Journal of Automation, Mobile Robotics & Intelligent Systems
VOLUME 6,
N° 2
2012
Decentralized PI Controller for Multimotors Web Winding System Submitted 27th October 2011; accepted 24th November 2011
Bousmaha Bouchiba, Abdeldjebar Hazzab, Hachemi Glaoui, Fellah Med-Karim, Ismaïl Khalil Bousserhane, Pierre Sicard
Abstract: Web winding systems allow the operations of unwinding and rewinding of various products including plastic films, sheets of paper, sheets, and fabrics. These operations are necessary for the development and the treatment of these products. Web winding systems generally consist of the same machine elements in spite of the diversity of the transported products. Due to the wide rang variation of the radius and inertia of the rollers the system dynamic change considerably during the winding/ unwinding process. Decentralized PI controller for web tension control and linear speed control are presented in this paper. The PI control method can be applied easily and is widely known, it has an important place in control applications. Simulation results show the effectiveness of the proposed linear speed and tension controller for web winding multi motors systems. Keywords: multi motors web winding system, PI controller, tension control, linear speed control
1. Introduction
Many types of materials are manufactured or processed in the form of a sheet or a web (textile, paper, metal, etc.) which then couples the processing rolls and the associated motor drives. The drives are required to work in synchronization to ensure quality processing and rewinding of the product. Tension is a very important web manufacturing and process setting. If severe tension variations occur, rupture of the material during processing or degradation of product quality can occur, resulting into significant economic losses due to material loss and reduced production rate. Therefore, in order to minimize a potential loss, the need arises to adequately control the tension within a predefined range in a mo-ving web processing section. Henceforth, due to their importance in industry, tension control problems have drawn the attention of many researchers. One problem is the establishment of a proper mathematical model. In [1], a mathematical model of a web span is developed, but this model does not predict the tension transfer. This problem was addressed in [2] and [3], with the assumption that the strain in the web is very small. However, the form of the nonlinear and coupling terms in the model are not always convenient for controller design so that other model structures, with comparable precision, are desirable. Several control strategies have been suggested to maintain quality and reduce sensitivity to external disturbances, including centralized multivariable control schemes for steel mill applications 32
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[4], [5] and an H∞ control strategy to decouple web velocity and tension [3], [6]. Also, for tension regulation in a web transport system, [7] proposed a control method based on a unique active disturbance rejection control (ADRC) strategy, which actively compensates for dynamic changes in the system and unpredictable external disturbances. In [8] and [9], Port-Controlled Hamiltonian with Dissipation (PCHD) modeling is considered to develop stabilization strategies with a physical interpretation and motivation of the control action, interpreted as the realization of virtual dampers added to the system, which resulted into a type of dual action controller with velocity feedback and velocity error feedback terms. Some limited improvements were obtained in disturbance rejection properties and robustness with respect to some parameter variations. The conventional PI control dominates industry, it is simple and easy to implement [15]. Tuning of PI controllers is intuitive and is well accepted by practitioners. PIs can at most achieve a compromise in performance in terms of system response speed and stability, and this approach becomes insufficient at the increasingly high web velocities demanded by the industry and with thin or fragile materials. Nonlinearities that appear at high velocities, disturbance rejection properties and robustness to some parameter variations must be accounted for by the controller. A decentralized nonlinear PI controller is proposed to respond to this demand. The model of the winding system and in particular the model of the mechanical coupling are developed and presented in Section 2. Section 3 shows the controllers design for winding system. Section 4 shows the Simulation results using Matlab Simulink. Finally, the conclusion is drawn in Section 5.
