Research on dual-mode switching fuzzy PID servo algorithm based on micro-linear motor

: Micro-linear motor, is the key feed components which is based on macro–micro-motion control technology, the accuracy of its movement directly determines the accuracy of ultra-precision machining level. Based on the study of the open servo characteristics of POWER program multiple axis controller (PMAC), a fuzzy proportional integral derivative (PID) composite control technology is applied to the servo control of the motor. The fuzzy control is used to improve the response speed and dynamic performance of the system, and the precise PID control is used to realise the precise position control. In this study, based on the analysis of linear motor installation and load characteristics, the use of smooth switching fuzzy PID composite control algorithm is applied to the micro-feed motor control. Due to the introduction of the smoothing weighting function, the composite fuzzy PID servo control mode of dual mode switching is implemented without disturbance switching. Finally, the effect of the control algorithm is verified by experiments, especially in the case of small errors, this algorithm still reflects the ability to adapt to the impact of interference.


Introduction
Micro-linear motor, is the key feed components which is based on macro-micro-motion control technology, the accuracy of its movement directly determines the accuracy of ultra-precision machining level. So the performance of servo system directly affects the positioning accuracy and trajectory tracking accuracy of the machine tools, and which ultimately affects the processing quality of the processing products. The adoption of good control strategy is an important technical means to improve the performance of the servo system. As the combination control of classic control with quantitative calculation control strategy and intelligent control with qualitative reasoning control becomes the focus of research [1-3], the research of fuzzy proportional integral derivative (PID) control and its application in AC-DC servo system are also increasingly improved. There are many types of fuzzy PID control strategies, such as fuzzy PID parameter selftuning control and fuzzy PID compound control [4][5][6][7]. The linear servo system adopts the direct drive mode, which makes the system have fast dynamic characteristics, simple structure, wide speed range and precise positioning. However, the influence of uncertainties, such as system parameter perturbation and load disturbance, caused by direct driving will be directly reflected in the static and dynamic characteristics of the precision feeding micro-linear motor system without any buffering in the middle. Therefore, the emergence of these uncertainties further increases the control difficulty that make the system non-linearity be more obvious, so it is difficult to establish an accurate mathematical model [8]. The mechanical simplification of the micro-linear motor servo feed system has led to the complexity of the control system. Therefore, traditional or modern control technology based on the mathematical model of the system is difficult to control the micro-linear servo system [9]. Therefore, it is necessary to adopt a more effective control technology than that of the rotary electric machine. With the development of the times, the requirements on the servo system are getting higher and higher. The intelligent control is introduced into the micro-linear servo system, and the system has higher performance index. It is an effective way to improve the performance of the linear servo system [10]. In the current linear motor control applications, although PID control is still the mainstream control strategy [11][12][13][14], the research, development and application of fuzzy technology have proved that the fuzzy PID compound control can make the linear motor control get better servo dynamic characteristics [15][16][17][18].
Fuzzy control is a control method based on fuzzy set theory, fuzzy linguistic variables and fuzzy logic reasoning, and it belongs to the category of intelligent control. It has the characteristics of knowledge expression and does not depend on the mathematical model of the object. Through the fuzzy logic and fuzzy reasoning, it makes experience become a control rule to do effective real-time control. PID is a traditional control technology. Due to its mature technology, good stability, high reliability and control precision, PID is still the most basic control form of AC servo motor [18]. There are many ways to tune PID parameters, but they are generally based on object characteristics. Fuzzy PID control technology will be advanced fuzzy control and classical PID control together, both advantages are complementary. Especially for the micro-linear motor drive and control, it is often influenced by external disturbances, load changes and magnetic field distortions during operation. The introduction of intelligent fuzzy control can change the output driving state of the motor in time to increase the stability of the reaction and the accuracy of positioning [19].
In this paper, fuzzy PID composite controller is used instead of the built-in PID controller for micro-linear motor servo control. The fuzzy control is used to improve the dynamic performance of the servo system, and the improved PID control algorithm is used to improve the servo accuracy and reduce the tracking error.
Micro-linear Motor Driver is the Copley series of drives for the TB3810 linear motor, equipped with analogue Hall element detection function to automatically perform commutation control of linear motors. Copley series driver has the function of current detection and linear current control with linear motor, so as to ensure the linear motor drive current is stable, so that the linear motor has good thrust output characteristics.
The design of the control algorithm is implemented by Turbo PMAC motion controller. For the servo motor, the control speed loop is closed on the drive. For linear motor control, the current loop is closed on the drive. So the design of the control algorithm in the motion controller must take into account the control that the drive already has to make the servo control overall good. In this paper, the controller designed is directly embedded in the Turbo PMAC to realise the servo control of the motor. It does not include the control algorithm that the driver already has.

Design and experiment of fuzzy PID dual-mode controller
Fuzzy controller is a kind of non-linear control. According to the file processing, using the query decision table method, the input amount needs to be rounded or rounding, there is quantisation error and static residuals, resulting in the control accuracy decreases. The traditional PID control can greatly improve the control accuracy and eliminate the steady-state error. The main idea of fuzzy PID composite control is to make full use of the control characteristics of the two, to improve the dynamic performance in the case of large error using fuzzy control and to use PID to realise precise control in the small error state.

