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Proportional-integral-derivative (PID) control, the most common controlstrategy in the industry, always suffers from health problems resulting fromexternal disturbances, improper tuning, etc. Therefore, there have been manystudies on control performance assessment (CPA) and optimal tuning. Minimumoutput variance (MOV) is used as a benchmark for CPA of PID, but it isdifficult 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, amulti-objective function simultaneously considering integral of absolute error(IAE) and MOV is proposed to optimize PID for better disturbance rejection. Thenon-convex problem and multi-objective problem are solved byteaching-learning-based optimization (TLBO). This stochastic optimizationalgorithm can guarantee a tighter lower bound for MOV due to the excellentcapability of local optima avoidance and needs less calculation time due to thelow complexity. Furthermore, CPA and the tuning method are extended to the PI/Pcascade case. The results of several numerical examples of CPA problems showthat TLBO can generate better MOV than existing methods within one second onmost examples. The simulation results of the tuning method applied to twotemperature control systems reveal that the weight of the multi-objectivefunction can compromise other performance criteria such as overshoot andsettling time to improve the disturbance rejection. It also indicates that thetuning method can be utilized to multi-stage PID control strategy to resolvethe contradiction between disturbance rejection and other performance criteria.

Performance assessment and tuning of PID control using TLBO: the single-loop case and PI/P cascade case