Rapid Control Prototyping in Cold Rolling using Piezoelectric Actuators

12th IFAC Workshop on Intelligent Manufacturing Systems 12th on Manufacturing December 5-7, 2016. Austin, TX, USA 12th IFAC IFAC Workshop Workshop on Intelligent Intelligent Manufacturing Systems Systems 12th IFAC Workshop on Intelligent Manufacturing Systems December 5-7, 2016. Austin, TX, USA December 5-7, 2016. Austin, TX, USA December 5-7, 2016. Austin, TX, USA Available online at www.sciencedirect.com

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Cold Cold Cold

Rapid Rapid Rapid Rolling Rolling Rolling

Control Prototyping in Control Control Prototyping Prototyping in in using Piezoelectric Actuators using Piezoelectric Actuators using Piezoelectric Actuators

∗ ∗∗ Matthias Wehr ∗∗ Sven Stockert ∗∗ ∗∗ Dirk Abel ∗ Gerhard Hirt ∗∗ ∗ Sven Stockert ∗∗ ∗∗ Dirk Abel ∗ ∗ Gerhard Hirt ∗∗ Matthias Wehr ∗ Matthias Wehr Wehr Sven Sven Stockert Stockert Dirk Dirk Abel Abel Gerhard Gerhard Hirt Hirt ∗∗ Matthias ∗ ∗ Institute of Automatic Control, RWTH Aachen University, ∗ of Automatic Control, Aachen University, ∗ Institute Institute of Control, RWTH Aachen 52064 Aachen, Germany (Tel: RWTH +49-241-28015; e-mail: Institute of Automatic Automatic Control, RWTH Aachen University, University, 52064 Aachen, Germany (Tel: +49-241-28015; e-mail: 52064 +49-241-28015; [email protected], [email protected]) 52064 Aachen, Aachen, Germany Germany (Tel: (Tel: +49-241-28015; e-mail: e-mail: [email protected], [email protected]) ∗∗ [email protected], [email protected]) Institute of Metal Forming,[email protected]) RWTH Aachen University, [email protected], ∗∗ ∗∗ Institute of Metal Forming, RWTH Aachen University, ∗∗ Institute ofGermany Metal Forming, Forming, RWTH Aachen University, University, 52064 Aachen,of (e-mail:RWTH [email protected], Institute Metal Aachen 52064 Aachen, Germany (e-mail: [email protected], 52064 (e-mail: [email protected]) 52064 Aachen, Aachen, Germany Germany (e-mail: [email protected], [email protected], [email protected]) [email protected]) [email protected])

