Wind Evaluation Breadboard: Mechanical Design and Analysis, Control Architecture, Dynamic Model and Performance Simulation

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1 Wind Evaluation Breadboard: Mechanical Design and Analysis, Control Architecture, Dynamic Model and Performance Simulation Marcos Reyes García-Talavera* a, Teodora Viera a, Miguel Núñez a, Pablo Zuluaga ab, Bernardo Ronquillo b, Mariano Ronquillo b, Enzo Brunetto c, Marco Quattri c, Javier Castro d, Elvio Hernández a a Instituto de Astrofísica de Canarias, Tenerife, Spain; b ALTRAN Technologies, Madrid, Spain; c ESO, Munich, Germany; d Grantecan S.A., Tenerife, Spain; ABSTRACT The Wind Evaluation Breadboard (WEB) for the European Extremely Large Telescope (ELT) is a primary mirror and telescope simulator formed by seven segments simulators, including position sensors, electromechanical support systems and support structures. The purpose of the WEB is to evaluate the performance of the control of wind buffeting disturbance on ELT segmented mirrors using an electro-mechanical set-up which simulates the real operational constrains applied to large segmented mirrors. The instrument has been designed and developed by IAC, ALTRAN, JUPASA and ESO, with FOGALE responsible of the Edge Sensors, and TNO of the Position Actuators. This paper describes the mechanical design and analysis, the control architecture, the dynamic model generated based on the Finite Element Model and the close loop performance achieved in simulations. A comparison in control performance between segments modal control and actuators local control is also presented. Keywords: segmented telescope, wind buffeting, dynamic model, modal control, primary mirror cell, IAC. INTRODUCTION The Extremely Large Telescope (ELT) Design Study (DS) is a technology development programme undertaken under the European Commission (EC) Sixth Framework Programme (FP6) by institutes and companies in Europe, Israel and Australia. The ELT DS covers the development of enabling technologies and concepts required for the design and construction of the future European ELT in the optical and infrared range, with a diameter in the order of 4m. This technology development programme covers, among other technological aspects underlying the feasibility of giant telescopes, the control schemes for segmented active telescopes, and the assessment of the performance of a segmented aperture exposed to wind on a representative site. To this aim was conceived the Wind Evaluation Breadboard (WEB), one of the largest ELT DS developments, with the participation of IAC, ALTRAN, JUPASA and ESO. The WEB is, therefore, a simulator of the primary mirror of the ELT. It contains 7 hexagonal segments simulators, 3 position actuators and accelerometers per segment, 24 edge sensors and all the hardware necessary to control and test responses to dynamic loads (wind) and pseudo-static loads (gravity and temperature variations). The segments array is mounted on representative supports and substructures. The high stiffness structures and mechanisms are designed to allow wind tests at different inclinations and orientations. The purpose of WEB is to study the effects of wind on the real time control of the positions of the segments. The WEB, of almost 7 meter diameter, 2.6 meter high, and 25 ton weight will be exposed to open wind flow on a representative astronomical observatory site (IAC Teide Observatory, Canary Islands, Spain), in order to ascertain the performance of the segments supports and control systems in relation to wind excitation, and verify that high spatial and temporal frequency wind disturbances can be controlled to acceptable accuracy on mirror structures. This paper summarises the WEB general requirements, the mechanical design and analysis, the electronics design, and concentrates on the dynamic model and the different control architectures for each segment, modal control and local control, comparing them in performance. * mreyes@iac.es; phone Ground-based and Airborne Telescopes II, edited by Larry M. Stepp, Roberto Gilmozzi, Proc. of SPIE Vol. 72, 72X, (28) X/8/$8 doi:.7/ SPIE Digital Library -- Subscriber Archive Copy Proc. of SPIE Vol X-

