# Dynamic High-Type Interval Type-2 Fuzzy Logic Control for Photoelectric Tracking System
## 3 DHT-IT2 FLC Design
### MPGA Design
#### 3.3.2 MPGA Design Process  
Determine the Optimized Parameters  
There are many ways to optimize FLC with GA, which can optimize parameters, such as rule base, membership function, scale factor, and so on. Through experimental comparison, it is found that the optimization rule base or membership function has a large amount of calculation, complex parameter settings, and low efficiency; the optimization scale factor is simple, the calculation speed is fast, and it is convenient to modify. Therefore, this project keeps the rule base and membership function unchanged and uses the three scaling factors Ke, Kec, and Ku (Figure 5) as the parameters to optimize the chromosome coding.  
The larger the Ke value, the faster the step response, but at the same time, the overshoot and adjustment time will increase, and even the system will not work steadily. Contrary to the Ke effect, the smaller the Kec, the larger the overshoot and adjustment time. Ku corresponds to the total magnification of the system. Generally, Ku increases and the rise speed is faster, but when Ku is too large, it will produce a larger overshoot which affects the steady-state operation.  
Therefore, using MPGA to optimize three parameters at the same time can give full play to the advantages of global search and find the optimal solution of the three parameters.  
Determine the Fitness Function  
The GA does not use external information in the optimization search. It only uses the fitness function as the basis and uses the fitness value of each individual in the population to search. In the control system, our commonly used objective function is the integral error criterion (ITAE):  
\[J(ITAE)=\int_{0}^{\infty}t\cdot|e(t)|dt, \tag{24}\]  
where \(t\) is the running time of the system, and \(1\,e(t)\,|\) is the absolute value of the system error. The smaller the _ITAE_ value, the better the performance. It can comprehensively evaluate the control system's response time, overshoot, and other dynamic and static performance. Since the genetic operation is carried out according to the size of the fitness value, and the optimization direction of the objective function should correspond to the direction in which  
Figure 9: The MPGA structure.  
the fitness value increases, the performance index function is appropriately transformed to obtain the fitness function:  
\[f=\frac{1}{1+J(ITAE)} \tag{25}\]  
Determine the Operating Parameters of the Genetic Algorithm  
Operating parameters include population size M, population number N, optimal individual minimum retention algebra MAXGEN, elite population ratio ELITE, mutation probability Pm, crossover probability Pc, etc. Among them, the population size, number, and the minimum number of optimal individuals have the greatest impact on the results and calculation time. If it is too small, the optimization result is not ideal, and if it is too large, the iteration will take more time. The mutation probability and the crossover probability determine the system's global and local search capabilities. When they are larger, the recombined individuals will have a high probability of appearing and converge quickly; but at the same time, the replacement of the old and the new is too fast, making some superior individuals may be eliminated prematurely [38; 39; 40].  
In this project, the MPGA parameters are set as M = 20, N = 10, MAXGEN = 10, ELITE = 20%, Pm is a random number between 0.7-0.9, Pc is a random number between 0.001-0.05, and different populations take different probabilities to prevent precocity.