Abstract: Precise manufacturing of cold rolled, thin, and narrow metallic strips has become Abstract: Precise manufacturing of rolled, thin, narrow metallic strips become Abstract: Precise manufacturing of cold cold rolled, thin, and narrow metallic strips has has become more important for various applications. The overall aimand is the reduction of thickness tolerances Abstract: Precise manufacturing of cold rolled, thin, and narrow metallic strips has become more important for various applications. The overall aim is the reduction of thickness tolerances more important for various various applications. The overall aim is To thereach reduction of thickness tolerances of steel and copper strips toapplications. an extent ofThe lessoverall than 1aim µm.is that of goal, an experimental more important for the reduction thickness tolerances of steel and copper to ansupplementary extent of less piezoelectric than 11 µm. To reach that goal, experimental of steel and strips to reach that an experimental rolling set upstrips in which stack actuators are an integrated. The of steelmill and iscopper copper strips to an an extent extent of of less less than than 1 µm. µm. To To reach that goal, goal, an experimental rolling mill is set up in which supplementary piezoelectric stack actuators are integrated. The rolling mill is set up in which supplementary piezoelectric stack actuators are integrated. The setup of the machine is presented. It contains a real-time system for rapid control prototyping rolling mill is set up in which supplementary piezoelectric stack actuators are integrated. The setup of is It aa real-time system for setup of the the machine machine is presented. presented. It contains contains real-time system for rapid rapid control control prototyping using model-based development. It enables a direct download of a controller from theprototyping simulation setup of the machine is presented. It contains a real-time system for rapid control prototyping using model-based development. It enables a direct download of a controller from simulation using model-based development. It enables enables bandwidth direct download download of aa controller controller from the the are simulation environment to the development. machine. Furthermore, requirements for the actuators derived using model-based It aa direct of from the simulation environment to the machine. bandwidth for the actuators are derived environment to Furthermore, bandwidth requirements for the actuators derived from strip measurements andFurthermore, machine properties. Therequirements bandwidth of identified environment to the the machine. machine. Furthermore, bandwidth requirements forthe theactuators actuatorsisare are derived from strip measurements and machine properties. The bandwidth of the actuators identified from strip and machine The of is identified by modeling the system’s dynamics. The comparison of both actuators revealsis their from strip measurements measurements and machine properties. properties. The bandwidth bandwidth of the the actuators actuators isthat identified by modeling the system’s dynamics. The comparison of both actuators reveals that by modeling the the system’s dynamics. dynamics. The tocomparison comparison ofoccurring both actuators actuators reveals that that their their complementary characteristics are suitable compensateof disturbances. by modeling system’s The both reveals their complementary complementary characteristics characteristics are are suitable suitable to to compensate compensate occurring occurring disturbances. disturbances. complementary characteristics are suitable to compensate occurring disturbances. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Cold Rolling, Piezoelectric Actuator, System Identification, Model-in-the-Loop, Keywords: Cold Rolling, Actuator, Identification, Keywords: ColdPrototyping, Rolling, Piezoelectric Piezoelectric Actuator, System Identification, Model-in-the-Loop, Rapid Control Model-Based Design,System Bandwidth Analysis Model-in-the-Loop, Keywords: Cold Rolling, Piezoelectric Actuator, System Identification, Model-in-the-Loop, Rapid Control Prototyping, Model-Based Design, Bandwidth Analysis Rapid Control Control Prototyping, Prototyping, Model-Based Model-Based Design, Design, Bandwidth Bandwidth Analysis Analysis Rapid 1. INTRODUCTION 1. 1. INTRODUCTION INTRODUCTION 1. INTRODUCTION Thin cold rolled metallic strips belong to a group of proThin rolled metallic stripsdifferent belong to to aa group group of proproThin cold rolled metallic strips of ducts cold which is used in many of technolThin cold rolled metallic strips belong belong toareas a group of products which is used in many different areas of technolducts which is used in many different areas of technology. Inwhich some isindustries, precision of materials ducts used in many different areas ofincluding technology. In precision of ogy. In some some industries, precision of materials materials including metallic stripsindustries, plays a major role e.g. electrical including industry, ogy. In some industries, precision of materials including metallic strips plays aa major role industry, metallic strips and playsmedical major role e.g. e.g. electrical electrical industry, space industry technology. The minimal stanmetallic strips plays a major role e.g. electrical industry, space industry and medical technology. The minimal stanspace industry and medical medical technology. The minimal