Abstract:
In one implementation, a method for operating a plurality of MEMS devices including applying a magnitude of a selected actuation signal equal to a first substantially constant magnitude to an actuator to cause a movable structure to begin to accelerate from a first position to impact a motion stop at a second position. The method also includes decreasing the magnitude of the selected actuation signal in a first manner. The method further includes varying at least one of a start time and a duration of the decreasing magnitude of the selected actuation signal and observing a settling time of the movable structure in response to the step of varying. In some implementations, the method includes ascertaining a range of values for the start times and the corresponding durations for each of the plurality of MEMS devices that are capable of providing settling times of the movable structure in conformance with a predetermined specification based on the steps of varying and observing. Such an implementation can include using the ascertained range of values for each device and the selected actuation signal for determining an operating start time and a corresponding operating duration to construct an operating actuation signal capable of providing a settling time for all devices in conformance with the predetermined specification. The method also can include controlling a signal source with a programmed processor to selectively apply the operating actuation signal to the plurality of MEMS devices.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of copending U.S. patent application Ser. No. 09/783,730 filed Feb. 13, 2001, by Kruglick, et al., entitled METHOD AND APPARATUS FOR ELECTRONIC DAMPING OF COMPLEX DYNAMIC SYSTEMS, herein incorporated by reference in its entirety. This application is also related to U.S. patent application Ser. No. 09/896,022, by Kruglick, entitled ELECTRONIC DAMPING OF MEMS DEVICES USING A LOOK-UP TABLE, filed herewith, herein incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Optical switching plays an important role in telecommunication networks, optical instrumentation, and optical signal processing systems. Optical switches can be used to turn the light output of an optical fiber on or off with respect to an output fiber, or, alternatively, to redirect the light to various different fibers, all under electronic control. Optical switches that provide switchable cross connects between an array of input fibers and an array of output fibers are often referred to as “optical cross-connects.” Optical cross-connects are a fundamental building block in the development of an all-optical communications network. 
     There are many different types of optical switches. One general class of optical switches may be referred to as “bulk optomechanical switches” or simply “optomechanical switches.” Such switches employ physical motion of one, or more, optical elements to perform optical switching. An optomechanical switch can be implemented either in a free-space approach or in a waveguide (e.g., optical fiber) approach. The free-space approach is more scalable compared to the waveguide approach. 
     In optomechanical switches employing the free space approach, optical signals are switched between different fibers by a number of different methods. Typically, these methods utilize selective reflection of the optical signal off of a reflective material, such as a mirror, into a fiber. The optical signal passes through free space from an input fiber to reach the mirror, and after reflection, passes through free space to an output fiber. The optical signals are typically collimated in order to minimize coupling loss of the optical signal between an input and output fiber. 
     Micro-Electro-Mechanical Systems or MEMS are electrical-mechanical structures typically sized on a millimeter scale or smaller. These structures are used in a wide variety of applications including for example, sensing, electrical and optical switching, and micron scale (or smaller) machinery such as robotics and motors. MEMS structures can utilize both the mechanical and electrical attributes of material to achieve desired results. Because of their small size, MEMS devices may be fabricated utilizing semiconductor processing methods and other microfabrication techniques such as thin film processing and photolithography. Once fabricated, the MEMS structures are assembled to form MEMS devices. 
     MEMS structures have been shown to offer many advantages for building optomechanical switches. Namely, the use of MEMS structures can significantly reduce the size, weight and cost of optomechanical switches. The switching time can also be reduced because of the lower mass of the smaller optomechanical switches. 
     Movable MEMS structures are capable of oscillating uncontrollably if they are not damped. Such oscillation is due to MEMS structure design and/or fabrication. For example, very low friction in the hinges of MEMS structures allows them to move easily and repeatedly bounce off of stationary objects such as motion stops. Known methods for damping MEMS structures do not provide quick and efficient damping for all types of structures. Thus, there is a need for a method and/or apparatus that provides quick and efficient damping of MEMS structures. 
     SUMMARY 
     In one implementation, a method for operating a plurality of MEMS devices including applying a magnitude of a selected actuation signal equal to a first substantially constant magnitude to an actuator to cause a movable structure to begin to accelerate from a first position to impact a motion stop at a second position. The method also includes decreasing the magnitude of the selected actuation signal in a first manner. The method further includes varying at least one of a start time and a duration of the decreasing magnitude of the selected actuation signal and observing a settling time of the movable structure in response to the step of varying. In some implementations, the method includes ascertaining a range of values for the start times and the corresponding durations for each of the plurality of MEMS devices that are capable of providing settling times of the movable structure in conformance with a predetermined specification based on the steps of varying and observing. Such an implementation can further include using the ascertained range of values for each of the plurality of MEMS devices and the selected actuation signal for determining an operating start time and a corresponding operating duration to construct an operating actuation signal capable of providing a settling time for each of the plurality of MEMS devices in conformance with the predetermined specification. In certain implementations, the method also can include controlling a signal source with a programmed processor to selectively apply the operating actuation signal to the plurality of MEMS devices. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a top view illustrating a two-dimensional optical switch having MEMS switching cells. 
