tmc2008

114 Technical Manufacturing Corporation • 978-532-6330 • 800-542-9725 (Toll Free) • Fax: 978-531-8682 • sales@techmfg.com • www.techmfg.com Technical Background (continued) Equation 16 becomes small, and the closed-loop response becomes large. The difference between the phase of GH and 180° at a unity gain frequency for GH is called the phase margin. The larger the phase margin, the lower the amplification at the unity gain points. It turns out, however, that larger phase margins also decrease the gain of the servo within its active bandwidth. Thus, picking the phase margin is a compromise between gain and stability at the unity gain points. Amplification at unity gain will always happen for phase margins less than 60°. Most servos are designed to have a phase margin between 20° and 40°. Amplification at a servo's unity gain frequencies appear like new resonances in the system. 5.3 Active Vibration Cancellation The previous section provided a qualitative picture of how servos function and introduced the broad concepts and terminology. In reality, most active vibration cancella- tion systems are much more complex than the simple figure shown in Figure 16. There are typically 3 to 6 degrees-of- freedom (DOF) controlled: Three translational (X, Y, and Z motions), and three rotational (roll, pitch, and yaw). In addition, there may be many types of sensors in a system, such as height sensors for leveling the system and accelerometers for sensing the payload's motions. These are combined in a system using parallel or nested servo loops. While these can be represented by block diagrams like that in Figure 16 and are analyzed using the same techniques, the details can become quite involved. There are, however, some general rules which apply to active vibration cancellation servos in particular. Multiple Sensors. Although you can have both an accelerometer measuring a payload's inertial motion, and a position sensor measuring its position relative to earth, you can't use both of them at any given frequency. In other words, the active bandwidth for a position servo cannot overlap with the active bandwidth for an accelerometer servo. Intuitively, this is just saying that you cannot force the payload to track two independent sensors at the same time. This has some serious consequences. Locking a payload to an inertial sensor (an accelerometer) makes the payload quieter; however, the accelerometer's output contains no information about the Earth's location. Likewise, locking a payload to a position sensor will force a payload to track Earth more closely – including Earth's vibrations. You cannot have a payload both track Earth closely and have good vibration isolation performance! For example, if you need more vibration isolation at 1 Hz, you must increase the gain of the accelerometer portion of the servo. This means that the servo which positions the payload with respect to Earth must have its gain lowered. The result is a quieter platform, but one that takes longer to move back to its nominal position when disturbed. This is discussed further in Section 5.6. Gain Limits on Position Servos. As mentioned above, position sensors also couple ground vibration to a payload. This sets a practical limit on the unity gain frequency for a height control servo (like TMC's PEPS ® Precision Electronic Positioning System). To keep from degrading the vibration isolation performance of a system, the unity gain frequency for PEPS is limited to less than 3 Hz. This in turn limits its low-frequency gain (which determines how fast the system re-levels after a disturbance). Its main advantages are more accurate positioning (up to 100 times more accurate than a mechan- ical valve), better damping, better high-frequency vibration isolation, and the ability to electronically “steer” the payload using feedforward inputs (discussed later). It will not improve how fast a payload will re-level. 1 PEPS can also be combined with TMC's PEPS-VX ® System, which uses inertial payload sensors to improve vibration levels on the payload. Structural Resonances. Another important concern in active vibration isolation systems is the presence of structural resonances in the payload. These resonances form the practical bandwidth limit for any vibration isolation servo which uses inertial sensors directly mounted to the payload. Even a fairly rigid payload will have its first resonances in the 100-500 Hz frequency range. This would be acceptable if these were well damped. In most structures, however, they are not. This limits the bandwidth of such servos to around 10-40 Hz. Though a custom-engineered servo can do better, a generic off-the- shelf active vibration cancellation system rarely does. 1 This is an approximate statement, since PEPS is a linear system, and mechanical valves are very non-linear. PEPS generally levels faster for small displacements and slower for large ones.