2 2. GENERAL REQUIREMENTS As a technology development programme, WEB has multiple purposes. On the one hand, it is a test bench for new position actuator and edge sensor technologies, developed in the framework of the European ELT Design Study. On the other hand, it is a demonstrator of mechanical and control design performance to control the wind effects on a segmented mirror. For this demonstration, the concept of WEB is based on a small assembly of segments simulators, from now on panels, that will be installed on an astronomy site, to work under realistic environmental conditions. The control loop consisting of the edge sensors and the position actuators should be capable of rejecting the effects of wind disturbances and vibrations up to frequencies such that the residual error shall be only a few nanometres. The sampling frequency of the real time control shall be Hz. The essential and indispensable requirements for the experimental setup are therefore: - The prototypes of the sensors and the actuators used in WEB must be identical or at least very similar to the ones that will be used later in the European ELT. - The major characteristics of the support system and the panels itself should be as close as possible to the final design. - The types of disturbances should be similar to the ones expected in an ELT. It is not possible to build WEB on a full scale. This affects both the characteristics and the types of supports and also the control algorithm that can be emulated by WEB. It should use panels with masses similar to the ones expected in an ELT. A pattern of seven panels has been chosen to simulate two types of segment substrates, 3 mirrors of each substrate plus a central panel. The heavy type panels correspond to Zerodur (44 kg each one) and the light-weight panels (3 kg each one) correspond to SiC. The central reference panel, passive, has the function of connecting the panels of the two types in one segmented mirror configuration. The stiffness of the actuators shall be similar to the ones expected in an ELT, so that the local aspects of the control loop can be well simulated and tested. Since the WEB support cell is much stiffer than an ELT cell, that is, has much higher lowest eigenfrequencies, tests of the crosstalk between modes of the full structure and the segment control have to be will not be fully representative. WEB shall have the first resonance mode higher than 2 Hz over the total Azimuth and Altitude kinematics ranges. One of the disturbances is the wind pressure on the panels and on the structure. The wind disturbances in an ELT depend strongly on local parameters like the altitude angle, the height above the ground, and obstacles in front of the telescope location. Changing the wind attack angle, the inclination, and measuring at different wind speeds, WEB shall be capable of generating conditions defined by a power spectrum and spatial correlations similar to the ones expected for adjacent segments in an ELT. The purpose of WEB is not to measure or characterize the wind but to study the effects of the wind on the control of the positions of the panels. The other major disturbance is given by vibrations. With similar parameters chosen for the segments and the actuator stiffness at least the effects of local vibrations should be well emulated by WEB. The first resonance frequency of the panels with supports shall be at least 6 Hz. 3. MECHANICAL DESIGN AND ANALYSIS The main requirements presented in the previous section are driving the design of WEB. From the mechanical point of view, WEB is formed by two main systems: the primary mirror simulator and the telescope simulator. The Telescope Simulator Assembly (TSA), designed by ALTRAN, provides the rotation and elevation capabilities. It is equipped with an azimuth axis to rotate the panels to different angles of incidence with respect to the wind ( to 36º), and with an elevation axis from º to 6º of inclination. It is divided in turn in 5 subsystems. The Azimuth Drive (AZD) is the base structure fixed to the ground. It consists of welded plates, and the rails separated into eight circular sectors. The Base Frame Structure (BFS) is the structure assembled on the AZD rails to allow the azimuth rotation,. It is used also to support the Altitude Drive(ALD), the Rear Support Structure (RSS) and the Cell Mechanical Structure (CMS). The Cell Mechanical Structure (CMS) is a high stiffness structure that simulates the telescope cell and supports the primary mirror simulator. The Altitude Drive (ALD) is the hydraulic system that provides the elevation of the CMS and Proc. of SPIE Vol X-2

3 primary mirror simulator. Finally the mission of the Rear Support Structure (RSS) is to secure the CMS at different elevations and to increase the WEB stiffness during the experiments. The complete WEB mechanical design is shown in figure. ICMSI Altitude Drive IAZDI Figure. WEB complete mechanical design The primary mirror simulator, designed by IAC, is formed by seven Hexagonal Panel Assemblies (HPA). There are 6 active HPAs, and fixed central panel. The central panel is supported by a truss and is used as a reference. 