generalization is rather obvious. If tracking and disturbance rejection
is to hold for a certain class of signals r(t) and w(t), two conditions are required: 1) the internal model system must contain the necessary dynamics to cover the entire class of signals, and 2) the closed-loop tranasient system NCT must remain locally (or globally) asymptotically stable over this class of signals.
Often in practice, the precise reference and disturbance signals acting on the system are not known in advance and hence neither are x*(t) and u*(t). In order to determine the dynamics which must be included in the internal model system it is necessary to have some apriori knowledge of the state and input signals which will occur during tracking. Usually, knowledge of the frequencies of the anticipated disturbance and reference signals is available. Generally, the
frequencies of the reference r*(t) and the disturbance w*(t) will directly affect the frequencies of the corresponding state x*(t) and input u*(t). Assuming this to be true, the mathematical model
describing the nonlinear system can be used to determine x*(t) and u*(t) for various combinations of r*(t) and w*(t). Fourier analysis can then be used to determine the dominant frequencies in the signals comprising the various x*(t) and u*(t) and the internal model system can be designed accordingly. Even when the mathematical is not used, an educated guess or perhaps trial and error can enable one to design an internal model system with the appropriate dynamics. For example, if
sinusoidal disturbance and reference signals are expected, it might be advisable to design the internal model system to accomodate for various harmonics and subharmonics of the anticipated sinusoidal signals.