Abstract : This paper employs a positional PID controller and applies it to the control of an AC servo system, designing a high-precision servo control system with superior control performance. Simulation results show that the system using this positional PID control overcomes the shortcomings of traditional ID controllers. By adjusting the PID control parameters, the system exhibits fast response, small overshoot, high stability accuracy, good robustness, and significant control effect.
Keywords : AC servo; positional PID; PID
In the early 1980s, a new era of AC servo control systems using AC servo motors as actuators began. Among these, induction AC servo motor drive systems, permanent magnet AC servo motor drive systems, and reluctance AC motor drive systems emerged first. In the early 1990s, various linear servo motors and their drive systems with direct drive capabilities appeared, marking the beginning of AC linear servo control systems replacing AC rotary servo control systems. Among these, permanent magnet AC servo motor drive systems saw the fastest development.
With the continuous development of computer technology, electronic technology and motor magnetic materials, AC servo control has gradually become the mainstream of motion control in the field of factory automation [2]. With the development of modern AC speed regulation technology, various new control algorithms have emerged, such as adaptive control, expert system, intelligent control, etc. [3]. From a theoretical point of view, many control strategies can achieve good dynamic and static characteristics of motors, but due to the complexity of the algorithm itself and the troublesome model identification of the system, it is difficult to implement in actual systems. For traditional PID controllers, the biggest advantage of position PID is that the algorithm is simple, the parameters are easy to tune, and it has strong robustness, strong adaptability, and high reliability. These characteristics have led to the widespread application of position PID controllers in the field of industrial control.
The application of conventional PID controllers cannot achieve the ideal control effect. Moreover, in actual production sites, due to the complicated parameter tuning methods, conventional PID controllers often have poor parameter tuning and poor performance, and are not very adaptable to the operating conditions. In addition, with the development of control theory, various branches have emerged, such as expert systems, fuzzy logic, neural networks, and grey system theory. These, combined with the traditional PID control strategy, have given rise to various new types of PID controllers.[4] Many algorithms have greatly improved the performance of traditional PID controllers.
1. Structure of AC Servo Control System
Position control systems typically employ a semi-closed-loop control structure, where the angular displacement of the servo motor shaft serves as the system's position feedback. This design offers advantages such as simple structure and low cost. The system mainly comprises three parts, as shown in Figure 1, which illustrates the structure of a semi-closed-loop AC servo position control system.
Figure 1. Structure of a semi-closed-loop AC servo position control system
(1) AC servo driver and servo motor. The input of the speed loop of the AC servo driver is the position error signal of the position board, and the motor speed is controlled according to the PI control law. The photoelectric encoder installed on the motor feeds back the angular displacement of the motor shaft to the position board in the form of pulses.
(2) Control Board. The computer generates interrupts at fixed time intervals (usually a few milliseconds). When accessing the position control interface board, it writes the position increment of the next cycle into the pulse buffer of the corresponding axis. The given position increment of the position loop is input in the form of serial pulses. The PID controller only converts the serial pulses into parallel ones, and its value is independent of the time factor, that is, it does not act as an integrator. The position control board mainly performs various transformations of the position feedback pulse signal, position deviation calculation and accumulation, D/A output, and timer interrupt and accumulated error overflow interrupt management.
(3) Transmission mechanism and worktable. This part serves as the load of the motor and has a significant impact on the structural parameters of the control system, in which nonlinear factors of the system are distributed.
2. Position PID Algorithm
Since computers entered the field of control, digital computers have replaced analog computer regulators to form computer control systems. This not only allows for the implementation of PID control algorithms in software, but also makes PID control more flexible due to the logical capabilities of computers. Therefore, it has found widespread application in industries such as electromechanical engineering and metallurgy. The control quantity is formed by a linear combination of the proportional (P), integral (I), and derivative (D) values of the deviation, thereby controlling the controlled object.
PID controllers were originally developed as compensators for process control. Due to their simplicity and ease of use, they are now widely used not only in process control but also in servo control systems [5]. However, with the widespread use of microprocessors, complex and high-precision control can also be achieved through software, and fully software-based servo control has been implemented in some high-performance machines. The method to be mentioned in this paper is also implemented through software technology [6].
In computer control systems, digital PID controllers are used. Digital PID control algorithms are usually divided into positional PID control algorithms and incremental PID control algorithms [7].
Computer control systems are a type of sampling control, which calculates the control quantity based on the deviation at the sampling time. Therefore, a discretization method is required. In computer PID control, a digital PID controller is used. According to the analog PID control algorithm, a series of sampling time points kT represent the continuous time t, the rectangular method numerical integration approximates the integral, and the first-order backward difference approximates the derivative, i.e. [8]
During the discretization process, the sampling period T must be short enough to ensure sufficient accuracy.
Simplifying error(kT) to error(k), i.e., omitting T, yields the discrete expression.
In the above formula, T is the sampling period, k is the sampling number, k=1,2,…error(k-1) and error(k) are the deviation signals at time (k-1) and time k, respectively.
Properties of the Z-transform
The Z-transform is:
Therefore, the z-transfer function of the positional PID controller can be obtained as follows:
Since the computer output u(k) directly controls the actuator, the value of u(k) and the position of the actuator are in one-to-one correspondence, so it is usually called a positional PID control algorithm. Figure 2 shows a schematic diagram of a positional PID control system.
Figure 2 Position PID control system
Position control has improved algorithms and has the following advantages:
(1) Because the computer output is incremental, the impact of malfunctions is smaller.
(2) The switching process is minimal, facilitating seamless switching. Furthermore, when a computer malfunctions, the output channel or actuator has a signal latching function, thus preserving the original value.
(3) No accumulation is required in the formula. The determination of the control increment △u(k) is only related to the most recent k sample values, so it is relatively easy to obtain a better control effect through weighted processing[9].
3. Experimental Simulation
Suppose the controlled object is a delayed object:
The sampling time is 20s and the delay time is 4 sampling times, i.e. 80s. The controlled object is discretized as y(k)=-den(2)y(k-1)+num(2)u(k-5). The step response of the integral separation PID controller is performed. The piecewise integral separation is adopted, i.e., different integral intensities are adopted according to the different absolute values of the error. In the simulation, the command signal is r(k)=40, and the controller output is limited to [-100, 100]. The positional PID controller is adopted, and its step response is shown in Figure 3 [10].
Figure 3. Step response of the positional PID controller
4. Conclusion
This paper employs position-based PID control in an AC servo position control system, which offers advantages such as fast response and small tracking error. Simulation results demonstrate that, for AC servo position control systems, using a position-based PID controller, with appropriate parameter tuning, can improve the static and dynamic performance and robustness of the control system, achieving high-precision position control requirements in many applications.