     FIG. 2 is a simplified perspective view illustrating one of the MEMS switching cells shown in FIG. 1 in the transmission position. 
     FIG. 3 is a simplified perspective view illustrating the MEMS switching cell shown in FIG. 2 in the reflection position. 
     FIG. 4 is a plot illustrating an actuation signal and resulting output signal when the actuation signal is applied to the MEMS switching cell shown in FIG.  2 . 
     FIG. 5 is a simplified perspective view illustrating the actuator plate of the MEMS switching cell shown in FIG. 2 bouncing off of the motion stop. 
     FIG. 6 is a plot illustrating an actuation signal in accordance with an embodiment of the present invention and the resulting output signal when the actuation signal is applied to the MEMS switching cell shown in FIG.  2 . 
     FIG. 7 is a plot further illustrating the actuation signal shown in FIG.  6 . 
     FIG. 8A is a representative plot illustrating the torque and velocity that result from the actuation signal shown in FIG.  4 . 
     FIG. 8B is a representative plot illustrating the torque and velocity that result from the actuation signal shown in FIG.  6 . 
     FIGS. 9A,  9 B,  9 C,  9 D,  9 E and  9 F are plots illustrating actuation signals in accordance with alternative embodiments of the present invention. 
     FIG. 10 is a plot illustrating an actuation signal in accordance with another embodiment of the present invention and the resulting output signal when the actuation signal is applied to the MEMS switching cell shown in FIG.  2 . 
     FIG. 11 is a block diagram illustrating an exemplary system for generating the actuation signal shown in FIG. 6 in accordance with one embodiment of the present invention. 
     FIGS. 12A and 12B are simplified perspective views illustrating the use of an actuation signal in accordance with another embodiment of the present invention with a complex dynamic system that is actuated using electromagnetic attraction. 
     FIGS. 13A and 13B are simplified perspective views illustrating the use of an actuation signal in accordance with another embodiment of the present invention with a MEMS switching cell that is actuated using electromagnetic attraction. 
     FIG. 14 is a block diagram illustrating an exemplary system for constructing and supplying the actuation signal to a MEMS array in accordance with an embodiment of the present invention. 
     FIG. 15 is a plot illustrating the effects of varying the offset and duration of the divot in the actuation signal of FIG.  6 . 
     FIG. 16 illustrates a method for determining a damping characteristic for each of the switches in an array in accordance with an implementation of the present invention. 
     FIG. 17 is a block diagram illustrating an exemplary system for constructing and supplying the actuation signal to a MEMS array in accordance with an embodiment of the present invention. 
     FIG. 18 is a block diagram illustrating an exemplary system for constructing and supplying the actuation signal to a MEMS array in accordance with an embodiment of the present invention. 
    
    
     DESCRIPTION 
     This application hereby incorporates by reference in its entirety, U.S. patent application Ser. No. 09/783,730, by Kruglick, et al., entitled METHOD AND APPARATUS FOR ELECTRONIC DAMPING OF COMPLEX DYNAMIC SYSTEMS, and hereby incorporates by reference in its entirety U.S. patent application Ser. No. 09/896,022, filed herewith, by Kruglick, entitled ELECTRONIC DAMPING OF MEMS DEVICES USING A LOOK-UP TABLE. 
     The following description is not to be taken in a limiting sense, but is made for the purpose of describing one or more embodiments of the invention. The scope of the invention should be determined with reference to the claims. 
     Referring to FIG. 1, there is illustrated an optical crossbar switch  100 , or simply, an optical switch  100 . The optical switch  100  is a two-dimensional (2D) optical switch that is capable of providing switchable cross connects between an array of input fibers  103  and an array of output fibers  121 . Specifically, the optical switch  100  provides an array of free-space optical connections between the input and output fibers  103 ,  121 . This enables each of a plurality of optical input channels to be directed to a desired optical output channel. Each of the optical input channels may also be dropped via the dropped channel fibers  123 , or other channels may be added via the add channel fibers  111  to replace certain input channels. That is, the optical switch is capable of performing optical switching as well as wavelength-selective add/drop filtering. 
