# A PID Parameter Tuning Method Based on the Improved QUATRE Algorithm
## 2 Related Work  
### PID Parameter Tuning Method  
The PID controller is a widely used control method [10], whose control performance depends on the parameter tuning of the PID controller, i.e., the combination and collocation of controller parameters. In 1942, [PERSON] and [PERSON] proposed the earliest PID parameter tuning method, namely the Z-N tuning method [11], by studying the PID parameter tuning of the first-order inertial pure lag link. Later, scholars all over the world continued to optimize and improve the Z-N tuning method and constantly proposed new tuning methods, such as the Cohn-Coon tuning method [12], relay feedback tuning method [13], internal mode PID parameter tuning method [14], RZN (refined Ziegler-Nichols) tuning method [15], etc. In the context of the continuous development of industrial control technology and the wide applications of power electronic devices, the actual industrial control object presents the characteristics of a high order, time delay, nonlinear, etc. ; whilst it is difficult to achieve optimal PID parameter tuning with the traditional PID parameter tuning method. For complex control objects, many scholars apply swarm intelligence algorithms to PID parameter tuning, which is applied in various fields. In Reference [16], the rules of the PID controller were derived by a method based on fuzzy logic; in Reference [17], a fuzzy PID controller was designed. In Reference [18], neural network theory was applied to parameter tuning and a parameter self-tuning method was proposed based on neural network PID. Simulation experiments have verified that this method can reduce the workload of parameter identification and realize online closed-loop tuning. In Reference [19], the authors introduced a genetic algorithm into PID parameter tuning and verified the feasibility of the tuning method in the simulation system. In Reference [20], a fuzzy PID controller based on a neural network was proposed, which has nonlinear control and self-learning mapping. In Reference [21], the authors used an immune information processing mechanism to optimize particle swarm optimization, solving the problem of algorithm prematurity, and applying it to the parameter self-tuning of the PID controller. In Reference [22], the neural network training algorithm was applied to PID parameter tuning and a PID neural network controller was designed. In Reference [23], the authors proposed a PID parameter tuning method based on the improved biogeography algorithm. From the simulation experiment, the classical test function was used to verify and compare with other swarm intelligence algorithms. What is satisfying is that the controller error and overshoot of the proposed method are smaller. In Reference [24], a nonlinear attenuation particle swarm optimization algorithm combined with an improved dynamic learning factor was proposed, and the algorithm was applied to the parameter tuning of the PID governor of hydro generator sets. In Reference [25], the authors proposed a multi-objective particle swarm optimization algorithm that only optimizes the overshoot and adjustment time of the system and realized the self-tuning of PID parameters. In Figure 1, the control system block diagram is a conventional PID controller used in engineering. The system is mainly composed of a PID controller, actuator, and controlled object. As a kind of linear controller, the linear control function of deviation is composed of proportional, integral, and differential by linear combination. The output of the control function is applied to the actuator by inputting the current deviation calculation, to complete the control of the controlled object. The specific change process is given in Equation (1). The specific formula:  
\[ \begin{array}{l}u(t)=K_{p}[e(t)+\frac{1}{T_{1}}\int_{0}^{t}e(t)d\tau+T_{D} \frac{d[e(t)]}{dt}]\\ =K_{p}e(t)+\frac{K_{p}}{T_{1}}\int_{0}^{t}e(t)d\tau+K_{P}T_{D}\frac{d[e(t)]}{dt} \\ =K_{p}e(t)+K_{I}\int_{0}^{t}e(t)d\tau+K_{D}\frac{d[e(t)]}{dt}\end{array}  \tag{1}\]  
Figure 1: PID control schematic diagram.