3 active HPAs are designed to hold heavy type aluminum panels (simulating Zerodur) and 3 are designed to hold lightweight aluminum panels (simulating SiC). The HPA integrates the Position Actuators (PACT) and the Edge Sensors (ES). In order to constrain the 6 degrees of freedom of the active panels, 3 different mechanical systems shall be developed: the axial support, the lateral support and the torsional constrainer. Each one is in charge of constraining one or more degrees of freedom e.g., the axial support constrains the translation in axial direction (Z) and two rotations (θx and θy), the lateral support constrains two translations (X and Y) in the panel plane and the torsional constrainer restricts the remaining rotation (θz). Figure 2 shows the active HPA. The whiffletree concept was used for the axial support. It consists of a kinematics support, which equally distributes the mass of the panel to three interfaces in which the PACT are attached. In each kinematics support, only traction or compression forces are allowed. The specified configuration consists of 8 axial support points. For the lateral support it is necessary to obtain a very stiff support in the plane XY and a low stiffness support in the axial direction. A membrane-flexure has been developed in order to obtain this behaviour. A slave actuator is provided to compensate the large axial stroke of the PACT during the panel insertion and removal (5 mm), since the membrane of the lateral support limits the axial displacement For the torsional constrainer a simple two bars directly loaded in traction or compression was designed. It has flexures at the ends in order to minimise the bending stiffness. Two TCS have been designed to fulfill the dynamical requirements (left and right sides), this way the TCS beams allow providing the required axial stiffness to fulfill the dynamic requirements and the low lateral stiffness to deform the beam in the full range of work of the PACT (+7.5mm). Proc. of SPIE Vol X-3

4 A subcell is provided to simplify the transport and integration of /J the HPA; it is the only interface with the CMS. uatof I -J Torsional I constrained Figure 2. Left: Hexagonal Panel Assembly (HPA) main subsystems. Right: Details of the design of the heavy panel (up) and light weight panel (down) Modal, Structural and Thermal analyses were done for the whole HPA and for critical components in order to guarantee the performance of each subsystem, and to determine the appropriate materials for each part. The dynamical analysis has been done in order to determine the eigenfrequencies and the eigenmodes presented in the range from to 25 Hz and to verify that the HPA design fulfills the requirement of 6Hz. The heavy type HPA first eigenfrequency is found at 62.9 Hz, and for the light weight HPA it is found at 75.2 Hz. Those first modes can be seen in figure 3. SPIEL SELOTSIOS STEP SUE IRSOPUS.55 US (Alt) PSYS SUE SUE : AN SEP S 25 7 : ES: PLOP 5. 29U4, 4'J.84 9' ( t' AN SEP :27:57 PIiOP 94. /fy / N r.2s S555 S775 / N Figure 3. HPA dynamical analysis. Left: Heavy HPA, first and second tip tilt eigenmode at 62.9 and 63.Hz. Right: Light Weight HPA, first torsional eigenmode combined with tip tilt and some panel deformation at 75.2Hz 4. CONTROL ELECTRONICS DESIGN 4. WEB general control electronics For the WEB control electronics hardware, a distributed solution has been chosen. It is composed by three computers and two communication switches creating two networks. The first network is for real time communication and is in charge of closing the loop between ES and PACT at KHz. The second network is in charge of the non real time tasks, controlling the azimuth drive, elevation drive, slave actuators, meteorological station, folding dome, and external communications. The network scheme of the WEB control electronics is shown in figure 4. For complete details, see []. The functional description of the computers and switches is the following: Proc. of SPIE Vol X-4

5 . Real time Computer. It is in charge of reading the ES, running the servo-control algorithm and commanding the PACT. It also transmits all the data to Monitoring and storing computer. It is a PXI-887RT computer by National Instruments, running the real time operating system ETS Phar-lap by Ardence. It has two ethernet cards, one for the real time network and another for the non real time one. 2. Switch. It is used only for the communication between the ES, the PACT and the real time computer. 3. GUI computer. It is the computer to be used by the human operator. It is the workstation running Windows XP. 4. Monitoring and storing computer. It checks that all variables in WEB are within range and it stores the data. It is a workstation with improved performance running Windows XP. It has two hard disks working in RAID configuration to store data and two RS485 ports card to communicate with the ultrasonic anemometers. V WEB DOME Triaxial Anemometer E:-] RS 485 RT nesork thdvo iondrive WE central control ele otro ni Cs n'putar for Slave actuators Figure 4. WEB control electronics hardware The software designed and implemented for the WEB has an architecture with three modules defined as:. webgui module, running in the GUI computer. It provides the interface to the user and translates macro commands from the user into small commands to the other modules. It has a service for logs and alarms. 