     A cable  102  containing a plurality of input fibers  103  is incident upon a demultiplexer  104 , which separates the optical beam carried by each fiber into a number of input channels. The input channels are provided, via a collimator array  106 , to an array  108  of optomechanical switching cells. Similarly, a cable  110  containing a plurality of add channel fibers  111  is incident upon a demultiplexer  112  followed by a collimator array  114 . The optomechanical switching cells can be configured to direct particular input channels to desired output channels, as well as to implement the channel add/drop functionality mentioned above. Separate multiplexers  116 ,  118  are provided for multiplexing the output channels and the “dropped” channels onto the fibers  121 ,  123  of separate cables  120 ,  122 , respectively. 
     The array  108  of optomechanical switching cells are connected to a substrate  124 . The optomechanical switching cells are preferably fabricated in accordance with Micro-Electro-Mechanical Systems (MEMS) technology. Each of the switching cells includes a mirror and an actuator. The lenses of the collimator arrays and the mirrors of each MEMS switching cell are aligned so that each switching cell can selectively intercept a beam output from one of the collimator arrays. 
     FIGS. 2 and 3 are simplified diagrams illustrating an exemplary MEMS switching cell  200  that may be included in the array  108  of optomechanical switching cells. A micromirror  202  is mounted to an actuator plate  204 . The actuator plate  204  is hingedly connected to the substrate  124  with a torsion hinge  206 , which by way of example may be of the type described in U.S. patent application Ser. No. 09/697,762, filed Oct. 25, 2000, entitled “MEMS Optical Switch with Torsional Hinge and Method of Fabrication Thereof”, by inventor Li Fan, and identified by attorney docket number  1008 , the entire contents of which are hereby expressly incorporated by reference into the present application as if fully set forth herein. The micromirror  202  is shown in a vertical position with the mirror surface being perpendicular to the substrate  124 . Another torsion hinge (not shown) may be used to permit the micromirror  202  to pivot relative to the actuator plate  204 . 
     FIG. 2 illustrates the switching cell  200  in its transmission state, and FIG. 3 illustrates the switching cell  200  in its reflection state. In the reflection state, the actuator plate  204  rests on a motion stop  208  (or other landing structure) mounted on the substrate  124 . By way of example, the motion stop  208  may comprise a jack stop of the type described in U.S. patent application Ser. No. 09/697,767, filed Oct. 25, 2000, entitled “MEMS Microstructure Positioner and Method of Fabrication Thereof”, by inventor Li Fan, and identified by attorney docket number  1013 , the entire contents of which are hereby expressly incorporated by reference into the present application as if fully set forth herein. During operation, an optical beam  210  is incident at an approximately 45° angle from the normal of the micromirror  202 . By pivoting the actuator plate  204  about the torsion hinge  206 , the micromirror  202  is moved in and out of the path of the optical beam  210 , switching the output of the optical beam  210  between a reflection direction  212  and the transmission direction ( 210  of FIG.  2 ). 
     The actuator plate  204 , an actuator electrode  214  mounted on the substrate  124 , and the gap therebetween form an electrostatic actuator. In one embodiment, the switching cell  200  is activated by a circuit that selectively develops an electrostatic force between the actuator plate  204  and the actuator electrode  214 . This force causes the actuator plate  204  and the micromirror  202  mounted thereto to pivot in angular position relative to the substrate  124 , i.e., in the direction indicated by arrow  216 . In other words, when a voltage bias, symbolized by voltage source  218 , is applied between the actuator plate  204  and the actuator electrode  214  (or substrate  124 ), the actuator plate  204  is caused to draw close and contact the motion stop  208 . Thus, a voltage bias is applied between the actuator plate  204  and the actuator electrode  214  to cause the switching process by electrostatic attraction. Alternate actuation methods/forces may also be used, such as for example, electromagnetic, thermal expansion, and piezoelectric. Such alternate actuation methods/forces will be discussed below. 
     Because of the presence of the motion stop  208 , the MEMS switching cell  200  forms a complex dynamic system for purposes of analyzing the angular movement of the actuator plate  204 . A complex dynamic system may also be referred to as a nonlinear system. The MEMS switching cell  200  forms a complex dynamic system because the motion stop  208  causes the actuator plate  204  to move in a vibrating manner when the actuator plate  204  impacts the motion stop  208 . 
     In order to bring the actuator plate  204  to rest on the motion stop  208  as quickly as possible, damping is used. The damping of moving structures in complex dynamic systems is difficult, and such systems do not lend themselves to conventional methods of damping. In order to illustrate this difficulty, reference is made to FIG. 4, which illustrates a conventional actuation signal  230  and the resulting output signal  232  for the MEMS switching cell  200 . In accordance with known principles, the actuation signal  230  can be made to provide effective damping in many non-complex dynamic systems that do not have motion stops. FIG. 4 illustrates the result of application of the actuation signal  230  to the switching cell  200 , which is a complex dynamic system. 
