The PID control is considered one of the most common
control schemes and it has been applied to many industrial
processes and mechanical systems. Since the control plays a
very important role in the improvement of production quality,
accuracy and in reducing production costs, auto-tuning PIDs
including self-tuning scheme and adaptive control strategies
have been attracted a great deal of interest and several
kinds of auto-tuning PIDs including self-tuning scheme and
adaptive control strategies have been proposed. Recently, an
adaptive PID control strategies based on the almost strictly
positive real (ASPR) property of the controlled system have
been proposed [1], [2]. The adaptive PID control scheme
based on the ASPR property of the system is expected as a
prospective adaptive method for PID control, since it can
easily guarantee the asymptotic stability of the resulting
Adaptive PID control system, and the practicability and
robustness of these ASPR based adaptive PID methods have
been confirmed through several numerical simulations and
practical experiments.