A new bio-inspired fuzzy immune PI λDμ structure with optimal PSO parameters tuning

A new non-integer-order proportional-integral-derivative PI lambda.D-mu controller structure inspired from the immune feedback mechanism is proposed in this paper. The main contribution lies in raising the degree of freedom of the standard PI lambda.D-mu controller from five to eight degrees, thus providing three additional tools to meet the most demanding specifications in terms of control performances. Two of the three extra parameters are provided by a Mamdani fuzzy model, which describes the nonlinear behavior of the immune feedback mechanism, according to some bio-inspired fuzzy rules available in the literature. The rest of the parameters are optimally tuned by minimizing a constrained optimization problem, based on an integral time absolute error criterion, using the particle swarm optimization algorithm. The proposed controller is tested in a level control loop of an interacting three-tank system. The simulation results confirm its effectiveness in terms of timedomain performances, control signal efforts, disturbance rejection and robustness against parametric variations compared to the integer-order PID, the immune PID and the standard PI lambda.D-mu controllers.