  Proportional-integral-derivative (PID) control, the most common control
strategy in the industry, always suffers from health problems resulting from
external disturbances, improper tuning, etc. Therefore, there have been many
studies on control performance assessment (CPA) and optimal tuning. Minimum
output variance (MOV) is used as a benchmark for CPA of PID, but it is
difficult to be found due to the associated non-convex optimization problem.
For the optimal tuning, many different objective functions have been proposed,
but few consider the stochastic disturbance rejection. In this paper, a
multi-objective function simultaneously considering integral of absolute error
(IAE) and MOV is proposed to optimize PID for better disturbance rejection. The
non-convex problem and multi-objective problem are solved by
teaching-learning-based optimization (TLBO). This stochastic optimization
algorithm can guarantee a tighter lower bound for MOV due to the excellent
capability of local optima avoidance and needs less calculation time due to the
low complexity. Furthermore, CPA and the tuning method are extended to the PI/P
cascade case. The results of several numerical examples of CPA problems show
that TLBO can generate better MOV than existing methods within one second on
most examples. The simulation results of the tuning method applied to two
temperature control systems reveal that the weight of the multi-objective
function can compromise other performance criteria such as overshoot and
settling time to improve the disturbance rejection. It also indicates that the
tuning method can be utilized to multi-stage PID control strategy to resolve
the contradiction between disturbance rejection and other performance criteria.