2. System model
In this system, the motor M1 carries out unreeling and M3 is used to carry out winding, the motor M2 drives two rollers via gears “to grip” the band (Fig. 1). The stage of pinching off can make it possible to isolate two zones and to create a buffer zone [8, 9]. The objective of these systems is to maintain the linear speed constant and to control the tension in the band. The used motors are three phase induction motors type which each one is supplied by an inverter voltage controlled with Pulse Modulation Width (PWM) techniques. A model based on circuit equivalent equations is generally sufficient in order to make control synthesis. The electrical dynamic model of three-phase Yconnected induction motor can be expressed in the d-q synchronously rotating frame as [13]:
Journal of Automation, Mobile Robotics & Intelligent Systems
VOLUME 6,
N° 2
2012
Articles
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IFOC
IFOC Linear speed IFOC Controller
IFOC Linear speed IFOC Controller
IFOC
V2 V2
IFOC Linear speed IFOC Controller
Linear speed Linear speed 4. Si V2 Controller T Controller 3 Linear speed Linear speed Tension V2-ref Controller Controller 4. Si Controller
Linear speed Controller Linear speedT2 Tension Controller Controller Tension T2 Controller T2 Tension T2-ref Controller
V 4.2-ref Si V2-ref
T3
T3
Tension Controller Tension T3-ref Controller
4. Decentralized control web winding system Fig.Fig. 4. Decentralized control forfor web winding system T2-ref T3-ref T3-ref system 2-ref Fig.T4. Decentralized control for web winding Where the parameters of the PI controller are Fig. 4. Decentralized control for web winding system
V
Fig. 7. The of unwinder M1 Fig.inertia 7. Themoment inertia moment of unwinder M1
K P = 2 rL
(17)
25
K I = 2 r2 L
(18)
25 20
In the sequel, the decentralized structure shown on (Fig. 4) will be considered. The control structure is composed of 3 elementary controllers associated respectively to each motor. The cascade control configuration uses the tension as primary measurement and velocity as secondary measurement. The manipulated variable is the torque applied to the motors.
4. Simulation Results
The system was simulated in the MATLAB SIMULINK environment for a three motors winding system the winding system and the control system parameters are given in Appendix. As shown in Fig. 5, Fig. 8 and Fig. 11. An improvement of the linear speed is registered, and has follows
15 V1 Vref
5
0.3 0.2 0.2 0.1
0
1
2 3 Times (s)
4
5
1
the reference speed for PI controller after 0.3 sec, in all 0.04 0.03 motors, with the overshoot in linear speed (5%). Fig. 6 and Fig. 70.03 show that the radius and the inertia moment of 0.02 unwinder M1 decrease compared with the radius and the 0.02 of Motor M3 is increase shown in Fig. 9 inertia moment 0.01 and Fig. 10. 0.01 0 0 1 2 3 4 5 0 Times (s) 0 1 2 3 4 5 J2 [N.m] J2 [N.m]
[m/sec] ref 1
V ,V
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0.4 0.3
2 3 4 5 Times (s) 1 2 3 4 5 Fig. 9. The radius of motor M2 Times (s) 0.05 9. TheM2 radius of motor M2 Fig. 9. The radius Fig. of motor 0.05 0.04
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Fig. 5. The linear speed of unwinder M1 34
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0.1 0 0 0 0
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V2 Vref V2
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Vref 05 0 1 2 3 4 5 0 Times (s) 0 1 2 3 4 5 Fig. 8. The linear speed of Motor M2 Times (s) Fig. 8. The linear speed of Motor M2 0.5 Fig. 8. The linear speed of Motor M2 0.5 0.4
25
0
20 15
J3 [N.m] J [N.m]
