardiac Echocardiography (ICE) catheters, which are typical commercial example of TSM, by periodic and non-periodic motions. Our results show that the errors from backlash hysteresis and dead zone are considerably reduced and therefore the accuracy of robotic control is improved when applying the presented methods.