Discussion of linguistics and the variables that constitute languages is off topic here. You can reply to the topic I have placed in the Science/Language subcategory. You might want to reconsider your conclusion that the Katseff et al. work shows that formants are not controlled.
What’s relevant to the present topic is that while testing for controlled variables one must be alert to the possibility of hidden or non-obvious conflict as the reason for the appearance that a variable is not controlled. As Katseff & Houde put it (Lab. Phon. 11):
These results suggest that both acoustic and sensorimotor feedback are part of one’s lexical expectation. Because auditory feedback is altered while motor feedback is not, feedback from these two sources can conflict. For small shifts in auditory feedback, the amount of potential conflict is small and the normal motor feedback does not affect compensation. But for large shifts in auditory feedback, the amount of conflict is large. Abnormal acoustic feedback pushes the articulatory system to compensate, and normal motor feedback pushes the articulatory system to remain in its current configuration, damping the compensatory response.
On another note, I agree that by varying the disturbance we can demonstrate that control outputs are quantitatively equal but of opposite sign (or vector). Neither Bill nor Phil mentions this as essential to the definition of the Test, but it is important. You are incorrect to say, however, that Katseff et al. did not vary the disturbance. After drawing a parallel to work on reaching with and without prismatic lenses, they say (op cit.):
In speech adaptation, subjects wear a headset. They speak into the microphone and hear their speech played back to them through the earphones. The auditory version of the task used here involves four stages: baseline, ramp, plateau, and adaptation. Subjects repeat a single word, in this case, ‘head’, over a large number of trials. In “reaching” sensorimotor adaptation experiments, subjects initially see the object on the table in its true position. In speech adaptation experiments, subjects hear their voices unaltered during the baseline stage. During each trial in the ramp stage, auditory feedback is altered a small amount until it reaches a maximum value. Feedback alteration is held at that maximum value during the plateau stage. In this experiment, there are 5 sets of ramps and plateaus, after which feedback drops suddenly back to normal for the adaptation stage.
… subjects generally change their speech to oppose the auditory feedback change. For example, when F1 in auditory feedback is raised, making their /ɛ/ sound more like an /a/, subjects compensate by speaking with a lower F1; the vowels they produce sound more like /ı/. Similar experiments show that subjects will compensate for alterations in F0, F1, and F2 feedback, indicating that all three of these formants are important to a speaker’s representation of the target utterance… .
(I don’t know why the publication has /a/ as in “haha” where it should have /æ/ as in “had”. To a phonetician or phonologist it’s an obvious typographical error.)