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Transient control performance of power systems is extremely important, especially during the recovery stage from a system temporary fault. A large power angle error or generator relative speed could result in unrecoverable failure or system damage. In this study, a class of novel excitation controllers is proposed for power systems to place user‐defined time‐varying constraints on the system errors. First, the direct feedback linearisation technique is employed to transfer the original non‐linear system to a linear one. An error transformation method is introduced to generate a new non‐linear system, whose stability ensures that the time‐varying constraints on the original system are satisfied. Thus, a backstepping‐based excitation control methodology is designed for ideal case by assuming all system parameters are known. Thereafter, the uncertainties of system dynamics are also considered and compensated by designing an adaptive excitation controller. By utilising the standard Lyapunov synthesis, the closed‐loop system is proved to be asymptotically stable, and all the other signals are bounded for the two control schemes. Furthermore, the system transient performance can be shaped arbitrarily with predefined trajectories, in the sense that the system errors never cross certain boundaries during transient phase. Eventually, extensive simulation studies demonstrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]