A novel HTD-CS based PID controller tuning method for time delay continuous systems with multi-objective and multi-constraint optimization

[Display omitted] •The PID controller tuning with multi-objectives and multi-constraints is solved.•A novel HTD-CS swarm intelligent search algorithm is proposed.•HTD sequences are introduced to the basic CS algorithm to improve the search performance.•The proposed HTD-CS algorithm can be extended to nonlinear system identification. Currently, there exist many traditional PID (Proportional-Integral-Derivative) controller tuning methods for the unconstrained single-objective optimization problems. However, when dealing with multi-objective optimization problems, the traditional methods face many theoretical challenges. Furthermore, the situations may be even worse in the presence of multi-constraint requirements. In the view of above situations, by applying the heavy-tailed-distribution (HTD) sequences into the basic cuckoo search (CS) algorithm, we firstly propose a novel HTD-CS-based PID controller tuning method for the multi-objective and multi-constraint optimization problems. In this proposed swarm intelligent optimization algorithm, the introduction of HTD sequences represents a novel heavy-tailed search strategy in order to improve the search performance. Thus, in terms of achieving global optimization, the modified HTD-CS algorithm can provide more accurate PID parameter estimates. The simulation experiments verify that the proposed algorithm is quite efficient.