Cuckoo Coupled Improved Grey Wolf Algorithm for PID Parameter Tuning

In today's automation control systems, the PID controller, as a core technology, is widely used to maintain the system output near the set value. However, in some complex control environments, such as the application of ball screw-driven rotating motors, traditional PID parameter adjustment methods may not meet the requirements of high precision, high performance, and fast response time of the system, making it difficult to ensure the stability and production efficiency of the mechanical system. Therefore, this paper proposes a cuckoo search optimisation coupled with an improved grey wolf optimisation (CSO_IGWO) algorithm to tune PID controller parameters, aiming at resolving the problems of the traditional grey wolf optimisation (GWO) algorithm, such as slow optimisation speed, weak exploitation ability, and ease of falling into a locally optimal solution. First, the tent chaotic mapping method is used to initialise the population instead of using random initialization to enrich the diversity of individuals in the population. Second, the value of the control parameter is adjusted by the nonlinear decline method to balance the exploration and development capacity of the population. Finally, inspired by the cuckoo search optimisation (CSO) algorithm, the Levy flight strategy is introduced to update the position equation so that grey wolf individuals are enabled to make a big jump to expand the search area and not easily fall into local optimisation. To verify the effectiveness of the algorithm, this study first verifies the superiority of the improved algorithm with eight benchmark test functions. Then, comparing this method with the other two improved grey wolf algorithms, it can be seen that this method increases the average and standard deviation by an order of magnitude and effectively improves the global optimal search ability and convergence speed. Finally, in the experimental section, three parameter tuning methods were compared from four aspects: overshoot, steady-state time, rise time, and steady-state error, using the ball screw motor as the control object. In terms of overall dynamic performance, the method proposed in this article is superior to the other three parameter tuning methods.