Patent Application
20110086578
The present invention relates, in general, to optical machining, and, in particular, to an apparatus and method with a dual-stage coarse/fine actuator and a tracking control specifically tailored for such a dual actuator.
Progressive lens, also called progressive addition lenses (PAL), progressive power lens, graduated lens and varifocal lens, are corrective lens used in eyeglasses to correct presbyopia and other disorders of accommodation. Progressive lens or “no-line” bifocals are increasing in popularity because of known advantages they offer to wearers.
Historically, progressive lens processing depends on molding a prescription surface on to the front of a lens blank and cutting a back surface of the blank in accordance with a patient's prescription. Alternatively, backside progressive lens processing depends on machining a complex surface representing the patient prescription, in addition to the progressive design on the back surface of a conventional spherical blank. A voice coil actuator under servo control is used to achieve the desired accuracy of error, low surface roughness, and throughput of progressive lenses an hour.
Although the voice coil actuator enables the production of backside progressive lenses, an additional process of polishing is required to achieve optical clarity and prepare the lenses for coating. The lenses can be coated if their surface roughness is less than 12 nm. However, the minimum surface roughness achieved by a voice coil actuator is 150 nm, which is too high for the lenses to be coated.
The voice coil actuator has further limitations. The bandwidth is generally less than 250 Hz and the positioning resolution is greater than 0.1 μm. Lens surfacing requires fast tracking and high accuracy of the cutter motion for high throughput. However, in the current systems, frequency increases to over 300 Hz leads to significant tracking error in both magnitude (about 50%) and phase (almost 90°).
Thus, there remains a need in the industry for a lens surfacing apparatus which can maintain high accuracy at unlimited bandwidth. There also remains a need for a tracking control for delivering control of the lens machining process.
The invention involves dual-stage servo actuator system for optical manufacturing that allows for both course and fine positioning in one tool. A connection mechanism is used for smooth and effective operation of the dual-stage actuation tool. The invention also includes a robust tracking control system using a hierarchal sliding mode approach specifically tailored to maintain sub-nanometer level resolution during micro-surfacing.
An actuator portion of the system comprises a voice coil, piezo stack actuator, and cutter in series. A connection mechanism seamlessly connects the piezo stack actuator to the cutter and to the voice coil. During operation, the voice coil covers the long-range motion of the actuator during the coarse positioning stage (multiple inch displacement with a motion frequency of less than 250 Hz and a positioning resolution of greater than 100 nm), while the piezo stack actuator covers the short-range motion of the cutter during the fine positioning stage (up to 200 μm displacement with a motion frequency of less than 3 kHz and a positioning resolution of less than 1 nm). The connection mechanism is designed to avoid vibration below 3 kHz while minimizing stroke loss from the piezo stroke to the cutting tool. The connection mechanism can be flexible or rigid depending on the embodiment. The connection mechanism can also be fixed or detachable depending on the embodiment. A tracking control system allows the dual-stage actuator cutter to deal with uncertain disturbances and vibrations the actuator will encounter while micro-surfacing.
Thus, the system allows optical manufacturers to minimize or eliminate the lens fining and polishing from conventional lens processing, creating substantial time and cost savings for optical labs in terms of labor and equipment reduction.
An object of the invention is to provide lens surfacing rate and accuracy never before achieved in lens manufacturing.
In addition, it is an object of the invention to have a tracking control for this machining process. The tracking control would maintain the lens surfacing rate and accuracy while rejecting the cutting force disturbances and other uncertainties.
Form error in machining lens is typically at 2-micron level, it is an object of this invention to produce a lens with form error to 1 micron or less. It is also an object to bring surface roughness to less than 12 nm.
The invention includes a dual stage coarse/fine actuator that has a voice coil and a piezo-stack actuator connected together in series. A tracking control system using a hierarchical sliding mode approach is specifically tailored for controlling such dual stage actuator for optical machining.
A closed loop servo control methodology as well as several other control systems for lens surfacing will have improvement in both bandwidth and positioning resolution by utilizing the present invention.
With the system of the present invention, the lens surfacing rate and accuracy will be enhanced, yielding increased throughput. The proposed system and method will eliminate the lens polishing process, therefore minimizing the labor, equipment, and consumables associated with these steps and at the same time increasing throughput. Since this is the first time such technology is applied, the degree to which the lens polishing step is either minimized or completely eliminated depends on the surface roughness of the optical surface and if the surface is adequate for coating.