Improved PID controller
PID is a deviation controller, the role of the premise is that the controlled amount must deviate from the set value. The controlled amount of the first need to deviate from the set value, to be controlled by the deviation, resulting in system lag. There are two reasons for the error in the closed-loop system using error control. One is that the system is subject to various disturbances and the other is the change in the structure and parameters of the system itself. Therefore, a compensation device is needed to exert a role on the control system to offset the influence of the disturbance on the system, and the so-called disturbance compensation. Servo motor control in computer numerical control (CNC) machine tools requires high servo tracking accuracy, and their input is known as a time-varying trajectory, requiring the system to respond to these inputs with zero steady-state error. In fact, the time-varying trajectory is a kind of disturbance constantly acting on the system. A simple PID controller cannot meet the requirements. Yusuf Altintas of Canada analysed the position servo of CNC machine tools [20], which shows that increasing the open loop gain of servo control can reduce the following error. However, the high open loop gain is affected by the mechanical inertia, motor torque and amplifier limitations. PID control with feedforward is a simple and effective method. It can be seen from the transfer function without feedforward that the feedforward control does not change the characteristic equation of the system, and feedforward compensation does not affect the stability of the original system. Therefore, in principle, this feedforward control is an ideal control method, which is much better than a closed-loop system based on error control alone. However, it is impossible to realise such idealised composite control completely. On the one hand, the linear range of the actual system is limited. On the other hand, the design of high-order differential devices is very difficult, and the higher the differential order is, the more sensitive the input noise is, but the worse the operating characteristics of the system. Usually feedforward device differential order of 2 can get satisfactory results.
In PID control, the feedforward of speed and acceleration are introduced to form first-order and second-order feedforward devices. The control structure in Fig. 3 is an improved PID controller with feedforward. The speed feedforward of the controller can obviously improve the servo tracking accuracy of the system. The degree of overlap between the membership functions of fuzzy sets directly affects the performance of the system. Based on experience, the distribution lists of membership values for each language value of E, EC, and U are determined. According to the input and output fuzzy subsets of fuzzifier, the fuzzy rules are established by using the conventional fuzzy conditions and the fuzzy relation 'IF A AND B THEN C' to form the fuzzy algorithm which describes the control process. The final fuzzy rules show in Table 1. Table 1 can be written in the sentence format as If E = Ai and EC = Bj then U = Cij (i, j = 1, 2, 3, 4, 5, 6, 7)

Specific design of fuzzy controller
Ai, Bj and Cij are fuzzy sets defined on E, EC and U, and the fuzzy relation can be expressed as R [21]: According to fuzzy reasoning synthesis rules can be obtained control U: (1) The membership function of U is

Dual-mode switching fuzzy PID composite control
As shown in Fig. 4, e v is the error threshold, and fuzzy control is used in the range of large deviation (|e|>e v ) to get good dynamic performance. In the small deviation (|e|< = e v ), PID control eliminate the system the steady-state error and improve the servo tracking accuracy. According to the above controller design of improving PID algorithm and fuzzy control algorithm, fuzzy PID composite controller control experiment is carried out on PRS-XY numerical control system. In the experiment, the servo cycle is fixed at 0.442 ms. The adjusted PID parameters and the main related parameters are shown in Table 2. The PID parameters are normalised according to the parameters of the Turbo PMAC and stored in the default variables for switching with the built-in PID algorithm.

Experiment
In the experiment, take the error threshold e v = 0.05 mm, and take No. 2 micro-linear motor and the servomotor with worktable X as the object. Servo period is 0.442 ms. In the step response test, the step distance is 1 mm (10,000 cts), and one-way time is 500 ms. The experimental results are shown in Figs. 5 and 6. In the following the error test, a parabolic trajectory as shown in Fig. 7 was used with a one-way travel of 1 mm and a one-way time of 500 ms. The testing software is PMAC Tuning Pro software of Delta Tau company [22]. Linear motor experimental results are shown in Fig. 8.
The main performance evaluation parameters of the microlinear motor obtained in the experiment are listed in Table 3.  The experimental results show that the switch-switched fuzzy PID control improves the dynamic characteristics of servo control. Especially for the control of the servo motor with the worktable, in addition to the motor commutation, its follow-up error is in the range of −1-2 μm, which basically maintain an ideal state. The experimental results meet the requirements of high precision servo tracking. For the micro-linear motor, although the dynamic performance is obviously improved, the follow-up error is still not ideal, and there is error fluctuation in the adjustment process.

Conclusion
In this paper, the fuzzy PID composite control technology is applied to the servo control of the motor. The fuzzy control is used to improve the response speed and dynamic performance of the system, and the improved PID control is used to realise precise position control. Adopting the dual-mode control made of improved PID and fuzzy PID improves the control switching process and further improves the servo tracking precision of the micro-linear motor.