     The actuation signal  230  is applied to the electrostatic actuator, i.e., between the actuator plate  204  and the actuator electrode  214 , to create a force that pulls the actuator plate  204  towards the motion stop  208 . The resulting output signal  232  represents the optical power of the output optical beam  212  that is reflected off of the micromirror  202 . 
     As illustrated, shortly after the actuation signal  230  is activated, the output signal  232  starts oscillating and then eventually settles in its on state, i.e., full optical power of the reflected output optical beam  212 . The output signal  232  oscillates because the downward force imparted on the actuator plate  204  by the actuation signal  230  causes the actuator plate  204  to bounce off of the motion stop  208  several times. This bouncing, depicted in FIG. 5, causes the micromirror  202  to move through and within the optical path several times, which switches the output optical beam  212  between the reflection and the transmission states several times creating the oscillating output signal  232 . In this example, it takes 11.36 milliseconds (ms) for the output signal  232  to reach 90% settlement. As evidenced by this rather lengthy settlement time, the actuation signal  230  does not provide quick and efficient damping in complex dynamic systems that have motion stops. 
     It is desirable to minimize the settlement time of the actuator plate  204  in order to reduce the switching time. Such a reduction in the switching time of the MEMS switching cells increases the performance of the optical switch  100 . The settlement time of the actuator plate  204  can be reduced by employing a damping method that provides more effective damping than the damping provided by the actuation signal  230 . 
     Referring to FIG. 6, there is illustrated an actuation signal  240  in accordance with one embodiment of the present invention. The actuation signal  240  provides highly effective damping of a structure in a complex dynamic system having a positive motion stop. Similar to above, the actuation signal  240  is the signal that is applied between the actuator plate  204  and the actuator electrode  214  to create a force that pulls the actuator plate  204  towards the motion stop  208 . The resulting output signal  242  represents the optical power of the output optical beam  212  that is reflected off of the micromirror  202 . 
     As illustrated, shortly after the actuation signal  240  is activated, the output signal  242  rises above 90% of its maximum level and stays there. The oscillations in the output signal  242  are small and do not fall below the 90% level. In this example, it takes only 3.5 ms for the output signal  242  to reach 90% settlement. Thus, the actuation signal  240  provides a greatly reduced settling time as compared to the settling time achieved with the actuation signal  230  of FIG.  4 . 
     The actuation signal  240  provides highly effective damping because it reduces the magnitude of bouncing off of the motion stop  208  and reduces the length of time that the actuator plate  204  bounces off of the motion stop  208 . These features reduce the settling time of the actuator plate  204 . In this way, the actuation signal  240  provides electronic damping of the actuator plate  204 . 
     Referring to FIG. 7, the actuation signal waveform  240  provides highly effective and simple to implement electronic damping for the actuator plate  204  (of FIGS. 2 and 3) at the mechanical motion stop  208  (of FIGS.  2  and  3 ). Important characteristics of the signal  240  are a decrease in drive timed with respect to the first impact of the moving actuator plate  204  on the motion stop  208 . Specifically, the actuation signal waveform  240  preferably begins with an acceleration phase  244  during which the actuator plate  204  accelerates towards the motion stop  208 . In one embodiment, the acceleration phase  244  involves the application of a substantially constant magnitude voltage between the actuator plate  204  and the actuator electrode  214  (of FIGS.  2  and  3 ). The acceleration phase  244  is followed by a coast phase  246  where the acceleration of the actuator plate  204  is decreased as it approaches the motion stop  208 . The coast phase  246  involves decreasing the magnitude of the actuation voltage in a linear manner prior to the actuator plate  204  impacting the motion stop  208 . Next, a segue phase  248  increases the downward force on the actuator plate  204  at about the time the actuator plate  204  impacts the motion stop  208 . The segue phase  248  involves increasing the magnitude of the actuation voltage in a linear manner. Finally, a hold down phase  250  applies maximum downward force to the actuator plate  204  to hold it against the motion stop  208 . The hold down phase  250  involves leveling off the magnitude of the actuation voltage. 
     FIG. 8A illustrates the torque and velocity of the actuator plate  204  (of FIGS. 2 and 3) resulting from the actuation signal  230  (of FIG.  4 ), and FIG. 8B illustrates the torque and velocity of the actuator plate  204  resulting from the actuation signal  240  (of FIG.  6 ). Torque and the actuation signal voltage have the following approximate electrostatic relationship:              Torque   ∝       Voltage   2       gap   2               (   1   )                                
     where the “gap” is the distance between the actuator plate  204  and the actuator electrode  214 . 
