PID controller structure is regarded as a standard in the control-engineering community and is supported by a vast range of automation hardware. Therefore, PID controllers are widely used in industrial practice. However, the problem of tuning the controller parameters has to be tackled by the control engineer and this is often not dealt with in an optimal way, resulting in poor control performance and even compromised safety. The paper proposes a framework, which involves using an interval model for describing the uncertain or variable dynamics of the process. The framework employs a particle swarm optimization algorithm for obtaining the best performing PID controller with regard to several possible criteria, but at the same time taking into account the complementary sensitivity function constraints, which ensure robustness within the bounds of the uncertain parameters’ intervals. Hence, the presented approach enables a simple, computationally tractable and efficient constrained optimization solution for tuning the parameters of the controller, while considering the eventual gain, pole, zero and time-delay uncertainties defined using an interval model of the controlled process. The results provide good control performance while assuring stability within the prescribed uncertainty constraints. Furthermore, the controller performance is adequate only if the relative system perturbations are considered, as proposed in the paper. The proposed approach has been tested on various examples. The results suggest that it is a useful framework for obtaining adequate controller parameters, which ensure robust stability and favorable control performance of the closed-loop, even when considerable process uncertainties are expected. 
Interval-model-based global optimization framework for robust stability and performance of PID controllers