2. webmonitor module, running in the Monitoring and storing computer. It analyzes all data to check that they are within configurable ranges, it produces statistics and stores data in a format suitable for processing off-line. 3. webrt module, running in the Real time computer. It interfaces with ES and PACT and runs the servo algorithm. 4.2 Real time control system The WEB Real Time Electronics is mainly composed of PACTs, Sensors (ES and Accelerometers), and processing units. The 8 Position Actuators (PACT), designed by TNO (The Netherlands), are installed supporting the whiffle trees, to control the panel active Degrees Of Freedoms (DOFs), which are the X,Y rotations (panel tip and tilt) and the Z displacements (panel piston). They are a two stage system. The coarse stage takes care of the required actuator stroke of 5mm with µm accuracy (5 mm if we include the segment extraction). The second stage is a voice coil actuator without friction and hysteresis that bridges the gap to nm accuracy with a translation capacity of about µm. The PACT has been designed as a soft force actuator with an axial stiffness that will give the panel a suspension eigenmode of less than Hz in the axial direction. There are two different types of sensors: 24 Edge Sensors and 8 Accelerometer Sensors. The Edge Sensors (ES), manufactured by FOGALE (France), are inductive sensors formed by two plates located on the side of the HPAs facing each other. These sensors measure the difference in position between two adjacent panels in the Z axis (perpendicular to the segment surface). The Accelerometers Sensors (AS), Si-Flex SF5S, manufactured by Colibrys, are located on the rear face of the panels (in the projection of the PACT over the panel), to measure its acceleration. Proc. of SPIE Vol X-5

6 There are two independent processing units. The WEB Real Time computer and The PACT Control computer. The WEB Real Time computer is a PXI-887RT, manufactured by National Instruments. The PACT Control computer is based on the Innovative Integration SBC673e Digital Signal Processor (DSP). Two DSPs are used, controlling nine PACTs each. Each DSP is connected to the WEB Ethernet network in order to communicate with the WEB Real Time computer. 5. WEB DYNAMIC MODEL The WEB dynamic model has been introduced in [2]. The control system and control algorithms to be used depend heavily on the dynamic behaviour of the mechanical system. For that reason a full WEB FEM model has been developed to derive the dynamic behaviour by modal analysis. The FEM model was generated as a free vibration analysis in Ansys.. The model has elements and 2228 nodes. Lineal beams were used for CMS, HPA lateral and torsion supports. Springs were used for joints between AZD and BFS and PACTs. Masses were used for PACT voice coils and subcells. Shells were used for BFS, AZD, Panels, PACTs and Whiffletrees (see figure 5). A N Figure 5. Left: WEB FEM model, provides the inputs for the dynamic model. Right: First WEB global mode, at 22 Hz. 5. Dynamic model general concept The matrix of the transfer functions between inputs and outputs of the system can be obtained by modal superposition [3][4], which can be expressed as: H ( s) () where ω = n T viui 2 i= s + 2ξ iωis + 2 i H is the matrix of the transfer functions between inputs and outputs of the system. u i is the column vector of displacements in the inputs into the system in mode i. v i is the column vector of displacements in the outputs from the system in mode i. ω i is the angular frequency of mode i. ξ i is the damping ratio of mode i. n is the number of modes considered in the model. In order for equation () to be valid, the modal displacements must be normalized to unit modal mass. As an alternative to the matrix of the transfer functions, the behaviour of the system can also be expressed via a space state model, as follows: x& = Ax + Bs y = Cx I A = 2 B C = [ V ] U = { ui} V = { vi} 2 = U Ω ΞΩ Ω is a diagonal matrix which includes the angular frequencies of the modes. Ξ is a diagonal matrix which includes the damping factors of the modes. (2) where Proc. of SPIE Vol X-6

