Abstract : In the correction control of printing presses, the focus is often on adjusting the parameters of the PID controller to improve the performance of the printing press. The characteristic of an active disturbance rejection controller (ADRC) is that it can still achieve relatively accurate disturbance compensation even when the model of the controlled object is unknown. This paper, starting from the physical structure of the printing press and the printing process, presents some of the derivation steps and complete ideas for the spindleless gravure printing press model. Then, simulations show that the model-based ADRC (even with a coarse model) outperforms both the ordinary PID controller and the conventional ADRC. Keywords : Spindleless gravure printing press; Printing press model; Application Analysis of Auto Disturbance Rejection Controller Based on Model for Control of Main-Shaft-Less Concave Printers , (1 School of Control Science & Engineering (Shandong University) Jinan 250061; 2 B&R (Shanghai) Industrial Automation Ltd cmp Shanghai 200235) Abstract : Tuning parameter of PID controller is the research direction in the correction control of printers in order to get better performance. Auto Disturbance Rejection Controller (ADRC) can approximately compensate the disturbance even the model is unknown. The paper gives partial demonstration and complete thoughts to deduce the printer model on the basis of physical structure of printers and printing arts. ADRC based on model (even the model is not exact) has better performance than ordinary PID controller and ordinary ADRC according to simulation. Keywords : Main-Shaft-Less Concave Printers; printer model; Auto Disturbance Rejection Controller 1 Introduction Currently, PID controllers are widely used in domestic printing presses. To achieve better printing results, research often focuses on adjusting the parameters of the PID controller. Active disturbance rejection controllers (ADRCs) inherit the characteristic of classic PID controllers that they do not depend on the object model, while overcoming the shortcomings of classic PID controllers, such as the contradiction between speed and overshoot, and the non-differentiable or even discontinuous nature of the reference input signal. This paper applies ADRCs to the correction control of printing presses for the first time. Through the examination of the physical structure of the printing press and the understanding of the printing process, a correction model for the printing press is obtained. The model-based ADRC is compared with ordinary PID controllers and ordinary ADRCs in simulation. The results show that the model-based ADRC has significant advantages, even if the parameters of the model differ from the actual object parameters [1][2][4]. 2. Model of a spindleless gravure printing press A spindle-based gravure printing press uses a single spindle to drive all color groups to ensure synchronization. When a deviation occurs, it is corrected by adjusting the position of the swing roller. However, this structure is prone to wear of the bearings connecting the spindle and each color group, leading to a decrease in printing accuracy. Moreover, it is difficult to maintain and the printing accuracy is not high. With the increasing requirements for the quality of printed materials, spindleless gravure printing machines have become the development direction. Each color group of this machine has its own drive, which is mostly driven by servo motors or frequency converters. Deviations are corrected by adjusting the drive speed or displacement. Its printing accuracy is high, but it is more complicated to control. In view of the development direction of gravure printing machines, this paper derives the model of spindleless gravure printing machine [3][7]. The following figure is a schematic diagram of the entire unit of spindleless gravure printing machine: [align=center] Figure 1 Schematic diagram of spindleless gravure printing machine[/align] Where MR is the rubber roller or pressure roller, ML is the guide roller between each color group, and MS is the printing roller, which is engraved with the printed pattern. One of the color groups is enlarged to analyze the relationship between them. [align=center] Figure 2 Printing Unit Diagram[/align] As mentioned above, MR and MS in Figure 2 are the rubber roller and the printing roller, respectively. T2 is the tension of the material between this color group and the previous color group, and T1 is the tension between the next color group. V is the velocity of the material. The linear velocity of MR is SPD1, and the linear velocity of MS is SPD2. For the force analysis of MR, Ts1-Tz1=J1 Formula (1) Where Ts1 is the dynamic torque of the rubber roller, which is the frictional force provided by the film to the rubber roller, Tz1 is the mechanical frictional force on the rubber roller, r1 is the radius of the rubber roller, and the rotational inertia J1 of the rubber roller is generally less than the inertia J2 of the printing roller, where J is equal to. The maximum value of Ts1 is the frictional force Tms1 when the rubber roller and the material slide relative to each other. For the printing roller MS, we have Tm-Ts2-Tz2=J2 Formula (2) Tm is the rotational torque provided by the motor, and the others are defined in the same way as the rubber roller. When the printing roller and the film slide relative to each other, the maximum