In robotic manipulation of deformable objects, the continuum nature of the object state leads to prohibitively high degrees of freedom when traditional modelling techniques are applied, leading to much research focusing on approaches that avoid an explicit object model. However, without such a model the opportunities for long horizon planning over the object shape or the application of optimal control methods are limited. In this work, we take a step to address this gap for the category of deformable linear objects by developing an accurate, low-dimensional manipulator-object model using the Affine Curvature strain parametrisation. We derive the model kinematics and dynamics, and detail a procedure for experimentally determining the unknown material parameters, using heavy electrical cables as a realistic test case. We then prove the viability of the model by experimentally demonstrating accurate feedforward control of the object in steady state, allowing for a significantly expanded reachable workspace and control of the endpoint orientation.