7 U is a matrix which brings together the modal displacements of the inputs for the different modes. V is a matrix which brings together the modal displacements of the outputs for the different modes. The matrix of the transfer functions (H) has been used to design the controllers quickly and the state space model has been used primarily to verify the stability of the closed system looking at the closed loops poles.the inputs which have been selected for the system are the forces applied on each panel by the PACTs and by the wind. The action of each PACT is applied as two opposing forces acting on two nodes of the model, which correspond to the interfaces of the PACT with the whiffletree and with the central support structure (figure 2). For this reason, in equation () and (2) the difference between the modal displacements of those two points is used.the force of the wind is modelled as punctual forces applied to the surface of the panel at the three points of intersection with the axes of the PACTs. The outputs considered are the displacement of the ES (obtained as the difference between the points of the panels where they are attached) and the displacements of the panels surface where the accelerometers are fixed. The accelerometers have not been explicitly modelled, having used the position instead of acceleration at those points. 5.2 WEB Case All modes of the model up to 5 Hz have been analysed, amounting to 96 modes. Figure 6 shows the transfer function between a PACT and the corresponding position of its accelerometer for one heavy panel (green) and one light panel (blue). Panels of the same type have very similar behaviour. The fundamental modes of the system are the 8 modes associated with the piston, tip and tilt vibration of the panels on the soft stiffness of the PACTs. These modes have frequencies between 8 and Hz for the heavy panels and between 3 and 8 Hz for the light weight panels. There are additional significant modes, local to the panels, starting at 7Hz. Global modes coming from the telescope simulator are at 22, 3 and 46Hz, however their effects are very small thanks to the decoupling of the soft PACTs. Amplitude Phase(deg) Figure 6. Bode plot of the transfer function between a PACT and the corresponding accelerometer position for one light panel (blue) and one heavy panel (green). Left: amplitude. Right: phase. The concept of the soft actuators comes from the concept of having the panels floating in the space with no mechanical link with the cell structure and controlled by the forces introduced with the force actuators. In this condition, the panels are independent. The purpose of the cell structure is to absorb the reactions of the force actuators. In practice it is necessary to link the panels to the cell with a soft stiffness. For frequencies above the natural vibration frequency of the mass of the panels acting on the soft stiffness the concept of decoupled panels is maintained, being coupled for frequency below these modes. 5.3 Model reduction In order to simplify the dynamic model, the number of modes has been reduced. The criteria selected for reduction was to eliminate those modes with a contribution to the global transfer function, acting in the direction of the mode and lower than a certain threshold. Retain mode if h j (s) > threshold H j (s) n T T v j v i u i u j 2 i= s + 2ξ i ω is + T T h j (s) = v j v j u j u j H j (s) = (3) s + 2ξ ω s + ω ω i i i Using a threshold of.5 the model has been reduced to 387 of the 96 initial modes without affecting the dynamical behaviour. i Proc. of SPIE Vol X-7

8 -r 6. MODAL CONTROL ARCHITECTURE The Modal Control Architecture has been presented in [2]. In Figure 7 is included the blocks diagram. There are two main functional blocks: the Panels Global Controller and the Panel Local Controller. The architecture is based on the assumption that the soft PACTs decouple the motion of the panels from the cell and other panels. This means that the control of each panel can be treated independently in a local panel controller, if the panel positions are also measured independently. The position of the panels can be estimated from the readings of the ESs by a matrix multiplication. This function is not local to the panel controller since it is necessary to know all the ES readings to estimate the position of each panel; so it is called global controller. The measurements of the accelerometers are by nature local to the panel and they provide high bandwidth measurements. These two functions will be distributed in the hardware architecture in a natural way: The Panels Global Controller is calculated by The WEB Real Time computer, which transmits the panel position to each local controller. The Panel Local Controllers are calculated by the PACT Control Platform. The Panels Global Controller is formed by a matrix B 8x24 which relates the reading of the ESs to the movements of the panels, 8 PI controllers (each movement of each panel has its own PI controller) and 8 low pass filters (see figure ). ES readings have a delay of 26 µseconds and they are filtered by Bessel low pass filters (cut-off frequency of 2 Hz), these facts are considered in simulations. Each Panel has its own Panel Local Controller, which