IFOC
M3
2 3 4 5 Times (s) 1.242 1.24 Fig. 6. radius2of unwinder 0 The 1 3 4M1 5 1.24 Times (s) 0 1 2 3 4 5 0.022 Fig. 6. The radius of unwinder M1 Times (s) Fig. 6. The radius of unwinder M1 0.0219Fig. 6. The radius of unwinder M1 0.022 0.0218 0.022 0.0219 0.0217 0.0219 0.0218 0.0216 0.0218 0.0217 0.0215 0.0217 0 1 2 3 4 5 0.0216 Times (s) 0.0216 0.0215 1 moment 2 of unwinder 3 4 M1 5 Fig. 7. The0 inertia 0.0215 Times (s) 0 1 2 3 4 5 Fig. 7. The inertiaTimes moment (s)of unwinder M1
From follows ItFroa follows controll betterItp control tracking better p trackin 5
4 [N]
T3
1
f
T2
M3
R [ ]
T3
R [ ] R [ ]
T2
R [ R] [ ]
M1
M3
,Vref [m/sec] V2,VVref 2 [m/sec]
M1
T3
R1 [m] R1 [m] R1 [m]
T2
1.246 1.25 1.248 1.244 1.248 1.246 1.242 1.246 1.244 1.24 1.244 1.242 0
R2 [m] R2 [m]
M1
Times (s) 50 Fig. 5.0The linear speed unwinder 1 2 of 3 4 M1 5 VOLUME 6, N° 2 2012 0 Times (s) 0 1 2 3 4 5 1.25 Fig. 5. The linear speed Times (s) of unwinder M1 1.248 Fig. 1.255. The linear speed of unwinder M1
J1 [N.m] J1 [N.m] J1 [N.m]
K I = 2 r L to (18) respectively each motor. (Fig.4) will be considered. The control structure is The cascade control configuration uses the tension as In the sequel, decentralizedcontrollers structure shown on composed of 3the elementary associated primary measurement and &velocity as secondaryis Journal of Automation, Mobile Robotics Intelligent Systems (Fig.4) will be considered. The control structure respectively to each motor. measurement. manipulated variable is the torque composed ofThe3control elementary controllers The cascade configuration uses theassociated tension as applied to the to motors. respectively each motor. primary measurement and velocity as secondary M2 The cascade The control configuration uses the as measurement. manipulated variable is tension the torque primary measurement and velocity as secondary applied to the motors. measurement. The manipulated M2 variable is the torque applied to the motors. M2
3
R [ ]
0.03 0.01
0.01
0
1
2 3 Times (s)
4
5
Figure.10 – The inertia moment of Motor M2. 0 Fig. 10. The25inertia moment 0 1 2 of Motor 3 M24 5 Times (s) 25 15
100
V3 Vref
5
0
1
2 3 Times (s)
V3 4 Vref
5
2 0
0
51
0
2 3 Times (s)
T2 Tref 4
5
*Cor
0
1
2 3 Times (s)
4
Refe [1] [2] 5
Fig. 15. The tension between Motor 2 and 3 Fig. 15. The tension between Motor 2 and 3 Table System parameters From the1. Figures (14-15), we can say that: the tension follows the reference tension with application of PI E 1.6e8 L1= L2= L3[m] 5 controller. 2 50 PI ƒn [Hz] control with S [m ] 2.75e-3 It appears clearly that the classical 4 R [m] 1.25 T = T [N] 1 1ref 2ref controller in linear speed control and tension control of20 R = R [m] 0.25 V [m/s] 2 3 2ref fers better performances in both of the overshoot control and the Jtracking 01=J02= error. However is easy to apply. p 2 0.022 J03[Kg.m2]
0.29
R3 [m] R [m] 3
3 1
4 0 14. The tension between Motor 1 and 2 Fig. 0 2 3 4 5 31 Times (s) T3 2 Fig. 14. The tension between Motor 1 Tref and 2 1
Fig. 11. The linear speed of winder M3 Fig. 11. The linear speed of winder M3
[3]
[4]
[5]
[6]
Table 1. System parameters
1
2 3 Times (s)
4
5. Conclusion
5
R [ ]R [ ]
