This paper presents a novel approach to the systematic construction of feedback solutions to some important control problems in timed discrete-event systems (TDES) with a global digital clock. Specifically, it deals with those systems which can be modelled by the framework described in the paper, and tackles the intended control problems formulated as a main problem (MP). MP is concerned with finding solutions under which the controlled behaviour of the system can satisfy the intended system specifications: the avoidance of certain forbidden conditions. A sufficient condition for the existence of solutions to MP is derived from the introduction of notions such as critical states and tolerable states as well as an analysis of event trajectories of a TDES in combination with a strategy for manipulating control mechanisms. On the basis of the solvability condition, a synthesis method is established. As the proposed synthesis method can solve the intended control problems systematically without relying on the exact information of event trajectories of a TDES, it provides an alternative for generating solutions efficiently. Finally, the applicability of the proposed method is demonstrated by an example of moderate complexity in a manufacturing system.