is explained in the next section. The bandwidth of the PACT Amplifier is 2 khz and it is considered in simulations. z m Co C) r r r H 2J z C) C) m 2J Piston In Out Edge Sensors Tip In 2 Out 2 Low Pass Filters Tilt In 3 Out 3 Panel - B PI Controllers Edge Sensors Tip Tilt Panel - B Piston In In 2 In 3 Out Out 2 Low Pass Filters Out 3 PI Controllers 6 PANEL GLOBAL CONTROLLER DETAIL m Panel Position Tilt Panel Position Tip Panel Position Piston High Pass Filter s 2 (PD+Notch) Piston Piston Accelerometers Tip Tilt High Pass Filter s 2 (PD+Notch) Tip m 2J Matrix C High Pass Filter s 2 (PD+Notch) Tilt PA Amplifier PA- Piston PA Amplifier PA-2 Tip PA Amplifier PANEL LOCAL CONTROLLER DETAIL Figure 7. Left: WEB Control Architecture., showing the panel global controller and panel local controller. Right up: Detail of the Panel Global Controller. Right down: Detail of the Panel Local Controller. 6. Tuning of Panel Local Controllers The Panel Local Controller consists of three PD+Notchs controllers working in the piston, tip and tilt modes of the panel (figure 7). The reading from the three accelerometers are projected to these modes by means of a matrix C, and the control forces produced by the three controllers are projected on the actuator forces by means of a matrix K. Figure 8 shows the outputs of the Matrix C, based on our dynamic model, when the PACTs are excited to provide each mode to the light and heavy panels. For each mode, a PD controller enhanced with notch filters to avoid the destabilizing effect of several modes has been independently tuned. One notch was introduced for the tip-tilt modes, and two for the piston PA-3 Matrix K Tilt Proc. of SPIE Vol X-8

9 modes. Once all 8 controllers are working together the system maintains stability, but the slight coupling requires a gain reduction of 2.24dB to get the same gain margin as in the original controllers. Amp(db) Amp(db) Phase(deg) Phase(deg) Figure 8. Left: Light panel response for piston excitation (blue), tip excitation (red) and tilt excitation (green). Right: Heavy panel response for piston excitation (blue), tip excitation (red) and tilt excitation (green). The use of the Panel Local Controllers to achieve attenuation at very low frequencies is not possible in practice. These controllers use feedback from accelerometers and the panel position has to be estimated by double integration. The first problem is that the acceleration noise integrated to low frequencies gives an inadmissible position noise. The second problem is that any bias error of the acceleration signal will also be integrated to infinite. These are the reasons why the Panel Local Controllers include a high-pass filter. 6.2 Tuning of Panels Global Controller Estimation of the 8 panel positions (piston, tip and tilt for 6 panels) is performed by multiplying the vector formed by the 24 measurement by an estimation matrix B 8x24. This matrix can be obtained from the matrix A 24x8 which relates ES signals to the position of the panels, by least squared method. However, the matrix A 24x8 is singular, due to the geometric disposition of the ES on the panels. When the six external panels rotate simultaneously around the edge common to the central panel, the ESs do not have any relative motion and the measurement is zero. For this reason matrix B is obtained from A 24x8 using a singular value decomposition (SVD). Other telescope such as Keck [3] [4] and GTC [5] [6] use a different disposition of sensors to avoid this singular mode. The attenuation of perturbation at low frequencies is the responsibility of the control loop closed using the ESs. The first attempt was to introduce a proportional gain with the edge sensors compensating a reduction of the proportional gain in the Panel Local Controllers; however this approach destabilized the system. The reason is the presence of local modes of the panels which affect the edge sensors, located at the panel edges, but that have no significant influence on the accelerometers, located in the middle of the panel. The solution was to introduce a low pass filter in the control action of the ESs. This filter is complementary to the high-pass filter used in the panel controller. Using this approach it has been possible to introduce integral and proportional gain to the position measurement performed by the ES. Figure 9 shows the attenuation of perturbations as measured by the accelerometers, using the complete modal control. The cut-off frequency used for the low and high pass filters is 5Hz. It can be seen that piston and tilt have a limited attenuation at low frequencies, as seen by the accelerometers. They do not show the 2dB/decade slope expected due to the integral gain. Figure 2 (left) shows the attenuation as seen by the edge sensors, including the low frequency attenuation. 7. LOCAL CONTROL ARCHITECTURE Figure shows the Local Control Architecture. There are two functional blocks: the Panels Global Controller and the Actuator Local Controllers. This architecture uses soft position actuators which decouple the motion of the panels from the cell and other panels and the same location of ES and accelerometers. The Panels Global Controller estimates the position of the panels from the readings of the ESs by a matrix multiplication. As in the case of the Modal Control, Proc. of SPIE Vol X-9