0.24 Fig. of 0 12.1 The radius 2 3 winder 4 M35 Fig. 12. The radius of winder M3 Times (s) 0.0221 Fig. 12. The radius of winder M3 0.0221 0.0221 0.0221 0.0221 0.022 0.0221 0.022 0.022 0.022 1 2 3 4 5 0.022 0 Times (s) 0.022 Fig. 13.0The inertia moment 1 2 3of winder 4 M35 Times (s) From the figures (14-15), we can say that: the tension follows the tensionmoment with application PI controller. Fig.reference 13. The inertia of winderofM3 It appears clearly that the classical control with PI Fig. 13. The inertia moment of winder M3 From the (14-15), we can that:control the tension controller in figures linear speed control and say tension offers follows the reference tension application PI controller. better performances in both with of the overshootofcontrol and the It appears clearly that theto apply. classical control with PI tracking error. However is easy J3 [N.m]J [N.m] 3
R [ ]
T2 4 2 Figure.14 – The tension between Motor 1 and 2 Fig. 14. The tension between Motor Tref 1 and 2
Fig. 0 11. The linear speed of winder M3 0 1 2 3 4 5 Times (s)
0.28 0.29 0.27 0.28 0.26 0.27 0.25 0.26 0.24 0.25 0
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Fig. 13. The inertia moment of winder M3 0.022 50 1 2we can 3 say 4that: the 5 tension From the figures (14-15), Times (s) follows the reference tension with application of PI controller. 4 It appears that moment the classical control Fig. 13.clearly The inertia of winder M3 with PI 3 controller in linear speed control and tension control offers From the figures (14-15), we can say that: the tension better performances in both of the overshoot and the T2ofcontrol follows the reference tension with application PI controller. 2 tracking error. However is easy to apply. It appears clearly that the classicalTref control with PI controller in linear speed control and tension control offers 1 5 better performances in both of the overshoot control and the tracking4error. However is easy to apply. 0 0 1 2 3 4 5 Times (s) 5 3
1
155
N° 2
T3,Tref [N]
V3,Vref [m/sec] V3,Vref [m/sec]
20 Figure.10 – The inertia moment of Motor M2.
20 10
4
[N]
0.020
2 3 Times (s)
[N]
R [ ]
0.04 0.02
1
2 ref
2 3 4 5 Times (s) Fig. 9. The radius of motor M2
VOLUME 6,
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T ,T
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0.05 0.03
0.022 0.022 0.022
R [ ]
J2 [N.m] J [N.m] 2
0.04
2 3 4 5 Times (s) Fig. 9. The radius of motor M2
2 ref
0 0.05 0
1
[N]T ,T
0.1
0
2 ref
0
0.0221 0.022
J3 [N.
Journal of Automation, Mobile Robotics & Intelligent Systems 0.2
T ,T
R2 [m]
0.3 0.1
The objective of this paper a 1.6e8 L1= L2consists = L3[m] in developing 5 model of a winding system constituted of three motors that 2 ƒn [Hz] S [mis ] coupled mechanically 2.75e-3 by a strap whose50 tension is adjustable and to develop the and 4 R1 [m] 1.25 T1ref= methods T2ref [N] of analysis synthesis of the commands robust and their application to 20 a constant R2=Rsynchronize [m] V2ref [m/s] the0.25 three sequences and to maintain 3 mechanical tension between the rollers of the system. J01=J02=Computer J03[Kg. 2 simulations pshow the robustness and the 0.022 m 2] performance of the winding system with the PI controllers, however PI control dominates industry and it is simple and easy to implement.
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5. Conclusion
The objective of this paper consists in developing a model of a winding system constituted of three moAUTHORS tors that is coupled mechanically by a strapHazzab, whose tenBousmaha Bouchiba*, Abdeldjebar Hachemi 1 Glaoui , Ismaïl Khalil Bousserhane of sion is adjustable and to develop the methods–ofLaboratory analysis command, Analysis and Optimization of the Electroand synthesis of the commands robust and their applicaEnergizing Systems, Faculty of Sciences technology, tion to synchronize the three sequences and toand maintain Béchar University B.P. 417 Béchar, 08000, Algeria. a constant mechanical tension between the rollers of the
[email protected],
[email protected], system.