minimal standardized tolerance for narrow steel strips with nominal space industry and technology. The standardized for steel strips with EN nominal dardized tolerance for narrow narrow steel with thickness tolerance of h = 1 mm is ∆h = ±15strips µm (DIN ISO dardized tolerance for narrow steel strips with nominal nominal thickness of = mm ±15 (DIN EN ISO thickness of h hThe =1 mm is is ∆h ∆h =copper ±15 µm µm (DIN EN same ISO 9445-1, 2010). for= strips of the thickness of h = 11 tolerance mm is ∆h = ±15 µm (DIN EN ISO 9445-1, copper strips of 9445-1, 2010). The tolerance forEN copper strips of the the same extent is2010). ∆h =The ±22tolerance µm (DINfor 13599, 2014). Forsame the 9445-1, 2010). The tolerance for copper strips of the same extent is ∆h = ±22 µm (DIN EN 13599, 2014). For the extent is ∆h = ±22 µm (DIN EN 13599, 2014). For the production of =those strips, usually cold rolling utilized extent is ∆h ±22 µm (DIN EN 13599, 2014).is For the production production of those those strips, strips, usually usually cold cold rolling rolling is is utilized utilized in industry. of production of those strips, usually cold rolling is utilized in industry. in industry. During a rolling process, the roll gap needs to be adjusted in industry. During rolling process, the needs to During rolling process,variations the roll roll gap gap needs to be be adjusted adjusted not onlya compensate in the incoming material During aato rolling process, the roll gap needs to be adjusted not only to compensate variations in the incoming material not only to compensate variations in the incoming material (as there can be variations in e.g. thickness, hardening and not only to compensate variations in the incoming material (as there can in hardening (as theretexture). can be be variations variations in e.g. e.g. thickness, thickness, hardening and surface Also, plant-related variations like rolland ec(as there can be variations in e.g. thickness, hardening and surface texture). Also, plant-related variations like roll ecsurface texture). Also, plant-related (Bryant, variations1973). like roll eccentricities need to be compensated Those surface texture). Also, plant-related variations like roll eccentricities to be (Bryant, centricities need to with be compensated compensated (Bryant, 1973). Those disturbancesneed grow increasing service life1973). of theThose plant centricities need to be compensated (Bryant, 1973). Those disturbances grow with increasing service life of the disturbances grow with increasing service life of the plant plant as they are accompanied by machine wear.lifeTherefore, an disturbances grow with increasing service of the plant as they accompanied machine an as they are areGauge accompanied by machine wear. Therefore, an Automatic Control by (AGC) needswear. to beTherefore, used in order as they are accompanied by machine wear. Therefore, an Automatic Gauge Control (AGC) to in Automatic Gauge Control (AGC) needs needs to be be used used product in order order to compensate those disturbances and guarantee Automatic Gauge Control (AGC) needs to be used in order to compensate those disturbances and guarantee product to compensate those disturbances disturbances andoverall guarantee product quality during machine life cycle. The aim isproduct the reto compensate those and guarantee quality machine life aim the quality during machine life cycle. cycle. The overall aim is ismetallic the rereductionduring of thickness variations of The thin overall and narrow quality during machine life cycle. The overall aim is the reduction of thickness variations of thin and narrow metallic duction of thickness variations of thin and narrow metallic strips to ∆h = ±1 µm. To achieve this goal supplementary duction of thickness variations of thin and narrow metallic strips to ±1 To this goal strips to ∆h ∆h = = ±1 µm. µm. To achieve achieve this goal supplementary supplementary piezoelectric stack actuators will be integrated in the mill strips to ∆h = ±1 µm. To achieve this goal supplementary piezoelectric stack actuators will be integrated in piezoelectric stack actuators actuators willmill. be integrated integrated in the the mill mill housing of a conventional rolling They are expected to piezoelectric stack will be in the mill housing of a conventional rolling mill. They are expected to housing of a conventional rolling mill. They are expected to bear complementary dynamic in comparison housing of a conventional rollingcapabilities mill. They are expected to bear dynamic capabilities comparison bear complementary dynamic capabilities in comparison to thecomplementary existing actuators. In such a way it in is expected to bear complementary dynamic capabilities in comparison to the existing actuators. In such a way it is expected to to the existing existing actuators. In such way roll it is isstands expected to achieve the tolerance goal In with ordinary which to the actuators. such aa way it expected to achieve the goal ordinary roll which achieve the tolerance tolerance goal with with ordinary roll stands stands which do not have to be optimized towards extreme stiffness and achieve the tolerance goal with ordinary roll stands which do not have to be optimized towards extreme stiffness and do not have to be optimized towards extreme stiffness and precision mechanically. do not have to be optimized towards extreme stiffness and precision precision mechanically. mechanically. precision mechanically.

