summary:
As the velocity and acceleration of the target being measured increase, higher demands are placed on the rapid acquisition capability of the photoelectric tracking servo system. Classical control methods cannot fully meet engineering requirements. This paper designs a proportional factor self-adjusting two-dimensional fuzzy controller to be incorporated into the photoelectric tracking servo system. Simulation results show that the dynamic performance of the servo system is significantly improved.
introduction:
In recent years, people have widely applied fuzzy control technology to various fields of production and life. It is favored by industry professionals because it does not rely on the precise mathematical model of the controlled object, has good adaptability, good system robustness, and is easy to achieve overshoot-free control [1]. In particular, the two-dimensional fuzzy controller has attracted much attention because of its relatively simple design and high control accuracy. Based on the classical control method, this paper adds a proportional factor self-adjusting two-dimensional fuzzy controller to form a servo control system model. The switching between the classical control method and the fuzzy controller is performed by writing the S function of the M file. The simulation results show that the dynamic performance of the photoelectric tracking servo system is greatly improved.
I. Mathematical Model of Photoelectric Tracking Servo System
The photoelectric tracking servo system is a dual-closed-loop, single-input, single-output position servo system, with an inner loop being the velocity loop and an outer loop being the position loop. This paper focuses on the control object of the photoelectric tracking system turntable, whose transfer function is:
The controllers for the speed loop and position loop are designed using the lead-lag compensation method. The main components of the closed-loop system can be found in reference [2], and will not be detailed here.
II. Fuzzy Controller Design
The Control System Toolbox is a collection of functions and tools within the MATLAB software package specifically designed for control system engineering. This toolbox provides a rich set of algorithms for designing, analyzing, and modeling general control systems.
SIMULINK is an interactive environment for modeling, analyzing, and simulating various dynamic systems. Through its rich set of function blocks, SIMULINK allows for the rapid creation of dynamic system models. The Fuzzy Logic Toolbox, utilizing fuzzy logic-based system design tools and a GUI, enables the entire process of designing fuzzy control inference systems. It allows for the modeling of complex system behaviors using simple fuzzy rules, which are then applied to the fuzzy inference system. S-functions are a powerful programming mechanism provided by SIMULINK, allowing users to implement their own algorithms.
1. Design and selection of input variables for fuzzy control
The fuzzy controller in the system is a dual-input single-output controller. The input variables are the deviation signal E and the rate of change of deviation EC. The output variable is the control variable U. The quantization universes of E, EC, and U are all (-6 6), and the fuzzy subsets are all {NB, NM, NS, ZO, PS, PM, PB}. Typing the FUZZY command in the MATLAB main interface command window will enter the FIS editor, the graphical user interface for the fuzzy controller, where membership functions for E, EC, and U are established. Here, the triangle (trimf) membership function is selected.
2. Establishment of fuzzy control rules
There are two methods for fuzzy control rules: empirical induction and inferential synthesis. This paper adopts the empirical induction method.
The establishment of fuzzy control rules follows these principles:
When the deviation is large in the positive direction and the change in deviation is also large in the positive direction, the output of the control quantity U should be large in the positive direction.
When the deviation is small or zero and the error change is small or zero, the output of the control quantity U should be small or zero.
When the deviation is small and the error change is small, the output of the control quantity U should be small and negative.
When the deviation is large in the negative direction and the change in deviation is large in the negative direction, the output of the control quantity U should be large in the negative direction.
Design fuzzy control rules in the FIS editor, as shown in Table 1:
Table 1. Fuzzy Control Rules for Photoelectric Tracking Servo SystemTable.1 Fuzzy control rule table of opto-electronic tracking servo system
III. Introduction to the Simulation Model of a Photoelectric Tracking Servo System with a Two-Dimensional Fuzzy Controller:
As shown in Figure 1, the photoelectric tracking servo system is a dual-loop follower system, consisting of a velocity loop and a position loop. In the position loop, the fuzzy controller and the conventional classical controller are designed to perform segmented control according to the magnitude of the system deviation.