     With the actuation signal  230 , the torque and velocity continue to increase right up to the motion stop  208 . This causes severe bouncing of the actuator plate  204 . In contrast, with the actuation signal  240 , the torque and velocity do not continue to increase right up to the motion stop  208 . Instead, the torque and velocity decrease somewhat from the values which signal  230  would cause before reaching the motion stop  208 , which reduces the strength of the bounce of the actuator plate  204 . 
     Referring to FIG. 7, important parameters for the actuation signal waveform  240  are: (1) the total time “η” for the acceleration and coast phases  244 ,  246 ; and (2) the decrease (or depth) in voltage “d” during the coast phase  246 . In one embodiment of the invention, the depth of modulation “d” is chosen to target an approximately 30-50% reduction in drive as the actuator plate  204  touches down on the motion stop  208 . By way of example, “d” may be approximately equal to 40-60% of the substantially constant magnitude of the acceleration phase  244 . Furthermore, by way of example, the coast phase  246  may involve decreasing the magnitude of the actuation signal from the substantially constant magnitude of the acceleration phase  244  by the value “d” in an amount of time “τ”, where “τ” falls in the range of 1 to 3 ms for the illustrated embodiment. 
     The value of “η” is preferably chosen to approximately target the first peak in the output signal  232  in FIG. 4, thus lowering the drive just as touchdown occurs. This way the “divot” formed by the coast and segue phases  246 ,  248  hits just as the actuator plate  204  (of FIGS. 2 and 3) touches down upon the motion stop  208  (of FIGS.  2  and  3 ), which minimizes the force at approximately the time of contact. Thus, the acceleration and coast phases  244 ,  246  comprise a total amount of time approximately equal to the time it takes the undamped actuator plate  204  to reach the motion stop  208 . 
     Thus, the actuation signal waveform  240  is typically tuned in amplitude or frequency. Namely, the amplitude sets “d” and thus the magnitude of the acceleration and hold down phases  244 ,  250 , and the frequency sets “η” and thus the coast and segue phases  246 ,  248 . 
     It was mentioned above that the coast and segue phases  246 ,  248  preferably involve decreasing and increasing, respectively, the magnitude of the actuation signal in a linear manner. It should be well understood, however, that such linear decreasing and increasing is not a requirement of the present invention. Namely, either or both of the coast and segue phases  246 ,  248  may alternatively be implemented by decreasing and increasing, respectively, the actuation signal in a nonlinear manner in accordance with the present invention. For example, FIG. 9A illustrates a linear coast phase  262  and a nonlinear segue phase  264 , and FIG. 9B illustrates a nonlinear coast phase  270  and a linear segue phase  272 . Although the linear scheme provides for ease of implementation, a nonlinear scheme may be employed by the present invention. 
     In addition, the acceleration and hold down phases  244 ,  250  are not required to have the same magnitude. For example, FIG. 9C illustrates the acceleration phase  278  having a greater magnitude than the hold down phase  280 , and FIG. 9D illustrates the acceleration phase  286  having a smaller magnitude than the hold down phase  288 . Nonlinear coast and segue phases  290 ,  292  are also shown. 
     FIG. 9E illustrates that one or more additional fluctuations  294  may be inserted into the actuation signal between the segue phase  296  and the hold down phase  298  in accordance with the present invention. 
     FIG. 9F illustrates that the coast and segue phases  261 ,  263  may also be implemented as a negative pulse in accordance with the present invention. Namely, the decreased voltage of the coast and segue phases  261 ,  263  form a pulse, providing in essence a pulsewidth modulated output signal. 
     Referring to FIG. 10, there is illustrated an actuation signal  275  in accordance with another embodiment of the present invention. The actuation signal  275  also provides highly effective damping of a structure in a complex dynamic system having a positive motion stop. Similar to above, the actuation signal  275  is applied between the actuator plate  204  (of FIGS. 2 and 3) and the actuator electrode  214  (of FIGS. 2 and 3) to create a force that pulls the actuator plate  204  towards the motion stop  208  (of FIGS.  2  and  3 ). The resulting output signal  277  represents the optical power of the output optical beam  212  (of FIG. 3) that is reflected off of the micromirror  202  (of FIG.  3 ). 
     The actuation signal  275  includes only two phases, namely, an acceleration phase  279  and a hold down phase  281 . Because there are only two phases, the actuation signal  275  may be referred to as a “two-step” actuation signal. In the illustrated embodiment, the acceleration phase  279  involves the application of a substantially constant magnitude voltage between the actuator plate  204  and the actuator electrode  214 . Following the acceleration phase  279  is the hold down phase  281 , which involves the application of a substantially constant magnitude voltage between the actuator plate  204  and the actuator electrode  214  that is smaller than the magnitude applied during the acceleration phase  279 . 