The piezoelectric effect describes a voltage caused by an The piezoelectric effect describes caused by The piezoelectric effect describes voltage caused by an an external force which is applied to aaa voltage piezoelectric ceramic. The piezoelectric effect describes voltage caused by an external force which is applied to a piezoelectric ceramic. external forceis which which is approximation applied to to aa piezoelectric piezoelectric ceramic. The voltage in firstis proportional to the external force applied ceramic. The voltage is approximation proportional to The voltage which is in in first first approximation proportional to the the deformation results from the applied force. The soThe voltage is in first approximation proportional to the deformation which results from the applied force. The sodeformation which results from the applied force. The called reciprocal piezoelectric effect achieves the opposite deformation which results from the applied force. The sosocalled reciprocal effect called reciprocal piezoelectric piezoelectric effect achieves achieves the opposite result (Isermann, 2005). If a voltage is appliedthe to opposite a piezocalled reciprocal piezoelectric effect achieves the opposite result (Isermann, 2005). If a voltage is applied to piezoresult (Isermann, 2005). If aa voltage voltage is applied applied to a piezoelectric(Isermann, ceramic, the material will extend. This principle is result 2005). If is to aa piezoelectric ceramic, the material will extend. This principle is electric ceramic, the material will extend. This principle is used to ceramic, build piezoelectric actuators. electric the material will extend. This principle is used to piezoelectric actuators. used to build build enlargement piezoelectric of actuators. The possible a piezoelectric ceramic is up used to build piezoelectric actuators. The possible enlargement of aa piezoelectric ceramic up The possible enlargement ofAs piezoelectric ceramic is has up to 0.2 % of itsenlargement own length.of a single ceramic diskis The possible a piezoelectric ceramic is up to 0.2 % of its own length. As a single ceramic disk has to 0.2heights % of of its its own length. length. As single ceramic ceramics disk has has only of about 1 mm, As several piezoelectric to 0.2 % own aa single ceramic disk only heights of about several piezoelectric ceramics only heightsin of order aboutto111 mm, mm, several piezoelectric ceramics are stacked achieve higher enlargement. They only heights of about mm, several piezoelectric ceramics are stacked in order to achieve higher enlargement. They are stacked in order to achieve higher enlargement. They henceforth called stack actuators. Piezoelectric ceraare stacked in order to achieve higher enlargement. They are stack actuators. Piezoelectric are henceforth called stack large actuators. Piezoelectric ceramicshenceforth can endurecalled relatively pressures while theyceraare are henceforth called stack actuators. Piezoelectric ceramics can relatively pressures while they mics can endure endure relatively large pressures while property they are are vulnerable for tensile loads large and torsion. Another mics can endure relatively large pressures while they are vulnerable for loads torsion. Another property vulnerable for tensile tensile loads and torsion. Another property of piezoelectric ceramics is aand nearly unlimited accuracy in vulnerable for tensile loads and torsion. Another property of piezoelectric ceramics is a nearly unlimited accuracy of piezoelectric ceramics is aa discretization nearly unlimited unlimited accuracy ina position. In theory position is limited to in of piezoelectric ceramics is nearly accuracy in position. In position limited to position. In theory theory position discretization is limited to a single electric charge. Duringdiscretization extension, no is friction occurs position. In theory position discretization is limited to aa single electric charge. During extension, no friction occurs single electric charge. During extension, no friction occurs withinelectric the actuator wear-out to aoccurs little single charge.which Duringdecreases extension, no friction within actuator decreases little within the actuator which decreases wear-out wear-out to to a little extent. the (Heywang et which al., 2008) within the actuator which decreases wear-out to aa little extent. (Heywang et al., 2008) extent. (Heywang et al., al., 2008) 2008) actuators for an increase of The idea(Heywang of using piezoelectric extent. et The idea using piezoelectric actuators for of The idea of of is using piezoelectric actuators for an an increase increase of bandwidth implemented in various applications. Those The idea of using piezoelectric actuators for an increase of bandwidth is implemented in various applications. Those bandwidth is implemented in various applications. Those applicationsisusually have in in common they work Those under bandwidth implemented variousthat applications. applications have common they applications usually have in in commonetthat that they work work under none or onlyusually little loads. Branson al. (2011) use under them applications usually have in common that they work under none or only little loads. Branson et al. (2011) use them none or only onlya little little loads. Branson etcylinder al. (2011) (2011) use them to actuate valveloads. in a Branson hydraulicet in use order to none or al. them to actuate valve hydraulic cylinder in order to actuate valve in in aaaOther hydraulic cylinder are in injection order to to increase its aaabandwidth. applications to actuate valve in hydraulic cylinder in order to increase bandwidth. Other are injection increase its(Stemme bandwidth. Other applications applications are(Gnad injection of e.g. inkits and Larsson, 1973) or fuel and increase its bandwidth. Other applications are injection of e.g. ink (Stemme and Larsson, 1973) or fuel (Gnad and of e.g. ink (Stemme and Larsson, 1973) or fuel (Gnad and Kasper, 2006). Another use of piezoelectric actuators for of e.g. ink (Stemme and Larsson, 1973) or fuel (Gnadisand Kasper, 2006). of actuators is Kasper, 2006). Another Another use of piezoelectric piezoelectric actuators is for for active vibration control.use A survey of different approaches Kasper, 2006). Another use of piezoelectric actuators is for active vibration control. survey active vibration control. A A (2003). survey of of different approaches was done by Moheimani Indifferent context approaches of rolling, active vibration control. A survey of different approaches was done by Moheimani (2003). In context rolling, was done by Moheimani (2003). In context of(2011) rolling, piezoelectric were(2003). used byInZhou et al.of as was done byactuators Moheimani context of rolling, piezoelectric actuators were used by Zhou et al. (2011) as piezoelectric actuators were used by Zhou et al. (2011) as the only actuators for roll gap adjustment. They presented piezoelectric actuators were used by Zhou et al. (2011) as the the only only actuators actuators for for roll roll gap gap adjustment. adjustment. They They presented presented the only actuators for roll gap adjustment. They presented

