# Cuckoo Coupled Improved Grey Wolf Algorithm for PID Parameter Tuning
###### Abstract  
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. controlled system generally has the characteristics of nonlinearity, time variation, and time delay. When there are many performance objectives for the controlled object, coordinating each performance objective with the turning parameters is difficult, and the traditional and old parameter optimisation methods are no longer suitable for the requirements of current control systems. Therefore, intelligent optimisation algorithms have emerged as new parameter optimisation methods for a new generation of controllers. For example, the genetic algorithm, a commonly used optimisation algorithm, has been applied to the optimisation of PID control parameters. In [5], the hydraulic servo system uses a genetic algorithm to search for the optimal PID controller gain to achieve accurate control of the displacement of the valve-controlled hydraulic cylinder in the system. [PERSON] et al. [6] proposed an improved genetic algorithm and verified it using eight test functions. The results showed that the probability of convergence to the optimal value was improved, and it was verified on a beer-filling machine system. In addition, the particle swarm optimisation (PSO) algorithm, an old optimisation algorithm, was proposed by [PERSON] and [PERSON] in 1995 and is also widely used for parameter tuning in its algorithm application. [PERSON] et al. [7] used a multi-objective particle swarm optimisation algorithm to tune PID parameters and proposed an evaluation system in the virtual model that focused on the evaluation of the establishment time, overshoot, steady-state error, and control performance. Finally, it proves the superiority of the method in UAV experiments. Based on predecessors, [PERSON] et al.