This paper presents a new algorithm for automatic tuning of decentrali
zed PID control for two-input two-output (TITO) plants that fully exte
nds the single-loop relay auto-tuner to the multiloop case. The tuning
procedure consists of two stages. In the first, the desired critical
point, which consists of the critical gains of the two loops and a cri
tical frequency, is identified. Unlike SISO plants, there are infinite
ly many such points, and knowledge of the desired one is essential to
the tuning procedure. The auto-tuner identifies the desired critical p
oint with almost no a priori information on the process. During the id
entification phase, all controllers are replaced by relays, thus gener
ating limit cycles with the same period in both loops. It is shown tha
t each limit cycle corresponds to a single critical point of the proce
ss. By varying the relay parameters, different critical points can be
determined, The auto-tuner contains a procedure that converges rapidly
to the desired critical point while maintaining the amplitudes of the
process variables as well as of the manipulated variables within pres
pecified ranges. In the second stage, the data of the desired critical
point and possibly of other critical points is used to tune the PID c
ontroller by the Ziegler-Nichols rule or its modifications. This paper
focuses on the first stage. The steady-state process gains, which are
required for the appropriate choice of the desired critical point, ar
e determined by the auto-tuner in closed-loop fashion simultaneously w
ith the identification of the critical points. The identification of t
he process gains is achieved at no extra plant time. On the basis of a
large number of simulated cases, the proposed auto-tuner seems to be
efficient and robust. This paper discusses the underlying principles o
f the auto-tuner and its properties and capabilities demonstrated via
examples. The algorithm is not limited to TITO cases, and can be exten
ded to any number of loops.