This paper presents a new control methodology based on active disturbance rejection control (ADRC) for designing the tension decoupling controller of the unwinding system in a gravure printing machine. The dynamic coupling can be actively estimated and compensated in real time, which makes feedback control an ideal approach to designing the decoupling controller of the unwinding system. This feature is unique to ADRC. In this study, a nonlinear mathematical model is established according to the working principle of the unwinding system. A decoupling model is also constructed to determine the order and decoupling plant of the unwinding system. Based on the order and decoupling plant, an ADRC decoupling control methodology is designed to enhance the tension stability in the unwinding system. The effectiveness and capability of the proposed methodology are verified through simulation and experiments. The results show that the proposed strategy not only realises a decoupling control for the unwinding system but also has an effective antidisturbance capability and is robust.
Tension control stability is essential to the printing process of the gravure printing machines because the fluctuation and variation of tension have great influence on the precision of the printing register. The unwinding system is vital for generating web tension in the tension control system of the machine. In the process of unwinding, the diameter and rotational inertia of the unwinding roller are timevariant, which creates an indeterminate tension control system that is nonlinear and strongcoupling. Hence, accurate tension control is essential for ensuring adequate printing performance.
Presently, the control synthesis methodology based on the proportionalintegralderivative (PID) algorithm is still the most common control strategy for the tension control system of the gravure printing machines. However, with the development of highspeed and highprecision printing technologies, a control strategy based solely on PID is insufficient for satisfying control requirements. Many researchers have focused their efforts on improving the traditional PID strategy [
The objective of this research is to design a tension decoupling control methodology based on ADRC for the unwinding system in gravure printing machines. First, a nonlinear model is established based on the working principle of unwinding system. Next, a decoupling model is constructed in detail and an ADRC decoupling controller is designed to enhance the tension stability of the unwinding system. Last, to test the effectiveness of the ADRC controller, simulations and experiments with PID and ADRC controllers are carried out.
Figure
Experimental setup for the fourcolour gravure printing machine.
The schematic diagram of the unwinding system in the experimental setup is presented in Figure
Schematic diagram of the unwinding system.
The standard model of the relationship between tension and velocity has been presented in [
Equation (
Assuming that the web does not completely slide on the roll and that the web velocity is equal to roll linear velocity and by applying Newton’s law to the rotational movement, (
Because
In the actual production process of the gravure printing machine, the thickness of the web is very small compared with the radius of the rollers over which the web is wrapped. Because
As shown in Figure
Combining (
According to Newton’s laws of motion and eliminating the influence of the weight of the dancer roll, the dynamic equation of the dancer roll is expressed as
Combining (
The controlled variables
According to (
We define the dynamic coupling vector
Substituting (
Equation (
Combining (
Because the dynamic coupling vector
In this work, because
So
Therefore, the relationships between the virtual control quantities
Based on the order and decoupling plant of the unwinding system, an ADRC decoupling control methodology is designed to enhance tension stability, as shown in Figure
Structure of the ADRC decoupling control methodology.
The secondorder TD is a nonlinear component; given an input signal, we can acquire a corresponding tracking input signal and an approximately differentiated input signal, even for a nondifferentiable or noncontinuous input signal. As shown in Figure
The thirdorder ESO is the core of the ADRC, and it not only tracks system output variables and their differentiated signals but also actively estimates dynamic coupling and external disturbances in real time. As shown in Figure
The NLSEF is a nonlinear combination of the resulting differences of the state variables and estimations generated by the TD and ESO, respectively, as shown in Figure
Combining (
After calculating the virtual control variables
Two diagrams are provided in Figures
Structure of the PID control methodology.
To investigate the performance of the proposed ADRC decoupling control methodology, a comparison of the unwinding systems of PID and ADRC control strategies was performed through simulation and experiments. The parameters of the unwinding system used in the simulation and experiments are summarised in Table
Mechanical parameters of the unwinding system.
Parameters  Value  Units 


1  m 

0.35  m 

5 × 10^{−6}  m^{2} 

0.064  m 

0.128  m 

0.03  m 

0.03  m 

1.6 × 10^{8}  Pa 

1 × 10^{4}  N/m 
MATLAB simulation models were constructed to test the performance of the ADRC and PID control strategies. The simulation adopted a fixedstep size mode; the fixedstep size is 10 ms. According to [
Controller parameters in simulation.
Controller  Controller parameters 

