The heat exchanger network (HEN) is an efficient energy recovery system to improve the energy integration between industrial process streams and thus able to reduce the use of utility. However, as a HEN becomes more integrated, potential control difficulties may arise significantly. In addition, these difficulties will further increase due to the uncertainty which is very likely to occur in a real operation of HEN. It is therefore crucial to ensure the controllability as well as the economy of HEN. Nevertheless, the previous researches aiming for controllable HENs sequentially addressed the network synthesis and improved the controllability. Its step-wise nature imposes restrictions on optimisation ability, consequently often leads to suboptimal solutions under global objective. Therefore, in this paper, an optimised-based framework is proposed for the simultaneous synthesis of controllable HEN where bidirectional communication between the network structure and the controllability is involved. The framework is based on a two-stage strategy, coupling the structure synthesis stage with the decision variables optimisation stage. In the first stage, the structure is synthesised incorporated with the proposed heuristic rules and renewed by the bypasses, resulting in the economical and controllable qualified HEN. In the second stage, the location and fraction of bypasses are used as the decision variables and their optimisation can still react on the network structure and control loop interaction to gain desirable economy and controllability. A case study is used to illustrate the effectiveness of the proposed framework.