  Current model-free adaptive control (MFAC) method has no been analysed in
linear system and is not straightforward for the practical engineers to
understand accurately. This correspondence presents a family of MFAC based on a
modified equivalent-dynamic-linearization model (EDLM), which facilitates to
show the working principle of method more directly and objectively. Compared to
the current work, i) the researches on MFAC focus on linear model, which is
easy to understand its working behaviour; ii) the full-form EDLM is extended
with unmeasured stochastic and measured disturbance, respectively. Then the
controllers is modified correspondingly; iii) the stability analysis of system
cannot be proved by current contraction mapping technique when the sign of
leading coefficient of control input changes, therefore we prove it by
analysing the function of the closed-loop poles. Several simulated examples are
used to show the principles of this kind of method.