     As illustrated, shortly after the beginning of the acceleration phase  279 , the output signal  277  starts a wide oscillation. This wide oscillation is a result of the actuator plate  204  accelerating toward the motion stop  208  and then bouncing off of it with fairly large magnitude bounces. The hold down phase  281  causes the magnitude of the bounces to decrease and the output signal  277  to eventually settle in its on state, i.e., full optical power of the reflected output optical beam  212 . In this example, the acceleration phase  279  continues for 3 ms, and the magnitude of the hold down phase  281  is equal to 40% of the magnitude of the acceleration phase  279 . With these values it takes 8.1 ms for the output signal  277  to reach 90% settlement. Thus, the actuation signal  275  provides a reduced settling time as compared to the settling time achieved with the actuation signal  230  of FIG.  4 . Referring to FIG. 11, there is illustrated an exemplary high voltage system  300  for generating the actuation signal waveform  240  in accordance with one embodiment of the present invention. An input voltage is received at V input . The input voltage is typically a conventional digital signal falling in the range of 0-5 Volts. The actuation signal waveform  240  is output at V 240 . 
     A microprocessor  302  monitors V input . When V input  goes high, the microprocessor  302  controls a high voltage source  304  to produce a high voltage at output V 240 . Furthermore, the microprocessor  302  controls the high voltage source  304  to produce the acceleration, coast and segue phases  244 ,  246 ,  248  in the output of the high voltage source  304 . The “divot” formed by the coast and segue phases  246 ,  248  is included in the high voltage signal produced at V 240 . The high voltage source  304  can be based on a standard drive voltage that, by way of example, may be equal to the magnitude of the hold down phase  250  of the actuation signal  240 . 
     The above discussion focused on the use of electrostatic attraction to cause the switching process in the switching cell  200  (of FIGS.  2  and  3 ). Namely, the actuation signal  240  (of FIG. 6) is illustrated as a voltage in the figures. It should be well understood, however, that the actuation signals described herein, i.e., the actuation signal  240  and the actuations signals illustrated in FIGS. 9A,  9 B,  9 C,  9 D,  9 E,  9 F and  10 , may be used with many different types of actuation methods/forces in accordance with the present invention. For example, the actuation signals described herein may be used with electromagnetic attraction, thermal expansion, or piezoelectric attraction. When used with these alternate actuation methods/forces, the actuation signals described herein provide highly effective damping of structures in complex dynamic systems. 
     FIGS. 12A and 12B illustrate the manner in which the actuation signals of the present invention can be used to provide highly effective damping in a complex dynamic system  400  that is actuated using electromagnetic attraction. Specifically, the complex dynamic system  400  includes a movable structure  402  that is connected to a hinge  404 . The movable structure  402  comprises a ferrous or paramagnetic material and is stopped by a motion stop  406 . An actuation signal  408  in accordance with the present invention is applied to an electromagnet  410 . In this embodiment, the actuation signal  408  is a current I 408  that causes the electromagnet  410  to create a force that pulls the moveable structure  402  towards the motion stop  406 . The actuation signal  408 , which may have the waveform shape of any of the actuation signals described above, provides highly effective damping for the same reasons discussed above. Namely, the actuation signal  408  provides a decrease in drive timed with respect to the first impact of the moveable structure  408  on the motion stop  406 . 
     FIGS. 13A and 13B illustrate a MEMS switching cell  430  that is actuated using electromagnetic attraction. A micromirror  432  is mounted to an actuator plate  434 . The actuator plate  434  comprises a ferrous or paramagnetic material and is hingedly connected to the substrate  436  with a torsion hinge  438 . FIG. 13A illustrates the switching cell  430  in its transmission state where the optical beam  440  is not reflected. FIG. 13B illustrates the switching cell  430  in its reflection state where the optical beam  440  is switched to a reflection direction  442 . In the reflection state, the actuator plate  434  rests on a motion stop  444  (or other landing structure) mounted on the substrate  436 . 
     The actuator plate  434 , an electromagnet  446  mounted on the substrate  436 , and the gap therebetween form an electromagnetic actuator. The switching cell  430  is activated by providing an actuation signal  448  to the electromagnet  446 . In this embodiment, the actuation signal  448  is a current I 448 . The current I 448  causes the electromagnet  446  to create a force that causes the actuator plate  434  and the micromirror  432  mounted thereto to pivot in angular position relative to the substrate  436 , i.e., in the direction indicated by arrow  450 . This force causes the actuator plate  434  to draw close and contact the motion stop  444 . Thus, by applying the actuation signal  448  to the electromagnet  446 , the switching process is effectuated by electromagnetic attraction. 