value of Ts2, Tms2, is less than Tms1 (generally, the surface of the rubber roller is rougher than that of the printing roller, so the force causing relative sliding between the printing roller and the film is less than the force causing relative sliding between the film and the rubber roller). Therefore, as long as the film tension does not exceed Tms2 during operation, normal printing can be achieved without slippage. Now, as long as the film tension is less than Tms2 during operation, normal printing can be guaranteed. This Tms2 is the maximum allowable tension during correction; the tension required by the material during normal printing is less than this value. As shown in Figure 1, assuming two adjacent color groups 1 and 2, the speed of color group 1 is V1, and the speed of color group 2 is V2. According to the generalized Hooke's law, within the elastic deformation of a material, strain is proportional to tension. Thus, the tension generated between the two rollers due to speed can be derived. Assuming V1 and V2 have the same speed, the film lengths passing through the two rollers in the same time t are the same. If V2 > V1, the distances traveled by the two rollers in time t are V1 * t and V2 * t, respectively. When time t has elapsed, the length of material traveled by G1 is t, and the distance traveled by G2 in this time is t * V2. Therefore, let K * (V2 - V1), where E is the elastic modulus of the material, t is the length between the two rollers under the set tension, and t is the length of the material after the tension changes. This is the most basic formula for correction. During operation, as long as K * (V2 - V1) is less than Tms², printing can proceed normally without material breakage. Based on this formula and the control method used, such as using speed or displacement as the control quantity and negative deviation as the output, the differential equation model of the negative deviation of the printing press and the control quantity can be derived. In this way, the output negative deviation can correct the deviation that occurs. 3. Model-based Active Disturbance Rejection Controller The Active Disturbance Rejection Controller (ADRC) consists of a tracking differentiator TD, an extended state observer ESO, and a nonlinear combination NLSEF. TD tracks a given V and provides a smooth input V1, while also providing its differential signal. The principle of NLSEF is a nonlinear proportional element with large error and small gain, and small error and large gain. ESO is used to provide the output tracking signal and its differential signal. Another major function of ESO is to estimate the disturbance term to eliminate steady-state error [5][8]. Assuming that the model is obtained, the specific form of the model-based ADRC is: (1) TD equation (2) ESO equation (3) NLSEF equation. For the above equations, after adjusting the parameters, the system can have both speed and stability. For specific parameter adjustment methods and the definition of each parameter, please refer to other papers on active disturbance rejection controllers. 4. Simulation Comparison of PID, ADRC, and Model-Based ADRC This paper uses the same second-order object model and the same disturbance in the MATLAB SIMULINK environment to conduct simulation comparisons using PID controllers, ADRC, and a composite ADRC. Based on the characteristics of the printing press control system, the setpoint is a step signal with an amplitude of 1, and the disturbance is a square wave with an amplitude of 10. The simulation results show the superiority of ADRC, and the composite ADRC combined with the model performs even better. Moreover, the performance remains good even when the model parameters used in the ESO simulation differ somewhat from the actual object model. [align=center] Figure 3: Simulation Results of PID Controller[/align] [align=center] Figure 4: Simulation Results of ADRC[/align] [align=center] Figure 5 : Simulation Results of Model-Based ADRC[/align] 5. Conclusion This paper, for the first time, derives a printing press model through theoretical analysis and simulates a model-based ADRC, which possesses the advantages of ADRC and also offers speed. The simulation results show that the ADRC has good performance, but its performance in specific applications needs further verification. References [1] Zhao Ke et al. Research on automatic color matching control system for 8-color gravure printing of BOPP film. Packaging Engineering, 2005, 26(3): 50-52 [2] Han Jingqing. Nonlinear PID controller. Acta Automatica Sinica, 1994, 20(4): 487-490 [3] Sun Yuqiu. Automatic color matching control system for domestic gravure printing machine. Packaging Engineering, 2005, 26(5): 72-74 [4] Huang Yi, Zhang Wenge. Development of active disturbance rejection controller. Control Theory and Applications, 2002, 19(4): 485-492 [5] Han Jingqing. Active disturbance rejection controller and its application. Control and Decision, 1998, 13(1): 19-23 [6] Han Jingqing. From PID technology to active disturbance rejection control technology. Control Engineering, 2002, 9(3): 13-18 [7] Wu Qingqi, Zhang Senlin. Implementation of pre-registration in automatic color matching system of gravure printing machine. Packaging Engineering, 2003, 24(3): 38-40. [8] Zhang Rong, Han Jingqing. Parameter identification using model-compensated active disturbance rejection controller. Control Theory and Applications, 2000, 17(1): 79-81.