1 Introduction
With the continuous development of power electronics, microelectronics, and microprocessors, the speed regulation performance of asynchronous motor variable frequency speed control systems has been greatly improved. Compared with traditional DC motor speed control systems, it features simple structure, wide speed range, high efficiency, good characteristics, stable operation, and high safety and reliability, and has been widely used in production practice. Variable frequency speed control systems composed of frequency converters and asynchronous motors have a strong trend of replacing DC speed control systems.
Programmable Logic Controllers (PLCs) are widely recognized as one of the three pillars of modern industrial automation. Their control systems are stable and reliable, their communication networks are flexible, and they can be easily integrated into fieldbus control systems, meeting the demands of increasingly sophisticated automation. PLC-based variable frequency speed control systems have gained increasing attention due to their superior performance. However, for multi-variable, nonlinear, and strongly coupled asynchronous motors, conventional fixed-parameter PID control methods suffer from poor adaptability to load changes, weak anti-interference capabilities, and significant susceptibility to variations in system parameters. Therefore, how to further improve the control performance of variable frequency speed control systems based on existing hardware is a pressing issue that needs to be addressed.
Here, an active disturbance rejection controller method is used in the asynchronous motor variable frequency speed control system. The internal and external disturbances of the system are regarded as the total disturbance of the system. The extended state observer observes and compensates for them in a unified manner, so that the controlled object is approximately linearized and deterministic, thereby realizing the nonlinear control of the system. The effectiveness of the control scheme is verified by experiments.
2 Mathematical Model of Asynchronous Motor Variable Frequency Speed Control System
The state equations of an asynchronous motor variable frequency speed control system powered by a current-tracking SPWM inverter in the d, q two-phase rotating coordinate system can be described by a fifth-order nonlinear model. When the inverter time delay is ignored, the system model can be described by a reduced-order second-order nonlinear model.
In the formula: ω1 is the electrical synchronous angular velocity; ωr is the rotor speed; isd and isq are the stator currents of the d and q axes, respectively; ψrd and ψrq are the rotor flux linkages of the d and g axes, respectively; np is the number of pole pairs; Lm is the mutual inductance; Lr is the rotor inductance; J is the moment of inertia; Tr is the motor rotor time constant; TL is the load torque.
As can be seen from the literature, the inverter system is reversible in vector operation mode, and the entire system can be simplified into a single-input, single-output speed system.
3. Asynchronous motor variable frequency speed regulation self-disturbance control system
3.1 Design of a First-Order Active Disturbance Rejection Controller
Figure 1 shows the structure of the active disturbance rejection controller. This controller is a nonlinear controller based on a tracking differentiator (TD) to arrange the transient process, an extended state observer (ESO) to estimate the system state, model and disturbance, and nonlinear error feedback (NLSEF) to provide the control signal.
For vector-controlled asynchronous motor drive systems, a first-order model controller is used, correspondingly employing a second-order ESO structure. In vector control, the rotor flux linkage is generally kept constant. Utilizing the characteristics of ADRC, system model errors caused by changes in moment of inertia and the effects of load disturbances are attributed to the extended state z2 for unified observation and compensation. The principle block diagram of the speed controller based on first-order ADRC is shown in Figure 2.
3.2 Optimization of ADRC
In the first-order ADRC structure, the ESO outputs the observed values of the controlled object and the unknown disturbance. There is no differential term output for the controlled object, and the controller does not need to track the output of the differentiator. Therefore, the tracking differentiator stage is omitted in the ADRC structure. For a first-order object, using linear proportional control instead of NLSEF effectively simplifies the model and reduces the computational load while ensuring controller performance, thus obtaining a structurally optimized first-order ADRC model. Figure 3 shows the block diagram of the structurally optimized first-order ADRC speed control. The complete algorithm of the optimized speed controller is as follows:
In the formula: is the setpoint for motor speed; is the tracking signal for motor speed feedback ωr; is the observed value of the total disturbance W(t); u is the control quantity; β01 and β02 are the ADRC output error correction gains; h is the sampling period; kp is the proportional coefficient; b0 is the compensation factor, which adjusts the control performance of the system by tuning kp and b0.
4. Experiment and Results Analysis
4.1 System Hardware Connection
The entire system includes a host computer and monitoring software (WinCC), an S7-300 PLC, a MicroMasterVector (MMV) frequency converter, an asynchronous motor, and a photoelectric encoder, as shown in Figure 4.
4.2 System Software Design
4.2.1 System Communication Design
The system communication consists of three parts: ① PROFIBUS-DP fieldbus communication between the PLC and the frequency converter, enabling remote field control of the frequency converter by the PLC; ② MPI communication between the industrial computer and the PLC, which on the one hand realizes communication between STEP7 and the PLC, completing program upload, download, debugging, fault diagnosis and online monitoring, etc.; on the other hand, it realizes communication between WinCC and the PLC, completing the transmission of process data and real-time monitoring of system status; ③ OPC communication between WinCC and Excel, which uses software to archive motor speed process data and enable OPC communication service, exporting process data to Excel for system response curve fitting and analysis of various dynamic and static performance indicators.
4.2.2 System Control Software Design
The experiment used the Statement List (STL) in the industrial software STEP 7 V5.2. The entire system adopted structured programming, and the system program structure is shown in Figure 5.
4.3 ADRC parameter tuning
Studies have shown that β01 and β02 are mainly determined by the discrete control period of the controller, generally: β01 = 1/h, β02 = 1/(5h²). In the experiment, the sampling period for speed was taken as h = 100ms, so β01 = 10 and β02 = 20 were chosen. For the controller parameters kp and b0 that need to be tuned, a trial-and-error method from small to large was used in the experiment. Through on-site debugging and parameter modification, a relatively ideal set of controller parameters was determined when good dynamic and static effects were obtained, making parameter tuning relatively easy.
4.4 Comparative Study of Experimental Results
The frequency converter was set to vector control mode. The initial speed was set to 200 r/min. After 40 seconds, the speed was set to a period of 60 seconds. The closed-loop response of the system was obtained by a triangular wave with n varying from 200 to 500 r/min. As shown in Figure 6, the tracking performance under ADRC control mode is significantly better than that of conventional PID control.
Figure 7a shows the system response curves under two control conditions. As can be seen from the figure, the robustness and anti-interference performance of the system under ADRC control are superior to those under PID control. Figure 7b shows a magnified view of the first 40 seconds of Figure 6.
As shown in the figure, the dynamic and static performance of ADRC control is significantly better than that of conventional PID control.
5. Conclusion
To address the need for further improvement in the control performance of PLC variable frequency speed control systems, this paper briefly introduces the mathematical model of such systems and designs an asynchronous motor variable frequency speed control system based on an active disturbance rejection controller (ADRC). Compared with the traditional linear PID control method, the ADRC-based system demonstrates significantly improved performance. While maintaining a fast dynamic response, the ADRC was optimized, reducing controller parameters, decreasing computational complexity, and enhancing the controller's engineering practicality.