10 this function is not local to the panel controller since it is necessary to know all the ES readings to estimate the position of each panel. It is a MIMO controller. The Actuator Local Controller is a SISO controller. It uses the measurement of the accelerometer to command the Actuator located next to it. There are three Local Actuator Controllers by panel, working independently. In this case, the Panels Global Controller is similar to the one in the Global Control Architecture, only adding a stage at the output, the Matrix K that relates the movements of the piston, tip and tilt of the panel with the commands applied to the PACTs. The main differences are in the Actuator Local Controller (figure 2). Each Panel has three Actuator Local Controllers. In this case, the Matrix C is the unit matrix. To tune the controllers in the Local Control, as in the Modal Control, we obtain the information of the mechanical behaviour from the Dynamic Model. Amp(db) Amp(db) Figure 9. Attenuation of perturbations measured by the accelerometers using the complete modal control scheme. Piston (blue), tip(red) and tilt (green). Left: Light panel. Right: heavy panel. PANELS GLOBAL CONTROLLER Actuator,2,3 Actuator 4,5,6 Actuator 7,8,9 Edge Sensors Actuator,,2 Actuator 3,4,5 Actuator 6,7,8 Actuators, 2, 3 PAs-, 2,3 Accelerometer, 2,3 Actuators 4, 5, 6 Pas-4,5,6 Accelerometer 4, 5, 6 Actuators 7, 8, 9 Pas-7,8,9 Accelerometer 7,8,9 Actuators,, 2 Pas-,,2 Accelerometer,, 2 PA- PA-2 m PA-3 PA- Accelerometers PA-2 PA-3 Matrix C PA Amplifier PA Amplifier High Pass Filter High Pass Filter High Pass Filter s 2 s 2 s 2 (PD+Notchs ) (PD+Notchs ) (PD+Notchs ) Actuators 3, 4, 5 PA Amplifier PAs-3,4,5 Accelerometer 3, 4, 5 Actuators 6, 7, 8 PAs-6,7,8 Accelerometer 6, 7, 8 Actuator Local Controller Figure. Left: Local Control Architecture. Right: Details of the Actuator Local Controllers Figure compares the crosstalk between modes. On the left, is shown the accelerometers signal for the light panel when there is a piston excitation in Modal Control. On the right, is shown the accelerometers signal when one PA is excited in Local Control. In the Modal Control, the output of the accelerometers is converted into piston, tip and tilt by Matrix C. In the Local Control, the output of Matrix C is directly the signal of the accelerometer. In the Modal Control, is observed that piston and tip are coupled at low frequencies due to the asymmetry of the panel support (due to the mechanical design); however coupling disappears at frequencies where panel inertia is dominant. Therefore, the controller can be designed only for piston, not taking into account potential coupling with the other modes (tip and tilt). The same holds for tip controller and tilt controller. In the case of the Local Control, the accelerometer signals are also coupled at low frequencies, but the coupling is much larger at high frequencies. The controller of each PACT has to take into account this coupling, and the design is much more complicated, and much less efficient if one wants to achieve the same performance as in the Modal Control. Proc. of SPIE Vol X-

11 As in the Modal Control, the Global Controller of the Local Control Architecture uses a low pass filter in the control of the ESs. This filter is complementary to the high-pass filter used in the Actuator Local Controller. Using this approach it has been possible to introduce integral and proportional gain to the position measurement performed by the ES Am p(db) -4-6 Amplitude (db) Figure. Modes coupling: Left: Amplitude of the transfer functions of piston (blue), tip (red) and tilt (green) to piston excitation in a light panel. Right. Amplitude of the transfer functions of Accelerometer- (blue), Accelerometer-2 (red) and Accelerometer-3(green) to one PA excitation of the light panel. Figure 2 shows the attenuation of the tilt signal of the six ES of one light panel, using the complete control scheme of the Modal Control (including Panels Global Controller plus Panel Local Controllers - left) and of the Local Control (including Panels Global Controller plus Actuator Local Controllers - right) when a tilt perturbation is introduced to that light weight panel. It uses a cut-off frequency for the low and high pass filters of 5Hz. In the Modal Control, each Actuator Local