     In accordance with the present invention, the actuation signal  448  may comprise the waveform shape of any of the actuation signals described above, i.e., the actuation signal  240  and the actuation signals illustrated in FIGS. 9A,  9 B,  9 C,  9 D,  9 E,  9 F and  10 . The use of such waveform shapes for the current I 448  provides highly effective damping of the actuator plate  434 . Highly effective damping is achieved because the current I 448  provides a decrease in drive timed with respect to the first impact of the actuator plate  434  on the motion stop  444 . 
     The entire contents of U.S. patent application Ser. No. 09/063,644, filed Apr. 20, 1998, entitled “Micromachined Optomechanical Switches”, and U.S. patent application Ser. No. 09/483,276, filed Jan. 13, 2000, entitled “Micromachined Optomechanical Switching Cell with Parallel Plate Actuator and On-Chip Power Monitoring”, are hereby expressly incorporated by reference into the present application as if fully set forth herein. 
     Turning to FIG. 14, as discovered by the present inventors, controlling system damping can be further complicated in a MEMS array  500 . This is because each of the switches  500   a   0 ,  500   a   1 ,  500   a   2 , etc., in the array  500  can have different damping characteristics. This may be due to device non-uniformities, which can result from the fabrication process. For example, switches near the periphery of the array may have different damping characteristics than switches near a central portion of the array. Such a situation further adds to the complexity of providing effective damping for the system. 
     Shown in FIG. 14, a single high voltage source  504  may be utilized to provide actuation signals to all of the switches  500   a   0 ,  500   a   1 ,  500   a   2 , etc., in the array  500 . In such a system, a single actuation signal can be selected to take into account damping non-uniformities occurring in the switch array  500 . 
     To determine a single actuation signal for operating the array, an actuation signal having a decreased drive portion is selected as discussed above with reference to FIGS. 6,  7 , and  9 A- 9 F. In the implementation of FIG. 14, during operation of the switch array  500 , the high voltage source  504  is applied not only to a selected switch for switching, as well as to any and all switches already energized. Thus, in this example, the actuation signal should be selected so as to inhibit already energized switches from moving, or otherwise changing their switch state. Hence, in the MEMS optical switch example discussed above with reference to FIG. 5, the depth of modulation “d” is chosen to reduce the drive of the actuator plate or actuator arm  204 , but not to allow release of any energized switches in the array  500 . 
     Turning to FIG. 15, the selected actuation signal  240  is applied to each of the switches of the array  500  to determine a range of values of a damping coefficient z for each switch that provide settling times in conformance with a predetermined specification. The damping coefficient z sets the time η (shown in FIG.  7 ). In addition, the damping coefficient z is used to define the relationship between an offset of the coast phase  246  with respect to beginning of the acceleration phase  244 , and the combined duration of the coast and seque phases  246  and  248  (both shown in FIG.  7 ). Thus, the damping coefficient z can be utilized to proportionally vary the offset and the combined duration as illustrated in FIG.  15 . Increasing the damping coefficient z decreases the time η (shown in FIG.  7 ). FIG. 15 depicts how the damping coefficient z can be used to proportionally change the offset and duration of the coast and seque phases (shown as divots  247   a-h ) of the selected actuation signal  240  of FIG.  7 . In FIG. 15, multiple divots  247   a-h  are shown in the selected actuation signal  240  in response to multiple selected damping coefficients z. Thus, In this way, a range of values for the damping coefficients z of the selected waveform can be expediently determined for each of the switches in the array  500 . 
     Turning to FIG. 16, in one implementation for example, an initial value for the damping coefficient z i  can be determined by using a test station to scan for an initial value of the damping coefficient z i  that provides a settling time in conformance with a predetermined specification as illustrated at box  1610 . The damping coefficient z may then be successively increased from its initial value z i  to determine a maximum value of the damping coefficient z max  that produces a settling time in conformance with the predetermined specification, illustrated in boxes  1620  and  1630 . The maximum damping coefficient z man  is then recorded  1640 . The minimum value of the damping coefficient z min  is determined, such as by returning to the initial damping coefficient z i  and successively decreasing the damping coefficient z to ascertain settling times in conformance with the predetermined specification, illustrated by boxes  1650 ,  1660 , and  1670 . The minimum damping coefficient z min  is recorded  1680 . 
     Typically, this is carried out at an ambient pressure similar to the device operating conditions. As such, it can be carried out after hermetically sealing of the package containing the MEMS chip. 