ADRC1 

ADRC2 

PID1 

PID2 

To verify the robustness against dynamic changes of the developed ADRC control methodology, the
Step response curves for
Step response curves for
As shown in Figure
The simulation results show that once the ADRC controller is set up properly, it can handle a wide range of dynamic changes. Compared with the PID controller, Figures
To determine the decoupling performance of the proposed controller, the
Decoupling response curves for
Decoupling response curves for
Figure
The simulation results illustrate that the designed ADRC controller has better decoupling capability than the PID controller. Because the dynamic coupling components and the unknown coupled dynamics can be combined as the total disturbance estimated and compensated in real time, the decoupling control of the unwinding system in the ADRC controller can be realised, depending on the system order which can be easily obtained and the decoupling plant which may be inaccurate. However, the decoupling control cannot be realised, only depending on the imprecise of decoupling plant in the PID controller.
To demonstrate the external antidisturbance ability of the proposed controller, a step disturbance of
Antidisturbance curves for
Antidisturbance curves for
Figures
The simulation results indicate that the proposed ADRC control methodology has a better external antidisturbance ability than the PID controller because the ADRC algorithm is less sensitive to disturbance.
To establish practical application results of the ADRC control methodology, comparative experiments between the ADRC and PID control methodologies are performed in the experimental setup, as shown in Figure
Controller parameters in experiments.
Controller  Controller parameters 

ADRC1 

ADRC2 

PID1 

PID2 

To determine the practical robustness against dynamic changes of the ADRC controller, the
Step response curves for
Step response curves for
Figures
To establish the practical decoupling performance of the proposed controller, the
Decoupling response curves for
Tension with PID controller
Tension with ADRC controller
Tension with PID controller
Tension with ADRC controller
Decoupling response curves for
Tension with PID controller
Tension with ADRC controller
Tension with PID controller
Tension with ADRC controller
Figures
Because tension control at steady speeds is essential for the performance of the gravure machine, further attention should be paid to tension fluctuation at steady speeds. To investigate the steady performance of the ADRC controller, tension control experiments were performed at motor steady speeds of
Conditions  Controller type  

PID controller  ADRC controller  






0.3683  0.2949  0.2400  0.2163 

0.5540  0.4271  0.2686  0.2350 

0.9326  0.6572  0.4880  0.4064 

1.3349  0.8514  0.5831  0.4658 
Tension experimental curves for
Tension experimental curves for
Figures
Based on ADRC, an innovative control synthesis methodology is proposed for the design of a tension decoupling controller for the unwinding system of the gravure printing machine. First, according to the working principle of the unwinding system, a nonlinear mathematical model is established. Second, a decoupling model is constructed to obtain the order and decoupling plant of the unwinding system, which establishes a basis for the ADRC decoupling control methodology. Last, the results of the simulation and experiments demonstrate that the proposed control methodology can achieve not only good decoupling control performance but also better stability and robustness than the traditional PID controllers. From this study, it can be found that in the ADRC framework, all of the unknown coupling terms that may contribute to the total disturbance can be actively estimated and cancelled out in the corresponding control signal in real time; this greatly simplifies the design of the decoupling control methodology.
The main contributions of this paper are as follows. (1) We have addressed the design of a tension decoupling controller based on ADRC for the unwinding system of gravure printing machines. (2) Simulation and experiments of the proposed decoupling controller for the unwinding system were completed. (3) The study demonstrates that the proposed method is a promising solution for the problem of tension control in the unwinding systems of gravure printing machines because it is inherently robust against internal and external disturbances and decoupling control over the unwinding system of the gravure printing machine can be achieved in a simple manner.
Constant tension of the unwinding roll (N)
Web tension in the
External disturbances that influence
Tangential velocity of the
Rotational speed of the
Torque control signal of the
Nominal span length of the web in the
The
Radius of the
Inertia of the
Inertia of the dancer roll (
Constant of the
Reference inputs of
Reference inputs of
Young’s modulus of the spring (N/m)
Crosssectional area of the web (
Modulus of elasticity of the web material (Pa)
Viscous friction coefficient (Nm/(rad/s))
Viscous friction coefficient of the dancer roll (Nm/(rad/s))
Angle of the dancer roll arm from a neutral position (rad)
Servo motors driving the
The authors declare that they have no financial or personal relationships with other people or organizations that can inappropriately influence their work; there is no professional or other personal interest of any nature or kind in any product or company that could be construed as influencing the position presented in, or the review of, the paper.
This research is supported by the Program for Changjiang Scholars (IRT1172) and the National Science and Technology Pillar Program of China, under Grant no. 2012BAF13B06.