Copyright@ 63 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016 2016, IFAC IFAC (International Federation of Automatic Control) Copyright@ 2016 IFAC 63 Peer review under responsibility of International Federation of Automatic Copyright@ 2016 63 Copyright@ 2016 IFAC IFAC 63 Control. 10.1016/j.ifacol.2016.12.161

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an experimental rolling mill for surface texturing in which micro-channels were imprinted on aluminum sheets. While there are numerous control strategies for AGC utilizing a single pair of hydraulic actuators or electric spindle drives in rolling mills, only a few concepts were developed using different types of actuators for roll gap adjustment within a single roll stand. An approach with two actuators was proposed and successfully tested by Zhang et al. (2014) on a plate mill at Handan Hongri Metallurgy Co. Ltd., China. They used a spindle drive for the upper roll which was counteracted by a hydraulic actuator driving the lower roll. Another approach was presented by Liu et al. (2016) where a rolling mill is adapted to be used with a linear motor instead of hydraulics. A problem typical for manufacturing plants is that usually Programmable Logic Controllers (PLC) are used where controllers are made in hardware allowing only a few settings to change within a rigid control scheme. Developing new control strategies, hence, is often tied to simulation and cannot be easily implemented on the manufacturing plant. Therefore the need for an experimental setup enabling Rapid Control Prototyping (RCP) techniques is present. This paper introduces a setup for an experimental rolling mill. It is shown how RCP techniques can be used to quickly develop and test various control algorithms for AGC in an industrial context. Also, the integration of piezoelectric stack actuators in the mill housing is shown. An enhancement of the dynamics of the experimental rolling mill is expected, if a piezoelectric stack actuator is used as support to an existing electromechanically actuated spindle drive. The enhancement of bandwidth will be shown.

are integrated in the lower part of the mill housing and drive the lower work roll. In such a way, torsion on the piezoelectric actuators caused by the spindle is avoided. Fig. 2 depicts the integration of the components in the mill housing. Integrating actuators in the lower part is uncommon, as the pass line of the strip is lifted which in general should be avoided. However, the maximum lift by the actuators is that small that it can be neglected (∆L = 150 µm). During the rolling process high precision load cells HMB 1 C10/50kN measure the rolling force. Additionally a strip thickness sensor (see section 3.1) and an incremental encoder WayCon A8 W 10 L 1000 KA02 for strip speed measurement are integrated on each side of the roll gap.

2. SETUP OF THE EXPERIMENTAL ROLLING MILL

2.2 Integration of the Real-Time Control System

Electromechanical spindle drives Strip Load cells Piezoelectric stack actuators Fig. 2. Schematic of the modified mill housing

The central control component of the project is a dedicated dSpace Real-Time (RT) system DS1006. It will be used for RCP purposes. The system bears all relevant interfaces like PROFIBUS, Controller Area Network (CAN), Analog-Digital inputs and Digital-Analog outputs (AD/DA). When disabling the RT prototyping device, the conventional rolling mill can be used as usual. The extended ‘research’ mode can be activated giving the control authority to the RT system which then can set reference values for all spindle drives. Because safety functions remain in the machine’s PLC, they do not have to be taken care of during developing of control strategies. The communication between the RT system and the mill’s PLC is tied to certain restrictions which will be discussed in section 4. The process variables of the spindle drive are controlled by an internal controller in the PLC of the rolling mill. The reference values as well as the measured position can be accessed by a PROFIBUS interface. The other sensors and actuators are directly connected to the RT hardware using AD/DA and CAN. It is worth noticing, that only communication via PROFIBUS bears time delays; all other components are assumed to work free of delays. Fig. 3 depicts the structure of the extended rolling mill. On the left-hand side a Model-in-the-Loop (MiL) setup is realized which has been used in a different context by e.g. Plummer (2006). MiL describes a technique in which

2.1 Components of the Rolling Mill The particular manufacturing plant is a tandem mill which bears a 2-high roll stand as well as a 4-high stand. In this work only the second, the 2-high roll stand is used. In that stand additional piezoelectric stack actuators PSt 1000/25/150 VS35 are integrated (see fig. 1). Contem-

Fig. 1. Rolling mill and integration of a piezoelectric actuator porary rolling mills are usually actuated hydraulically or have electromechanical spindle drives. The experimental rolling mill uses the latter actuators. Therefore the actuators come with mechanical properties such as self-locking which are caused by the worm gear spindle. The original machine only contains electromechanical spindle drives adjusting the upper work roll. The piezoelectric actuators 64

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functionalities such as control algorithms and physics of plants are designed within a model-based approach. They can be run in the same simulation environment. In such simulations, interfaces of the components already need to be fully implemented. This enables a direct download of the controller-model without any changes for the RT system. With that setup it is furthermore possible to quickly identify the plant’s dynamics and derive a model upon which a controller can be designed. After a successful test in simulation, the controller can immediately be downloaded to the RT system without any need for manual changes. This dramatically increases the pace of develop-

Plant model

1.02

Process PLC PROFIBUS

Code generation

Controller model Model-in-the-Loop

shown in fig. 4. It shows that the strip satisfies the standardized tolerances. The maximum strip speed of the machine is vmax = 5 m s−1 (300 m min−1 ). Considering a strip speed of vmax , the strip will pass the process within two seconds. Applying a Fast Fourier Transform (FFT) a spectrum is revealed as can be seen in fig. 5. As the strip results from an unknown industrial process, only assumptions can be made of the origin of the frequency peaks. However, they have to be compensated regardless of their origin. Considering

Thickness [mm]

System identification

AD/DA

CAN

57

AD/DA

Strip thickness Average strip thickness Tolerance

1 0.98 0.96 0

C-Code

2

Real-time system Experimental setup

4 6 Length [m]

8

10

Fig. 4. Measurement of an example strip

ment. On the RT system, finally, all process variables can be monitored and particular experiments can be run by an operator.

the peaks flatten during the rolling process, peaks up to f = 50.5 Hz have to be considered. The peaks of the frequencies beyond that will decrease below 1 µm after rolling. As the amplitudes can interfere, they can shrink to a minimum or grow to a maximum which is as large as the largest extension of the strip (thickness tolerance).