     Referring to FIG. 14, the ranges of values that produce settling times in conformance with the predetermined specification for each of the switches in the array  500  are used to select an operating damping coefficient z oper  to be utilized by the microprocessor  502  to control the high voltage source  504 . In one implementation, the operating damping coefficient z oper  is selected midway between, the largest value of the minimum damping coefficient z min  for all the switches in the array, and the smallest value of the maximum damping coefficient z max  for all the switches in the array  500 . 
     The microprocessor  502  is programmed to construct a single operating actuation signal having the values of the offset and combined duration corresponding to the operating damping coefficient z oper . To construct the operating actuation signal, the microprocessor  502  monitors for commencement of an actuation signal to a switch, such as by monitoring the incoming digital user input supplied to the selector  506 . After commencement of an actuation signal has been detected by the microprocessor  502 , the microprocessor controls the high voltage signal source  504  to provide a divot, or other selected signal reduction at its output. As discussed above, in the implementation of FIG. 14, the divot or other selected signal reduction is supplied not only to the structure being moved but also to any switches currently energized or otherwise receiving a signal from the high voltage source  504 . 
     It is also possible to construct a custom operating actuation signal for each switch using the determined settling characteristics for each switch. This may be accomplished by using the stored values of the minimum and maximum damping coefficients z min  and z max  for each switch. Or, a custom damping coefficient z cust  that provides the best measured settling time for each switch could be stored and utilized by the microprocessor  502  to construct a custom operating actuation signal for each switch. The custom values may be stored in a look-up table format that is accessed by the microprocessor  602  for selecting the corresponding stored custom damping coefficient for each switch. An individual damping coefficient could be stored in the look-up table with reference to the switch&#39;s position in the array, i.e. by column and row. The custom values in the look-up table, which can be the corresponding offset and combined duration, can be utilized to construct a custom operating actuation signal for each switch. 
     Turning to FIG. 17, it is also possible to employ several high voltage sources  604   a-d  to provide actuation signals to the switches of the array  600 . In the implementation of FIG. 17, one high voltage source  604   a  provides actuation signals for a column  600   a  of switches  600   a   0 -a 3 . This allows switches in the different columns  600   a-d  to be switched contemporaneously and/or near contemporaneously without having to wait for a single shared high voltage source  502  to return to an acceleration phase voltage. For example, a switch may be actuated before the divot  246 ,  248 , shown in FIG. 7, which is being applied to a switch in another column has finished. 
     Further, because obtaining values from a large look-up table can be microprocessor intensive, utilizing several microprocessors  604   a-d  allows for smaller look-up tables be used in implementing the custom operating actuation signals. For example, one look-up table associated with processor  602   a  stores the values for the switches in column  600   a , and another look-up table associated with processor  602   b  stores the values for the switches in column  600   b,  and so on. This can reduce costs by allowing slower less expensive microprocessors to be used. Multiple processors also facilitates contemporaneous and/or near contemporaneous switching of switches in the different columns. 
     It is possible to provide separate microprocessor controlled high voltage sources for each of the switches in the array  600 . In a conventional optical cross-connect, however, no more that one switch in a column is switched at a time. Thus, for the 4×4 array  600 , four high voltage sources are sufficient. Further, as array sizes grow to 8×8, 16×16, and beyond, providing a microprocessor, a DAC, and a high voltage supply for each column ultimately will be more practical than providing a microprocessor, a DAC, and a high voltage supply for each switch. 
     Turning to FIG. 18, a single microprocessor  602  may be utilized to construct custom operating actuation signals using multiple high voltage sources  604   a-d.  As discussed above, a single microprocessor requires a larger look-up table, and therefore typically would require a higher performance microprocessor than with the multiple processor implementation of FIG.  17 . 
     Referring to FIGS. 14,  17  and  18 , although shown as a single block, the selector  506 ,  606  may be a single component, or it may comprise, or equivalently be, several individual selectors. Thus, a selector  506  or  606  may be a selector that is a single or multiple component device. 
     Constructing a custom actuation signal for each switch allows better settling time for the switches in the array. The custom actuation signal has been discovered by the present inventors to provide about 50% better settling times. 
     Although in some implementations discussed above the offset of the coast phase with respect to the commencement of the acceleration phase and the combined duration of the coast phase and the seque phase can be varied proportionally, it is also possible to independently vary the offset and/or the combined duration. Further, it is possible to vary one of the waveforms controlling parameters, such as the offset, the combined duration, or the independent durations of the coast or seque phases while an other is held constant. 
     While the invention herein disclosed has been described by the specific embodiments and applications thereof, numerous modifications and variations could be made thereto by those skilled in the art without departing from the scope of the invention set forth in the claims.