A Non-linear Disturbance-decoupled Elevation Axis Controller for the Multiple Mirror Telescope

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1 A Non-linear Disturbance-decoupled Elevation Axis Controller for the Multiple Mirror Telescope D. Clark a, T. Trebisky a, K. Powell b a Multiple Mirror Telescope Observatory, University of Arizona b Steward Observatory Center for Astronomical Adaptive Optics, University of Arizona 933 N. Cherry Avenue, Tucson, Arizona USA ABSTRACT The Multiple Mirror Telescope (MMT), upgraded in 2000 to a monolithic 6.5m primary mirror from its original array of six 1.8m primary mirrors, was commissioned with axis controllers designed early in the upgrade process without regard to structural resonances or the possibility of the need for digital filtering of the control axis signal path. Postcommissioning performance issues led us to investigate replacement of the original control system with a more modern digital controller with full control over the system filters and gain paths. This work, from system identification through controller design iteration by simulation, and pre-deployment hardware-in-the-loop testing, was performed using latestgeneration tools with Matlab and Simulink. Using Simulink s Real Time Workshop toolbox to automatically generate C source code for the controller from the Simulink diagram and a custom target build script, we were able to deploy the new controller into our existing software infrastructure running Wind River s VxWorks real-time operating system. This paper describes the process of the controller design, including system identification data collection, with discussion of implementation of non-linear control modes and disturbance decoupling, which became necessary to obtain acceptable wind buffeting rejection. Keywords: Telescope, control system, non-linear, Matlab, digital filter, system identification, generated code 1. INTRODUCTION The Multiple Mirror Telescope Observatory (MMTO), a joint project of the Smithsonian Institution and the University of Arizona, operates the MMT, a 6.5m telescope located at the summit of Mount Hopkins near Tucson, Arizona. It was upgraded from its original array of six 1.8m primary mirrors with a new 6.5m borosilicate honeycomb primary mirror cast at the Steward Observatory Mirror Lab in Construction and installation of the major telescope components (mirror cell, forward truss structure, secondary mirror hub, etc.) was completed during the late 1990 s and first light was achieved in May The early design of the telescope and drives was undertaken without particular regard to FEA (finite element analysis) of the drive system and stiffness of structural elements in the interest of quickly realizing telescope operation. The resulting controller design for the azimuth and elevation axes assumed perfectly stiff drive components, which naturally does not obtain in practical systems. In order to increase the telescope servo controller performance, MMTO began the process of designing and deploying new controllers. We describe here the elevation controller design, as that particular axis had significant issues with structural resonant modes and concomitant difficulties in controller tuning, and we have not yet started upgrading the other telescope axes. 1.1 Original Elevation Controller The as-commissioned controller used a dual-loop architecture with the outer position loop closed on the on-axis Inductosyn absolute encoder and an inner velocity loop closed on one of two available motor shaft encoders. The outer loop ran in software on a MVME167 Motorola CPU with a gain-switching PID (Proportional Integral Derivative) algorithm. The inner loop used a National Semiconductor LM628 motor controller to accept velocity commands over the VME bus and output torque commands via a DAC (digital-to-analog converter) to the motor amplifiers (figure 1). The amplifiers in turn drive a pair of DC brush motors with friction wheels to move the elevation axis. This controller was commissioned and used with tuning parameters obtained empirically and the motor amplifiers set to voltage-source mode for the first 18 months or so of operation [1]. Empirical tuning led us to increase the servo

2 gains and investigate changes to the controller operation to improve wind disturbance rejection during science object tracking, at the cost of gain peaking in the closed-loop controller (figure 2). Figure 1. Simplified original MMT elevation controller block diagram. Figure 2. Closed-loop Bode diagram of the MMT elevation axis controller taken using an HP 35670A Dynamic Signal Analyzer showing the difference between voltage-source and current-source motor amplifiers. Clearly, the controller exhibited marginal stability in the 2-3Hz region and positive gain at the main structural resonant frequency of 6Hz. In addition, a strong 20Hz mode is present. This poor performance motivated the improvement of the elevation controller.

