4. The controller is rather simple to implement. The internal model
system is linear and stabilization is accomplished by the use of
well known linearization techniques.
The main results of this paper are contained in Chapter Two. Here the servomechanism problem is solved for a nonlinear system having the same number of inputs as outputs. Later, a method is introduced so that the results can be extended to a nonlinear system having more inputs than outputs.
The assumptions needed in the derivations are that a solution to the problem does indeed exist and that when tracking does occur, both the state and input will satisfy a linear differential equation.
Although the latter assumption is restrictive, when it does not hold, a design based on such an approximation may still result in very small tracking error.
After the assumptions are stated, an internal model system is introduced. This internal model system replicates the dynamics found in the state and input signals which are necessary to achieve tracking. The concept of including the dynamics of the state and input rather than the common practice of including the dynamics of the reference and disturbance is believed to be new.
The next step in the design involves the use of constant gain feedback with the internal model systm incorporated into the feedback loop. It is shown that observability of the internal model system, through its associated feedback gain, insures that zero tracking error will occur for all time provided the initial state of the combined plant and controller has the correct value. Since such an initial state is unlikely to occur in practice, it is next shown that certain stability