3. ESTIMATION OF BANDWIDTH REQUIREMENTS

3.2 Requirements Arising from the Machine

Compensation of different disturbances occurring in the process is necessary to reach the desired thickness tolerance. That requires the actuators to work at a certain frequency, i.e. their bandwidth must be sufficiently high. The requirements will on the one hand be derived from the strip’s thickness variations; on the other hand they will be taken from the machine’s properties. Both disturbance categories’ frequencies directly depend on the strip’s speed which will turn out to be a key factor in the process.

In order to determine the required bandwidth, not only the incoming strip needs to be measured, also the physical properties of the machine matter. Requirements from the machine are easier to handle than those arising from the strip. Bryant (1973) proposes various disturbances and their shapes which can occur in a rolling mill. Among them are variations with different influences. Parameter variations usually have a constant influence. Also there are motor-speed errors which have the effect of a drift during time and roll eccentricities which have a periodic waveform. For the needs of bandwidth identification only the roll eccentricities are considered as an influ-

Fig. 3. Model-in-the-Loop setup and structure of the RT system

3.1 Requirements Arising from Strip Measurements

2 Magnitude [µm]

As mentioned in section 1, thickness variations appear up to ∆h = ±15 µm for strips with nominal thickness of h = 1 mm. Those variations originate from prior process steps and according to Bryant (1973) are among the most difficult ones to handle due to their off-specification. A representative strip example with nominal thickness of h = 1 mm is taken to determine major and minor thickness variations and their frequencies. From there the needed bandwidth of the actuators at a certain strip speed is determined for compensation of input strip variations. The particular steel strip of material SAE 1008 / DC01 (number 1.0330) with length of l = 10 m is measured with a high precision laser thickness gauge utilizing two laser distance sensors Keyence LK-G10 with a precision of 0.02 µm each (Stockert et al., 2016). The strip measurement result is

1

0

0

20

40 60 80 Frequency [Hz]

100

Fig. 5. Frequency spectrum of the measured strip 65

120

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ence due to their periodic character. Therefore geometry of the rolls as well as strip speed has to be investigated. In the 2-high stand the rolls have a diameter of d = 120 mm (radius r = 60 mm). If their peripheral speed is vmax = 5 m s−1 , the frequency f of the rolls’ rotation turns out to be: vmax 5 m s−1 vmax = = = 13.26 Hz. (1) f= 2πr πd π · 0.12 m

numerical optimization with a quadratic error function given in eq. (2). Hereby J denotes the cost function which is to be minimized; e is the error between the measured and the simulated displacement of the actuator; y denotes the measured as well as the simulated displacements of the spindle. In a second-order system K denotes the system’s gain. D is the damping ratio while ω0 is the undamped natural frequency. As closed loop identification is done, no steady state error is expected (nor has it been observed during machine operation). Thus the gain of the system is assumed K = 1. 

4. SYSTEM DYNAMICS 4.1 Dynamics of the Electromechanical Spindle Drive

min J = min eT · e = min

Table 2. Parameters of fitted second-order model

Table 1. Time delays originating from communication

Parameter K D ω0

Time [ms] 57.9 35.4

Displacement [µm]

4.2 Dynamics of the Piezoelectric Stack Actuator The properties of the piezoelectric actuators are limited by the used amplifiers. If an amplifier generates noise or ripple voltages, it will affect the actuator in a negative way, too. Also limited current will influence the actuator’s dynamics. The used piezoelectric actuators have characteristics as shown in table 3. The used amplifier RCV 1000/3

100

Table 3. Characteristics of the used piezoelectric actuators

Reference position

Parameter Length Displacement Capacitance Natural Frequency Blocking Force

Meas position 0.53 kN Meas position 8.34 kN Meas position 34.3 kN

0 0.9

Simulated position

1

1.1 1.2 Time [s]

1.3

Value 1 0.53 23.30 rad s−1 (3.71 Hz)

this identification one can see that if the strip moves at vmax = 5 m s−1 , the conventional actuator is only in a very limited way able to compensate strip thickness variations which are measured in advance. If higher strip velocities are desired, its bandwidth cannot keep up with the process anymore. Additionally the communication delays make quick feedback reactions to e.g. measured loads impossible. Thus the electromechanical spindle will in the first place be used to apply preloads and to compensate trends in thickness variations.

