Abstract: This paper describes a model reference adaptive control method based on the CNC machine tool cutting process. The machine tool cutting process model under three conditions—closed-loop, open-loop, and model reference adaptive control—was simulated using MATLAB/SIMULINK. Simulation results show that the model reference adaptive control method is more effective than the other two methods in timely adjusting cutting parameters according to changing machine tool cutting conditions, thus maintaining good cutting performance during machining.
Machining on a system consisting of machine tools, cutting tools, and workpieces is a dynamic process. Many factors and parameters (such as uneven workpiece blank allowance, varying material hardness, tool wear, built-up edge, stress deformation, cutting vibration, and thermal deformation) can prevent the cutting process from operating optimally, thus affecting production efficiency, machining quality, and economic benefits, and even hindering the normal operation of the cutting process. To address this issue, an adaptive control method for machine tools was proposed in the 1960s. This method, applied during machining, allows for timely adjustments to cutting parameters based on constantly changing actual cutting conditions.
Based on the Model Reference Adaptive Control (MRAC) concept, an MRAC model of the CNC machine tool cutting process was established, and then the dynamic process of the model was simulated. Simultaneously, feedback closed-loop control and open-loop control of the machining process were simulated separately, and the results of these three simulations were compared. The simulation results show that MRAC achieves the best machine tool cutting performance.
1. Working principle of MRAC in CNC machine tools
MRAC (Modular Recognition Control) of a CNC machine tool uses the cutting process completed by the machine tool, cutting tool, and workpiece system as the regulating object. The principle structure of this control system is shown in Figure 1. In addition to the position and speed control loops of a typical CNC machine tool, it also adds an MRAC feedback loop. When the system is disturbed by various random factors, the state parameters of the cutting process change immediately. The values of these parameters are detected by sensors at any time and converted. In the MRAC control unit, they are judged and compared with the given evaluation index or constraint conditions (i.e., the desired performance index), and the deviation of the performance index is obtained. Then, a correction signal is output to the host CNC to correct the input parameters of the system, thereby transforming the cutting process towards the predetermined index and conditions to achieve the optimal state.
Figure 1. Structure of MRAC system for CNC machine tool
2. Establishment of MRAC Model for Machine Tool Cutting Processing
The MRAC model of the machine tool cutting process is shown in Figure 2. It consists of a servo mechanism, a cutting process, a reference model adjustment mechanism, a feedforward device, and a feedback device.
Figure 2. MRAC model block diagram of the cutting process
The servo link can be represented by a two-section system:
(1)
In the formula: s is the Laplace transform operator; u is the servo input (V); Kn is the servo gain (mm/(V·s)); ωn is the natural frequency of the servo system (rad/s); v is the feed rate (mm/s); ξ is the damping coefficient; f is the feed amount (mm/r), which can be expressed as:
(2)
In the formula: n is the spindle speed (r/min); p is the number of teeth of the tool during milling, and p=1 during turning.
Considering that the reference model adjustment mechanism is taken as an ideal performance indicator, this component remains the same as the servo mechanism component, i.e.
The static cutting force Fs during the machining process can be expressed as:
(3)
In the formula: Ks is the cutting specific force (N/mm2), m is the exponent (generally m<1), Ks and m both depend on the workpiece material and the tool shape; a is the depth of cut (mm).
Depending on the characteristics of different processing steps, the dynamic process of Fs can also be represented by equation (3). Assuming m=1, its dynamic process can be represented by a first-order system:
(4)
In the formula: τ is the time constant.
Both the feedforward and feedback devices in the model are proportional elements with a proportionality coefficient of K.
Therefore, based on the composition of each system component above, the mathematical control model of the cutting process MRAC, as shown in Figure 3, can be obtained.
Figure 3. MRAC mathematical model of the cutting process
Figure 4 MRAC simulation diagram
3. Machining performance of MRAC during machine tool processing
In machine tool processing, the quality of cutting performance not only greatly affects the quality of parts but also easily damages cutting tools. The cutting process of the machine tool, cutting tool, and workpiece system is unstable, frequently affected by many uncertain external factors, causing the state parameters during cutting to change constantly. If not adjusted in time, cutting performance will significantly deteriorate. MRAC (Mechanical Ratio Adjustment Control) can stabilize the cutting performance parameters. Taking the example of a constant cutting force during machine tool processing, we illustrate how MRAC can adjust the cutting force in a timely manner to maintain the desired cutting force when disturbed by external factors (such as changes in depth of cut). Based on experiments, the machining model parameters are known as Ks = 1500 N/mm², n = 600 r/min, Kn = 0.95 mm/(V·s), ξ = 0.68, p = 1, m = 1, ωn = 22 rad/s, the depth of cut varies sinusoidally from 1 to 3 mm, and the desired cutting force is set to 1000 N. Substituting the above parameters into the mathematical control model in Figure 3, the simulation diagram shown in Figure 4 can be obtained using MATLAB/SIMULINK tools, and the simulation results are shown in Figure 5.
Figure 5 Simulation results
As can be seen from the simulation results in Figure 5, the change in depth of cut is exactly the opposite of the change in feed rate. That is, if the depth of cut increases, the feed rate decreases to keep the cutting force constant at 1000N, and vice versa. Therefore, the MRAC system achieves constant force control in the machining process by automatically and accurately adjusting the feed rate.
4. Comparison of cutting performance between MRAC and traditional closed-loop and open-loop control
4.1 Simulation of Cutting Performance of Traditional Closed-Loop and Open-Loop Control Systems
Referring to MRAC simulation diagram 4, closed-loop and open-loop simulation diagrams can be established respectively (the open-loop simulation diagram has no feedback, and other aspects are the same as the closed-loop simulation, which can be referred to in the closed-loop diagram, which has been omitted in this article), as shown in Figure 6. The simulation results are shown in Figures 7 and 8. It can be seen from the simulation results that the cutting force of the closed-loop control can basically keep it constant at around 1000N, while the cutting force of the open-loop control deviates far from 1000N.
Figure 6. Closed-loop control simulation diagram
Figure 7. Simulation results of closed-loop control
Figure 8. Simulation results of open-loop control
4.2 Analysis of Cutting Performance Errors Among the Three Control Systems
From the simulation results of the three control methods above, we can roughly analyze their machining performance errors. First, the error of the MRAC system can be roughly calculated:
The error of the closed-loop control system can be obtained as follows:
The error of the open-loop control system can be obtained as follows:
In the formula: E(X) and E(S) represent the upper and lower deviations of the error, respectively.
By comparison, it can be found that the MRAC system has the smallest error. Therefore, MRAC is better able to maintain good cutting performance of lathes during machining than traditional closed-loop and open-loop systems.
5. Conclusion
Simulations and experiments using MATLAB/SIMULINK demonstrate that MRAC can maintain stable cutting performance on CNC machine tools, thus allowing its application to other automated equipment. It's important to note that conventional MRAC is only suitable for minimum-phase systems, while the machining process, under certain sampling conditions, may be a non-minimum-phase system with unstable inverse zero points. In such cases, a modified MRAC scheme is required.