Controller (Fig 2) has one PD plus three Notchs (zeros on 63 Hz, 2 Hz and 48 Hz) and one leadlag phase. It can be observed that the high frequencies are contaminated in the Local Control (right) due to this complex design, while it is not the case in the Modal Control. In the figure the low frequency attenuation is larger in the Local Control because it has been optimized, while the Modal Control is only a basic one that can be improved a lot (improve attenuation and bandwidth) without degrading high frequency performance. - - Amp(db) -2 Amp(db) Figure 2. Attenuation of perturbations of the six sensors connected to one light-weight panel for a tilt excitation on the same panel using the complete control scheme. Left: Modal Control. Right: Local Control 8. CONCLUSIONS A mechanical design has been generated that complies with the high eigenfrequencies required, even local modes are above it. The WEB control system achieves the KHz real time samplig rate specified, providing simultaneously all the other capabilities needed. Proc. of SPIE Vol X-

12 The approach of using soft position actuators to decouple the panels allows to tune the controller of each panel independently without having to use a MIMO system with a large number of inputs and outputs. The use of accelerometers to sense panel position, independently of the motion of the cell structure, contributes to this decoupling. The Global controller using ESs needs to process simultaneously all sensors to estimate the panel positions. The use of accelerometers allows this Global Controller to be performed at lower frequencies. In the case of an ELT using thousands of PACTs and ESs this supposes a significant reduction of computational power required, which can be an advantage even taking into account that currently there are techniques to broach this global controller in the range of kilohertz. From the comparison between Local and Modal Control we can draw the following conclusions. In the Local Control, each actuator has a controller that controls all modes that the coupling of the structure and panels have. In the Modal Control, each fundamental mode (piston\tip\tilt) has a controller that controls this mode and its coupled modes, it allows better optimization of the controllers. In the WEB case, for similar attenuation curves, the Local Control has two Notchs and one lead-lag phase more than the Modal Control. The tuning of the coupling modes makes the difference. These coupling modes depend on whether we consider the weight of one panel or the weight of the seven panels over the structure, and the controllers must increase the gain and phase margins (in special on the coupling modes) to avoid instability. For the Local Control is more difficult to achieve this improvement. The decoupling concept is valid having cell modes with natural frequencies larger than the natural modes of the panels on the soft stiffness. In the case of an ELT the structure will have very low frequency modes. These modes will couple the segments, but in a frequency region well within the closed loop bandwidth of the local controllers. It is necessary to check if this coupling destabilize the system. In that case, the coupling can be treated at the level of the global controller, where all the segments are considered simultaneously. 9. ACKNOWLEDGEMENTS We would like to acknowledge all IAC staff also involved in WEB development, as well as ALTRAN team, José Luis Robles from JUPASA and ESO ELT DS Project Office. This activity is supported by the European Community (Framework Programme 6, ELT Design Study, contract No 863) and the Spanish Science and Technology Ministry. [] [2] [3] [4] [5] [6]. REFERENCES M, Núñez, M. Reyes, T. Viera, P. Zuluaga, Wind Evaluation Breadboard Electronics and Software, Advanced Software and Control for Astronomy, Proc. SPIE Vol. 79, Paper 79-2 to be published. Viera Curbelo, T. A, Zuluaga, P., Reyes Garcia-Talavera, M., Núñez Cagigal, M., Castro López-Tarruella, F. J., 28, Wind Evaluation Breadboard Control Architecture, Dynamic Model and Performance, Paper WeA5., 7th IFAC World Congress, July 6-, 28. Jared, et al, The W.M. Keck Telescope segmented mirror active control system, Advanced Technology Optical Telescopes IV, Lawrence D. Barr, Editor, Proc. SPIE Vol. 236, pp 996-8, 99. R.W. Cohen, T.S. Mast, J.E. Nelson, Performance of the W.M. Keck Telescope active mirror control system, Advanced Technology Optical Telescopes V, Larry M. Stepp, Editor, Proc. SPIE 299, pp 5-6, 994. P. Alvarez et al., Gran Telescopio CANARIAS, Conceptual Design, GTC project document GEN/STMA/2-L, 997. Castro, J. et al, Image quality and Active Optics for the Gran Telescopio Canarias, is Advanced Technology Optical/IR Telescopes VI, Larry M. Step, Editor, Proceedings of SPIE Vol. 3352, pp (998). Proc. of SPIE Vol X-2