control parameters have not been revealed by the plant’s manufacturer, therefore closed loop identification is necessary. As the spindle’s speed can be limited in the Human Machine Interface (HMI), no linear behavior is to be expected. Its maximum speed is vmax,spindle = 1 mm s−1 . Despite that, a second-order system is taken to describe the dynamics which can be achieved doing a step response analysis (e.g. Franklin et al., 2014). The maximum difference of thickness variations within the material is around 30 µm. Therefore, containing some margins e.g. expansion of the mill housing, a maximum step height of 100 µm for travel is chosen. The experiment was done under different preloads in order to determine their influences. Fig. 6 shows the step response of simulation and measurement. The optimal values were found using

50

(2)

The transfer function of the electromechanical spindle drives (without units written) is: Y (s) Kω02 = 2 Gspindle (s) = Yref (s) s + 2Dω0 s + ω02 542.89 . (3) = 2 s + 24.70s + 542.89 Although the model does not fit the process exactly in the area of overshoot, it can still be taken for an estimation of dynamics. The parameters are shown in table 2. From

The rolling mill has a servomotor which drives a spindle to adjust the roll gap. As the servo controller is part of the PLC of the rolling mill, reference values can only be set via PROFIBUS interface, which takes time to process values. This time was measured in an experiment. A reference position was sent to the mill’s PLC. When the spindles’ displacement happened, a force reaction could be measured on the RT system. That time was taken as reaction time. At a certain time the displacement is sent back to the RT system. When it arrives, the time from force reaction to arrival of the displacement’s measurement is taken as measurement time. The results are shown in table 1. The

Delay Td,reaction Td,measurement

2

(ymeas − y(D, ω0 )) dt

1.4

Symbol L ∆L C f0 F0

Value 154 mm 150 µm 3.1 µF 7 kHz 25 kN

comes with characteristics shown in table 4. From the characteristics provided by the manufacturer, one can see that the undamped natural frequency of the actuator is f0 = 7 kHz. The bandwidth, hence, can be assumed to be

Fig. 6. Step responses of the electromechanical spindle drives 66

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the system cannot work at that frequency. The strip speed, hence, needs to be slowed down by at least 43 %. Nevertheless, as that value comes from an off-specification disturbance, this statement is not universal. Besides bandwidth, the maximum possible displacement is as important. The forces appearing in this particular process do not affect the spindle drives in their dynamics, neither in bandwidth, nor in gain. Thus, an unlimited capability for displacement is assumed (the spindle can actually travel by about 100 mm). The piezoelectric actuator, however, comes with significant limitations in displacement. When it works under its maximum force (blocking force F0 ) it cannot achieve any displacement anymore. Thus, the displacement abilities decrease with increasing force. Fig. 8 depicts the characteristics schematically. It shows which areas in the process can be visited. It suggests that the piezoelectric actuator should always be kept in a suitable operating point where not much displacement is necessary. The system can fully cope with the requirements which

Table 4. Electrical properties of the amplifiers Parameter Voltage Current

Value 0 V to 1000 V 0 A to 3 A

beyond that frequency. The limitations of the amplifier, however, lead to the assumption of a smaller bandwidth. That assumption was investigated by recording an open loop step response. In order not to stress the ceramics too much, only step-sizes of Vset = 100 V and Vset = 200 V were taken under different preloads. Analyzing the step

30

t

Voltage Step

Position200V,0kN 100V,0kN

Position Pos 200V 0kN 100V,4kN

10

Pos 100V 4kN Position 200V,4kN Pos 200V 4kN

0 0

0.05

Time [s]

Spindle drive

0.1

Piezoelectric actuator

0.15

25 Force [kN]

Position [µm]

Voltage step

Position t 100V,0kN

20

59

Fig. 7. Step responses of the piezoelectric actuators under various conditions response (see fig. 7) of the actuators with the same technique as had been used for the spindle drive reveals that the amplifier strongly limits the dynamics of the actuator. It can be approximated to a first-order system (see eq. (4)) where the time constant is T = 0.0056 s and therefore ω0 = 178.57 rad s−1 (f = 28.42 Hz). One can observe that with increasing preload F the maximum displacement decreases. The transfer function is identified to: K(F ) Gpiezo (s) = Ts + 1 K(F ) . (4) = 0.0056s + 1 It must not be hidden, that piezoelectric actuators bear a hysteresis due to remanent polarization. The effect is explained by e.g. Heywang et al. (2008). However, for the first estimation of the dynamics that characteristic is neglected.

