This article develops a systematic framework for dynamic tracking control of soft robots. To this end, we propose a new projector for the proper orthogonal decomposition algorithm to significantly reduce the large-scale robot models, obtained from finite-element methods (FEM), while preserving their structure and stability properties. Such a property preservation enables an effective equivalent-input-disturbance-based scheme for dynamic tracking control of elastic soft robots with various geometries and materials. The proposed control scheme is composed of three key components, i.e. , feedforward control, disturbance-estimator control, and feedback control. To account for the trajectory reference, the feedforward action is designed from the dynamic FEM reduced-order robot model. The disturbance-estimator control action is obtained from an unknown input observer, which also provides the estimates of the reduced states for the feedback control design. The feedback gains of the observer-based controller are computed from an optimization problem under linear matrix inequality constraints. The closed-loop tracking properties are guaranteed using the Lyapunov stability theory. The effectiveness of the proposed dynamic control framework has been demonstrated via both high-fidelity SOFA simulations and experimental validations, performed on two soft robots with different natures. In particular, comparative studies with state-of-the-art control methods have been also carried out to highlight the interests of the new soft robot control results. This article is complemented with a video: https://bit.ly/2VVwtLn .