[email protected] Fellah Med-Karim – Laboratory of ICEPS Intelligent 35 Articles Control and Electrical power Systems University of Sidi
[7]
[8]
[9]
[10]
[11]
Journal of Automation, Mobile Robotics & Intelligent Systems
Authors
Bousmaha Bouchiba*, Abdeldjebar Hazzab, Hachemi Glaoui, Ismaïl Khalil Bousserhane – Laboratory of command, Analysis and Optimization of the ElectroEnergizing Systems, Faculty of Sciences and technology, Béchar University B.P. 417 Béchar, 08000, Algeria.
[email protected],
[email protected],
[email protected] Fellah Med-Karim – Laboratory of ICEPS Intelligent Control and Electrical power Systems University of Sidi Bel-Abbes, Algeria.
[email protected] Pierre Sicard – Department of electrical and computer engineering, Université du Québec à Trois-Rivières, Canada.
[email protected] *Corresponding autor:
[email protected]
References
[1] D. P. Cambell, Process Dynamics, Wiley, 1958, pp.113-156. [2] G. Brandenburg, “New Mathematical Model For Web Tension and Register Error”. In: Proceedings of the 3rd IFAC Conference on Instrumentation and Automation in The Paper, Rubber and Plastics, vol. 1, May 1976, pp. 411-438. [3] H. Koç, D. Knittel, M de Mathelin, G. Abba, “Modeling and Robust Control of Winding Systems for Elastic Webs”, IEEE Trans. Contr. Syst. Technol., vol. 10, March 2002, pp.197-208. [4] J. E. Geddes, M. Postlethwaite, “Improvements in Product Quality in Tandem Cold Rolling Using Robust Multivariable Control”, IEEE Trans. Contr. System. Technology, vol. 6, March 1998, pp. 257-267. [5] S. H. Jeon et al., “Decoupling Control of Bridle Rolls for Steel Mill Drive System”, IEEE Trans. Ind. Application, vol. 35, January/February 1999, pp. 119-125.
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[6] D. Knittel et al., “Tension Control for Winding Systems With Two-Degrees of Freedom H∞ Controllers”, IEEE Trans. Ind. Applicat. Syst., vol. 39, January/February 2003, pp. 113-120. [7] B.T. Boulter, Y. Hou, Z. Gao, F. Jiang., “Active Disturbance Rejection Control for Web Tension Regulation and Control”. In: IEEE Conference on Decision and Control, Orlando, USA, December 2001, pp. 4974- 4979. [8] F. Mokhtari, P. Sicard, N. Léchevin, “Damping Injection Control of Winding System Based on controlled Hamiltonian Systems”. In: 12th IFAC Symposium on Automation in Mining, Mineral and Metal Processing – IFAC MMM’07, Québec, Canada, August 2007, pp. 243-248. [9] F. Mokhtari, P. Sicard, N. Léchevin, “Stabilizing Winding Systems by Injection Damping Control Based on controlled Hamiltonian Systems”. In: Proc. of IEEE International Electric Machines and Drives Conference – IEMDC’07, Antalya, Turkey, May 2007, pp. 95-100. [10] Bousmaha Bouchiba, Abdeldejbar Hazzab, Hachemi Glaoui, Fellah Med-Karim, Ismaïl Khalil Bousserhane, “Sliding Mode Speed Control for Multi-Motors System” , JAMRIS, vol. 4, no. 3, 2010, pp. 50-54. [11] Christian Thiffault, Pierre Sicard, Alain Bouscayrol, “Tension Control Loop Using a Linear Actuator Based on The Energetic Macroscopic Representation”. In: CCECE 2004–CCGEI 2004, Niagara Falls, Canada, May 2004. [12] S. Charlemagne, A. Bouscayrol, Slama Belkhodja, J.P. Hautier, “Flatness based control of non-linear textile multimachine process”. In: Proc. of EPE’03, Toulouse, France, September 2003, CD-ROM. [13] Adlane Benlatreche Dominique Knittel “State Feedback Control with Full or Partial Integral Action for Large Scale Winding Systems”. In: Industry Applications Conference, Oct. 2005, vol. 2, pp. 973-978.