3 2. Post-commissioning Servo Improvements After commissioning, several avenues of improving the performance of the elevation drives were investigated. A major impediment during this period was the inability to log and analyze the controller signals during operation as the controller architecture did not lend itself well to telemetry with the tools available at the time. Most of the early work with the servos involved measuring the analog signals in the controller with an HP 35670A Dynamic Signal Analyzer (DSA), along with judicious use of an accelerometer and dial gauges to discover where the drive system compliances were located. 2.1 Motor Compliance The elevation drive motors use a unique drag-link parallelogram to hold the motor s friction wheel in alignment with the elevation drive arc section (figure 3). A Belleville washer spring stack underneath the motor assembly maintains the necessary preload of the friction wheel against the drive arc. Early measurements showed that the motor housing assembly walked across the drive arc in a way that was out of parallel with the telescope s elevation motion. This means that small changes in the drive arc runout and drive housing orientation resulted in a non-linear and nonrepeatable change in the mechanical advantage and encoder scaling in the velocity loop. The drag-link assembly also lacks an anti-rotation outrigger to prevent the housing from relaxing and rotating away from the motor load during torque reversals. In short, the motor mounts were insufficiently stiff. To cure this, we a) carefully aligned the motor into the center of the drive arc track, b) stiffened the drag-link flexure members, and c) installed tape encoders. Figure 3. One of two elevation drive motor assemblies with drag link, tape encoder head, and friction drive arc shown. 2.2 Tape Encoders Part of the design of the new MMT primary mirror cell and elevation drive system was the provision to install linear tape encoders along both drive arcs. The mounting surface for the tapes was precision ground during construction of the cell by grinding the tape surface on trunnions using the mirror cell bearings as a turning support for the entire assembly. This allowed us to install a fixed encoder read head without worry about maintaining the air gap tolerance with a follower assembly thanks to the high precision of the grinding operation. We installed Heidenhain LIDA105C tapes to these surfaces with EXE602E 25X interpolators for quadrature counting of the tape marks. Using one of the two tapes as a velocity loop feedback greatly improved the linearity and performance of the velocity loop.

4 2.3 Motor Amplifiers The motor amplifiers used for the MMT elevation axis are Copley Controls Model 262A PWM (pulse-widthmodulated) amplifiers with internal LC filters for low-noise output. They are easily switchable from a current-source output (e.g. a current is output proportional to the input control voltage), to a voltage-source output. As mentioned above, one of the early changes to the controller was to go to current-source output. 3. Servo Re-design The next round of servo work was aimed towards development of a completely new controller that included modal frequency suppression and native telemetry for debugging and performance measurement. We also migrated away from the now-obsolete Motorola VME CPU to a commodity PC chassis with PCI i/o boards. 3.1 System Identification The first step in design of the new servo was to identify the elevation axis response to torque inputs. Reduction of the open-loop response data to an LTI (Linear Time-Invariant) model enabled the offline analysis of the elevation axis and candidate control loop designs using Simulink. To collect the open-loop data, we used a surplus desktop PC with PCI i/o boards running The Mathworks real-time kernel, xpc Target. This kernel is one of several possible targets using Real Time Workshop, a tool for automatic generation of real-time executable code from Simulink diagrams, available as an add-on to Simulink from The Mathworks. With xpc Target s tight integration with the Matlab/Simulink environment, controller code can quickly be generated, and native telemetry allows for immediate data analysis and visualization, either during operation (hardware-in-the-loop), or post hoc. It also includes drivers for many different i/o boards to eliminate the work of driver development [2]. Since MMTO did not have any supported boards on hand, custom drivers were written for the boards that we did have available and installed in the xpc Target test machine. Since xpc Target is a fairly lightweight kernel, this was not as insurmountable as it may sound; the source code for all the other drivers under xpc Target is provided as part of the xpc Target installation so many examples are available. Other Simulink S-functions were created for utilities and to enable generation of excitation chirp signals. Figure 4. Simulink diagram for generating real-time code to collect open-loop data with xpc Target. Yellow blocks are hardware i/o, and the numbered elliptical ports are signal logging points.

5 Figure 5. Open-loop Bode plots for all 3 available MMT secondary mirror configurations. 3.2 Initial Controller Design Once the open-loop data was collected, the responses were reduced to mathematical models for simulation and analysis with candidate controller topologies. Several iterations of the simulation/comparison process resulted in a dual-loop topology with modal suppression filters (figures 6 and 7). Figure 6. Simplified elevation controller block diagram.

6 Figure 7. Overlay of the notch filter center frequencies with the measured open-loop structural resonant modal frequencies. 3.3 Design Verification The next step in design was to confirm that the controller performed as predicted by simulation. We generated code from the Simulink controller design, replacing the signal i/o points driving the telescope model with hardware driver blocks for the DAC output and encoder feedback input. Testing with the xpc Target controller gave good agreement with the Simulink model (figure 8). Figure 8. Comparison of the step response and Bode frequency response for the new elevation controller. The model is strictly linear, so we neglect for the purposes of tractable simulation physical nonlinearities such as friction and hysteresis.

7 3.4 Wind Disturbance Rejection Measurement Next, we needed measurements of the tracking performance of the new controller in the presence of wind disturbance. Figure 9. Time series tracking error of the LM628-based controller and the xpc Target test controller in wind. Figure 10. Comparison of the PSDs of the two controllers tracking error in wind.

8 From the above, it is easily seen that while modal suppression was successfully achieved with the xpc Target controller since the peaks at 6 and 20Hz were eliminated, it had less disturbance rejection than the LM628-based controller due to the higher error power present between 0.5 to 2Hz. 3.5 Improving Disturbance Rejection Since the wind disturbance rejection needed improvement below about 2Hz, the first step was to increase the lowfrequency gain in the controller. This is in tension with the requirement to maintain stability during large motions and when the telescope secondary/instrument configuration changes. Figure 11. Non-linear integral gain block in the position loop PID. The input is the position error signal, and the output is the current Integral gain that is subsequently multiplied by the error signal value. The non-linear integral gain block is similar to that used for the command pre-processor implemented for limiting velocity and acceleration; it smoothly varies the gain without inducing switching transients [3]. Using this approach improved the wind disturbance rejection about 20%, so further improvements were necessary. The command preprocessor also provides the important function of smoothing command signal inputs so transients in the signal path don t excite structural resonances in the drive system. We next augmented the controller with a Luenberger observer [4]. Using a model of the telescope plant response to known inputs running in parallel with the actual system allows estimation of an external disturbance so a scaled inverse of the disturbance can be used to cancel it. This approach is also known in industry as disturbance decoupling.