20 15 10 0

0

50 Displacement [µm] 100

30

15 Frequency [Hz]

Fig. 8. Force-related capabilities in frequency and displacement arise from the particular process. When rolling the above mentioned steel with a strip width of b = 20 mm, a nominal thickness of h = 1 mm and a thickness reduction of 5 %, the expected rolling force on each side is about F = 15 kN. At that operating point, the piezoelectric actuators still have capabilities to sufficiently extent and, hence, to work on the material. Finally the self-locking characteristics of the worm gear spindle should be emphasized. In a twoactuator-setup it can be used advantageous such that the spindle can simply be set to a certain position without the possibility of further displacement due to applied forces. Thus, no additional effort is needed to keep the spindle in a steady position when the piezoelectric actuator is working. This greatly simplifies the control effort and leads to a setup where, if necessary, only the piezoelectric actuators can work.

5. DYNAMICS OF THE COMBINED SYSTEM From section 4 one can see that the dynamics of the actuators are very different in bandwidth. Considering a linear representation of the systems, the transfer function matrix G for displacement of both actuators is: Y (s) = G(s)U (s)   Uspindle (s) = [Gspindle (s) Gpiezo (s)] · . (5) Upiezo (s)

6. CONCLUSION

That 1 × 2 matrix has two inputs and one output. According to Skogestad and Postlethwaite (2005) the bandwidth for those systems is the bandwidth of the faster system. Therefore the bandwidth of the piezoelectric actuator can be taken as the system’s total bandwidth. The maximum disturbance peak from section 3.1 occurred at f = 50.5 Hz. With a cut-off frequency of f = 28.42 Hz

In this work, an experimental rolling mill was presented on which it is possible to rapidly develop new control algorithms, quickly analyze the results and obtain the control algorithms directly from simulation. In such a way, time of developing cycles can be reduced to a minimal extent. 67

2017 IFAC IMS 60 December 5-7, 2016. Austin, TX, USA

Matthias Wehr et al. / IFAC-PapersOnLine 49-31 (2016) 55–60

The authors expect a rapid development process of control algorithms. As cycle times from simulation to experiment are minimized, the hurdle of setting up an experiment is cleared. It has been shown that adding another pair of actuators will increase the bandwidth of the process in a manner that thickness disturbances and roll eccentricities can be compensated, if the machine is run at most by 56 % of its maximum speed. The combination of an RT system for rapid controller development with unconventional, but highly suitable piezoelectric actuators is a promising setup which enables the development and test of various control strategies. Even if the combination of the actuators is capable of working up to needed bandwidth, components will be necessary to be developed: first, a state observer indispensable to determine physical quantities within the roll gap. In the first place it will be necessary to estimate the current rolled strip thickness. Secondly, a controller capable of actuating both the spindle as well as the piezoelectric actuator is needed to achieve best possible results. Here, the authors tend to develop a Model Predictive Controller (MPC) which can cope with the challenges of multiple actuators.

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ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support of the German Research Foundation (DFG) received within the research project ”Hochpr¨ azisionswalzen von metallischen B¨ andern mittels eines piezoelektrisch unterst¨ utzten Regelungssystems” (High Precision Rolling of Metallic Strips Utilizing a Piezoelectric Supported Control Strategy). REFERENCES Branson, D.T., Wang, F.C., Johnston, D.N., Tilley, D.G., Bowen, C.R., and Keogh, P.S. (2011). Piezoelectrically actuated hydraulic valve design for high bandwidth and flow performance. Proceedings of the Institution of Mechanical Engineers Volume 225, Part I: Journal of Systems and Control Engineering, 345–359. doi: 10.1177/09596518JSCE1037. Bryant, G.F. (ed.) (1973). Automation of tandem mills. Iron and Steel Institute, London. DIN EN 13599, 2014 (2014). Copper and copper alloys - Copper plate, sheet and strip for electrical purposes; German version EN 13599:2014. DIN EN ISO 9445-1, 2010 (2010). Continuously cold-rolled stainless steel Tolerances on dimensions and form Part 1: Narrow strip and cut lengths. Franklin, G.F., David, P.J., and Emami-Naeini, A. (2014). Feedback Control of Dynamic Systems. Pearson, London, 7th edition. Gnad, G. and Kasper, R. (2006). Power Drive Circuits for Piezo-Electric Actuators in Automotive Applications. In Industrial Technology, 2006. ICIT 2006. IEEE International Conference on, 1597–1600. doi: 10.1109/ICIT.2006.372454. Heywang, W., Lubitz, K., and Wersing, W. (eds.) (2008). Piezoelectricity - Evolution and Future of a Technology. Springer, Berlin Heidelberg. doi:10.1007/978-3-54068683-5. 68