Register accuracy is an important index to evaluate the quality of electronic products printed by gravure printed electronic equipment. However, the complex relationships of multilayer register system make the problem of decoupling control difficult to be solved, which has limited the improvement of register accuracy for the gravure printed electronic equipment. Therefore, this paper presents an integrated decoupling control strategy based on feedforward control and active disturbance rejection control (ADRC) to solve the strong coupling, strong interference, and timedelay problems of multilayer register system. First of all, a coupling and nonlinear model is established according to the multilayer register working principle in gravure printing, and then a linear model of the register system is derived based on the perturbation method. Secondly, according to the linear model, a decoupling control strategy is designed based on feedforward control and ADRC for the multilayer register system. Finally, the results of computer simulation show that the proposed control methodology can realize a decoupling control and has good control performance for multilayer register system.
Rolltoroll (R2R) gravure printing machine is considered one of the highest throughput printed electronic equipment for manufacturing disposable and flexible electronic devices on flexible substrates at a low cost [
Register errors directly reflect the register accuracy, including two kinds [
Some new control methods have been applied to register control system in the recent years. A nonlinear control law is designed with the Lyapunov stability theorem such that the register errors converge to zero in [
The objective of this research is to design a decoupling control strategy based on feedforward control and ADRC for the multilayer register system of gravure printed electronic equipment. First, a nonlinear mathematical model of the fourlayer register system is constructed and a linear model of the nonlinear model is derived in detail based on perturbation method. Next, according to the linear model, a decoupling control strategy is designed based on feedforward control and ADRC for the multilayer register system. Last, to test the effectiveness of the proposed decoupling strategy, simulations and analysis compared with PID and proposed controllers are carried out.
The schematic diagram of a R2R gravure printed electronic equipment is shown in Figure
Schematic diagram of a gravure printed electronic equipment.
Figure
Schematic diagram of the gravure and fourlayer register system.
Gravure schematic
Schematic diagram of a fourlayer register system
The machine directional register error of a moving web is defined in two adjacent printing cylinders as the relative difference of the distance between the previous pattern printed by the upstream printing cylinder and the later printed one in the downstream printing cylinder. According to [
It is assumed that the nominal span lengths within adjacent printing units are typically same and there are no manufacturing errors in the register system. Thus, we can obtain (
Combining (
According to (
Equation (
Substituting (
Considering
With Laplace transform, the transfer functions of the fourlayer register system can be got:
According to (
As shown in (
According to (
Block diagram of the integrated decoupling control strategy.
Figure
As shown in Figure
According to Figure
The feedforward controller can be designed based on invariance principle for canceling out the register errors caused by the variations of
Hence, the feedforward controller (namely,
Because (
The TD is a nonlinear component in which a tracking signal and an approximately differential signal of the system input can be acquired according to the system input signal, even for a nondifferentiable or noncontinuous input signal. Figure
The ESO is the core of ADRC which can not only track the system output variables and their differentiated signals but also actively estimate unmodeled coupling dynamics and disturbances in real time. Figure
The NLSEF is a nonlinear combination of the resulting difference
Combining (
In actual printing process, the reference input of the register system is zero, scilicet
As shown in Figure
The comparative simulation of the fourlayer register system between proposed decoupling control strategy and PID and ADRC control strategies is performed to investigate the performance of the proposed decoupling control strategy. The structure of the decoupling control strategy for fourlayer register system is shown in Figure
Structure of the decoupling control strategy for fourlayer register system.
Structures of the PID and ADRC control strategies for fourlayer register system.
Structure of the PID control strategy
Structure of the ADRC control strategy
The simulation adopts a fixedstep size mode and the fixedstep size is 10 ms (namely, the sampling step
System parameters in simulation.
Parameters  Value  Units 


6.28  m 

0.2  m 

100  N 

2 × 10^{−5}  m^{2} 

2.1 × 10^{9}  Pa 
ESO parameter
The ESO parameter
The TD parameter
Under the closedloop condition, the NLSEF parameter
The adjusted parameters of the PID and ADRC controllers are listed in Table
Controller parameters in simulation.
Control strategy  Controller  Controller parameters 

PID  PID1 

PID2 


PID3 




ADRC  ADRC1 

ADRC2 


ADRC3 




Proposed decoupling control  ADRC1 

ADRC2 


ADRC3 

Performance against tension interference for
Register error
Register error
Register error
Performance against tension interference for
Register error
Register error
Register error
Response curves of the proposed decoupling control strategy.
Register error
Register error
Register error
Figures
The simulation results indicate that the feedforward and ADRC controllers can effectively compensate the register errors caused by the variations of
A sinusoidal interference of
Performance against speed interference for
Register error
Register error
Register error
Performance against speed interference for
Register error
Register error
Register error
Response curves of the ADRC control strategy.
Register error
Register error
Register error
Response curves of the proposed decoupling control strategy.
Register error
Register error
Register error
Figures
The simulation results show that because the feedforward and ADRC controllers can obviously alleviate the register errors caused by the interference of
The elastic modulus of the web material decreases to 80% in order to establish the performance against characteristic change of web for the proposed decoupling control strategy. With the step change of
Response curves of the PID control strategy.
Register error
Register error
Register error
Response curves of the ADRC control strategy.
Register error
Register error
Register error
Response curves of the proposed decoupling control strategy.
Register error
Register error
Register error
Figures
The simulation results illustrate that because the ADRC controllers can actively estimate and compensate the register errors caused by characteristic change of web, the ADRC and proposed control strategies have better capability against web characteristic changes than the PID control strategy.
In gravure printed electronic equipment, register accuracy is the most important index for the quality of multilayer register system. Therefore, in order to improve the register accuracy of multilayer register system, this paper proposes an innovative decoupling control synthesis strategy based on feedforward control and ADRC for the design of a register decoupling controller for the multilayer register system. The strategy is unique in which it uses feedforward controllers to compensate the register errors caused by the modeled interferences and uses ADRC controllers to adjust the inputs of the register system and actively estimate and compensate the register errors caused by the unmodeled disturbances in real time, which makes the accuracy of the register controller greatly improve.
The simulation results illustrate that the proposed decoupling control strategy not only can effectively compensate the register errors caused by the variations of
Register error between
Steadystate value of the
Variable value of the
Reference inputs of the
Image function of the
Angular velocity of the printing cylinder
Steadystate value of the
Variable value of the
Image function of the
Radius of the printing cylinder
Web tension of the infeeding unit (N)
Web tension in the
Steadystate value of the
Variable value of the
Image function of the
Nominal span length of the web in the
Transmission time of the web from
Modulus of elasticity of the web material (Pa)
Crosssectional area of the web (m^{2}).
The authors declare that there is no conflict of interests regarding the publication of this paper.
This project is supported by the National Natural Science Foundation of China (Grant nos. 51505376 and 51305341) and by the Natural Science Basic Research Plan in Shaanxi Province of China (Grant no. 2016JQ5038).