9 Figure 12. Block diagram of the complete elevation controller. The lower three blocks form the Luenberger Observer and disturbance decoupling signal path. The command pre-processor in the command signal path is not shown. Figure 13. Comparison of closed-loop Bode responses through the command-signal path (left side) and disturbance rejection (right side) for the non-linear position loop integral and the disturbance decoupling augmentation. In disturbance decoupling, the controller s torque command signal is used to drive a model of the open-loop telescope rigid-body plant, or observer model. The observer s output is the predicted encoder position; the real telescope encoder value is compared to form an observer error signal. This is compensated via PID and fed back into the observer to ensure that observer model inaccuracies don t accumulate without bound. If the observer model is sufficiently accurate and the observer compensator bandwidth is high enough, deviations from the rigid-body observer prediction may be presumed to be disturbances. This is scaled through a non-linear gain block that only allows disturbance decoupling authority when the position error is small and summed into the controller s DAC output signal to cancel the disturbance torque. This ensures that disturbance decoupling is only active while tracking.

10 Figure 14. Actual tracking performance achieved with the non-linear disturbance decoupled controller during operation. 3.6 New Controller Deployment Part of deploying the new controller was migrating away from the ancient VME hardware, which used the now-obsolete MC68040 CPU and getting-scarce IP (IndustryPack) i/o modules. We built a completely new rack-mount PC with an Intel Pentium IV processor and new PCI-bus i/o boards for encoder feedback and DAC output, all on a commodity Intel motherboard. This was then connected to our existing signal handling infrastructure in place of the old controller hardware. Simulink s Real Time Workshop (RTW) makes use of a scripting language to control generation of real-time code from the block diagram called the Target Language Compiler (TLC), in addition to a template makefile, and make command. A number of standard packaged targets are available in RTW; for our purposes, a custom TLC script was needed for code generation into our existing Wind River VxWorks target environment. Using the TLC and make scripts supplied with Simulink RTW for the VxWorks Tornado target as a template, we developed a modified version to generate code for our licensed VxWorks PC-486 target, which does not include Tornado. Running GNU gcc on a Fedora Linux host, we use the generated source code to cross-compile to an executable code object for the VxWorks target rack-mount PC. We use fairly simple Simulink S-functions to bring encoder data and commands into the controller, and status and logging information out of it. Two real-time tasks comprise the control system. One is the controller itself; the second runs the server that handles the Simulink remote protocol. This Simulink support library has been straightforward to build for VxWorks. As the Intel Pentium processor line retains backward-code compatibility for earlier x86 architectures, the PC-486 code runs on the newer processor without modification. We did spend substantial effort to write device drivers for the PCIbus i/o boards, including writing a PCI-bus support library for VxWorks. Much of the driver code for our legacy IPmodule devices could be compiled with only a few changes once the PCI code for the carrier card was working. We needed to modify our timekeeping code to allow us to compensate for the bizarre base clock frequency used in an industry-standard PC (e.g. the clock crystal is MHz which does not neatly divide down to the 1kHz servo rate). We use the Intel eepro100 network card that is supported by VxWorks. We were able to use the PXEboot software built into this card for diskless boot, simplifying the controller hardware.

11 4. Future Directions MMTO continues to pursue improvements in the elevation controller s performance. We are currently investigating optimization of the controller gains and disturbance-decoupling signal path to improve tracking in high-wind conditions. We also plan to upgrade the azimuth and instrument rotator axes in a manner similar to that used for the elevation axis. References and Further Reading [1] D. Clark, MMTO Internal Technical Memorandum #03-5, Selected Results of Recent MMT Servo Tuning, [2] D. Clark, MMTO Internal Technical Memorandum #04-3, Control System Prototyping, A Case Study, [3] W. Gawronski and W. Almassy, Command Preprocessor for Radio Telescopes and Microwave Antennas, IEEE Antennas and Propagation Magazine, Vol. 44, No. 2, April [4] G. Ellis, Observers in Control Systems, Elsevier Press, 2002 ISBN X Author Contact Dusty Clark Tom Trebisky Staff Engineer, Senior Staff Engineer, Senior MMT Observatory MMT Observatory University of Arizona University of Arizona 933 N. Cherry Avenue 933 N. Cherry Avenue Tucson, Arizona Tucson, Arizona (520) voice (520) voice (520) fax (520) fax dclark@mmto.org tom@mmto.org Keith Powell Steward Observatory Center for Astronomical Adaptive Optics University of Arizona 933 N. Cherry Avenue Tucson, Arizona (520) voice (520) fax kpowell@as.arizona.edu