This paper describes a simple "high-level" controller called a "supervisor" which is capable of switching into feedback with a single-input/single-output (SISO) process a sequence of linear positioning or set-point controllers from a family of candidate controllers so as to cause the output of the process to approach and track a constant reference input, The process is assumed to be modeled by a SISO linear system whose transfer function is in the union of a number of subclasses, each subclass being small enough so that one of the candidate controllers would solve the positioning problem if the transfer function of the process were to be one of the subclasses’ members, Each subclass contains a "nominal process model transfer function" about which the subclass is centered, The supervisor’s unique feature, sharply distinguishing it from other logics which might be used for the same purpose, is that controller selection is made by i) continuously comparing in real time, suitably defined normed-squared output estimations errors or "performance signals" determined by the nominal process model transfer functions and ii) by placing in the feedback loop from time to time the candidate controller whose corresponding performance signal is the smallest, It is shown that in the absence of unmodeled process dynamics, the proposed supervisor can successfully perform its function (i.e., achieve a zero steady-state tracking error) even if process disturbances are present, provided they are bounded and constant, A sequel to this paper proves that without any further modification, the supervisor defined herein can also perform this function in the face of unmodeled process dynamics and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance or noise inputs, be they constant or not.