Figure 1. SIMULINK simulation model of an optoelectronic tracking servo system with a two-dimensional fuzzy controller featuring a self-adjusting factor.
Fig.1 simulation model of SIMULINK of opto-electronic tracking servo system with self-tuning two-dimension fuzzy controller
Figure 2. SIMIULINK simulation model of Subsystem 1
Fig.2 simulation model of SIMULINK of Subsystem1
Subsystem 1 is shown in Figure 2. The deviations E and EC are the two inputs of the S-function, and the outputs of the S-function are the proportional factors Ke, Kec, and Ku, as well as the input jd of the position loop conventional controller.
The S-function ep11_he.m can be used to switch between two controllers, and the switching point is selected as 0.1. When the absolute value of the system deviation is greater than the switching point, the fuzzy controller works to reduce the system deviation rapidly; when it is less than the switching point, the output of the jd port of the Subsystem1 subsystem is e, and the conventional controller works to ensure the system control accuracy [3]. ep11_he.m configures the scaling factors Ke and Kec of the two inputs E and EC of the fuzzy controller. Since the values of scaling factors Ke and Kec have a great influence on the dynamic performance of the photoelectric tracking servo control system, if Ke is larger, the overshoot of the system is also larger, the transition process is longer, but the rise time is shorter; if Ke is larger, the overshoot of the system is smaller, but the response speed of the system is slower. At the same time, if the output scaling factor Ku of the fuzzy controller is too small, the dynamic process will be longer, and if it is too large, the system will oscillate [4]. Following this principle (verified through simulation experiments), in the S-function ep11_he.m, the two inputs E and EC are specifically linked to two input scaling factors Ke and Kec, respectively. This causes Ke and Kec to change with variations in E and EC. When the deviation is large, Ke takes a larger value, resulting in a shorter system rise time and a faster response; when the deviation is small, Ke should be a smaller value, reducing system overshoot. Similarly, the deviation variation can be linked to EC, maintaining a larger value during the rise time of the system response to reduce system overshoot; when EC is small, the value of Kec decreases rapidly, maintaining a fast system response. The principle for the value of Ku in ep11_he.m is to take a larger value during the rise of the system response to reduce the dynamic process time; when E and EC are relatively small, Ku takes a smaller value to avoid system oscillation.
IV. Results Analysis:
The step response curves of the conventional controller (Figure 3) and the photoelectric tracking servo system with a two-dimensional fuzzy controller (Figures 4 and 5) were obtained through simulation as follows:
Figure 3. Step response curve of a classic controller in an optoelectronic tracking servo system.
Fig.3 step response of classic control of opto-electronic tracking servo system
Figure 4 shows the step response curve of the photoelectric tracking servo system with a two-dimensional fuzzy controller.
Fig.4 step response of opto-electronic tracking servo system with two-dimension fuzzy control
Figure 5 shows the step response curve of the photoelectric tracking servo system with a two-dimensional fuzzy controller and self-adjusting factor.
Fig.5 step response of opto-electronic tracking servo system with self-tuning two-dimension fuzzy control
Comparing the step response curves of the photoelectric tracking servo system with a self-adjusting factor (Figure 5), the classical controller, and the general two-dimensional fuzzy controller (Figures 3 and 4), it can be concluded that the self-adjusting factor two-dimensional fuzzy controller has a smaller overshoot (0.6%) and a smaller settling time (0.04 seconds to ±5%) compared to the classical controller (which has a larger overshoot, higher than 15%, and a settling time of more than 0.4 seconds to ±5%) and the general two-dimensional fuzzy controller (which has an overshoot of 1.2%, and a settling time of approximately 0.3 seconds to ±5%). Simulation results show that the photoelectric tracking servo system with a self-adjusting factor two-dimensional fuzzy controller has better dynamic performance.
The author's innovative points:
This paper specifically employs the S-function to integrate the switching between two controllers in the photoelectric tracking servo system and the self-adjustment of the fuzzy controller scaling factor. Furthermore, it improves the dynamic performance of the photoelectric tracking servo system by simultaneously adjusting the three two-dimensional fuzzy controller factors, Ke, Kec, and Ku.