115Technical Manufacturing Corporation • 978-532-6330 • 800-542-9725 (Toll Free) • Fax: 978-531-8682 • sales@techmfg.com • www.techmfg.com 10 5.4 Types of Active Systems Although we have alluded to “position” and “accelera- tion” servos, in reality these systems can take many differ- ent forms. In addition, the basic performance of the servo in Figure 16 can be augmented using feedforward. The following sections introduce the most common configurations and briefly discuss their relative merits. Figure 17: The basic inertial feedback loop uses a payload sensor and a force actuator, such as a loudspeaker “voice coil,” to affect the feedback. Feedforward can be added to the loop at several points. 5.4.1 Inertial Feedback By far the most popular type of active cancellation system has been the inertial feedback system, illustrated in Figure 17. Note that the pneumatic isolators have been modeled here as a simple spring. Neglecting the feedforward input and the ground motion sensor (discussed in Section 5.4.3), the feedback path consists of a seismometer, filter, and force actuator (such as a loudspeaker “voice coil”). The seismometer measures the displacement between its test mass and the isolated payload, filters that signal, then applies a force to the payload such that this displacement (X 1 - X 2 ) is constant – thereby nulling the output of the seismometer. Since the only force acting on the test mass comes from the compression of its spring, and that compression is servoed to be constant (X 1 - X 2 ? 0), it follows that the test mass is actively isolated. Likewise, since the isolated payload is being forced to track the test mass, it must also be isolated from vibration. The details of this type of servo can be found in many references. 2 The performance of this type of system is always limited by the bandwidth of the servo. As mentioned previously, structural resonances in the isolated payload limit the bandwidth in practical systems to 10-40 Hz (normally towards the low end of this range). This type of system is also “AC coupled” since the seismometer has no “DC” response. As a result, these servos have two unity gain frequencies – typically at 0.1 and 20 Hz. This is illustrated in greater detail in Section 5.6. As a result, the servo reaches a maximum gain of around 20-40 dB at ~2 Hz – the natural frequency of the passive spring mount for the system. The closed-loop response of the system has two new resonances at the ~0.1 and ~20 Hz unity gain frequen- cies. Due to the small bandwidth of these systems (only around two decades in frequency), the gain is not very high except at the natural (open-loop) resonant frequency of the payload. The high gain there completely suppresses that resonance. For this reason, it is helpful to think of these systems as inertial damping systems, which have the property of damping the system's main resonance with- out degrading the vibration isolation performance. (Passive damping can also damp this resonance but significantly increases vibration feedthrough from the ground.) 5.4.2 More Bandwidth Limitations These servos are also limited in how low their lower unity gain frequency can be pushed by noise in the inertial sensor. This is described in detail in the reference of Footnote 2. Virtually all commercial active vibration cancellation systems use geophones for their inertial sensors. These are simple, compact, and inexpensive seismometers used in geophysical exploration. They greatly outperform even high-quality piezoelectric accelerometers at frequencies of 10 Hz and below. Their noise performance, however, is not adequate to push an inertial feedback system's bandwidth to below ~0.1 Hz. To break this barrier, one would need to use much more expensive sensors, and the total cost for a system would no longer be commercially feasible. Another low-frequency “wall” which limits a system's bandwidth arises when the inertial feedback technique is applied in the horizontal direction. (Note that a six degree- of-freedom [DOF] system has three “vertical” and three “horizontal” servos. Horizontal DOFs are those controlled using horizontally driving actuators – X, Y, and twist [yaw]). This is the problem of tilt to horizontal coupling. Feedfor war d Input Isolated Payload Gr ound Motion Sensor X 1 + + + + X 2 K s Seismometer Earth Te s t Mass Pos. Sum Sum For ce Filter Filter Figure 17 2 See for example, P.G. Nelson, Rev. Sci. Instrum., 62, p.2069 (1991).

978-532-6330800-542-9725TollFreewww.techmfg.com, in.mmin.mm, in.mmin.mm, thenpositionedtowithinH110070.001in.in, in.mmin.mm, in.mmin.mm, 978-532-6330800-542-9725TollFreewww.techmfg.com,
www.publitas.com, www.publitas.nl
tmc2008 main