Therefore it is possible to reduce the surface roughness to a level where a very fast polishing process could still be needed to bring the optical quality to the level necessary for coating. In either case the benefits in throughput would still be realized.
The present invention will be understood and appreciated more fully from the following detailed description taken in conjunction with the drawings in which:
An exemplary embodiment of the present invention is a dual-stage actuator cutting tool having a novel connection mechanism and hierarchical sliding mode control system. The invention allows for both coarse and fine movements of the cutting tool during surfacing and maintains fast tracking and high precision.
In this exemplary embodiment, the actuator portion of the system consists of a voice coil, piezo stack and cutter in series. The voice coil covers the long-range motion of the cutter during the coarse positioning stage, and the piezo stack covers the short range motion of the cutter during the fine positioning stage. The displacement range of the coarse positioning stage can be multiple inches at a motion frequency below 250 Hz. The displacement range of the fine positioning stage can be 200 μm at a motion frequency of less than 3 kHz and a positioning resolution of less than 1 nm.
In this embodiment of the invention, the piezo stack's size can be about 10 mm to about 40 mm for a stroke of about 50 μm to about 200 μm. The actuation system can be constructed with a commercially available off-the-shelf stack with 0.2%-thickness actuation stroke (25 mm in length for 50 μm stroke) or a specially ordered PMN-32% PT stack with 0.5%-thickness actuation stroke (40 mm in length for 200 μm stroke). The compactness of the piezo stack allows its' easy insertion between the cutter head and the voice coil without affecting the overall dynamics of the cutter.
The voice coil and piezo stack are seamlessly connected through a connection mechanism, which is designed to avoid vibrations below 3 KHz and minimize the stroke loss during surfacing. The connection mechanism's symmetrically distributed hinges guarantee the perfect alignment of the piezo actuation in the moving direction without twisting. The hinge profiles are directly related to the actuation system's axial stiffness, torsional stiffness and bending stiffness. The connection mechanism's clamping enforcement is designed so that the natural frequencies of the actuation system are adjusted higher enough to avoid vibration and effectively transmit the piezo stack's displacement.
The connection mechanism, depending on the embodiment, can be designed so that one end of the piezo stack is rigidly connected to the voice coil, and the other end of the piezo stack is connected to the cutter through a hinged flexure. The hinge configuration provides for the optimized overall bending and torsion stiffness while minimizing the actuation stroke loss.
In this exemplary embodiment, the actuator is regulated by a novel closed loop lens surfacing control system based on a new MIMO hierarchical sliding algorithm. This hierarchical sliding mode control system has the robustness to deal with disturbances and vibrations from the cutting force, and provides for the smooth interaction and coordination between the coarse and fine motions. There are two basic phases in the hierarchical sliding mode control: (1) a reaching phase in which the system states are driven to pre-determined sliding manifold; and (2) a sliding phase in which the controller constrains the states to the sliding mode whereas the sliding mode dynamics is asymptomatically stable.
The hierarchical sliding mode control of this embodiment is further characterized by two sliding hyper-planes, and their intersection called a sliding manifold. The first hyper-plane relates to the voice coil only and was constructed using the partial states related to the coarse motion. The second hyper-plane relates to the fine motion only. After the partial states reach the first hyper-plane, the piezo stack acts as the sole input to drive the states to reach the final sliding manifold, which is the intersection between the two hyper-planes.
This embodiment of the invention is characterized by the following dynamic equation: x=Ax+ΔAx+Bu+d, where x=[x1,x2,x3,x4] is the vector of the system states. x1 and x2 correspond to the fine motion. u=[u1, u2] is the vector of control inputs. u1 is the input to the voice coil and u2 is the input to the piezo stack. A and ΔA are the system parameter matrix and the corresponding uncertainty. B is the control input matrix and d is the disturbance.
The hierarchical sliding mode control system of this embodiment provides for the refined and smooth coordinated action of the voice coil and piezo stack, where the voice coil moves the cutter to the appropriate coarse position and the piezo stack guarantees a high accuracy of lens surfacing based on its extremely high positioning resolution and bandwidth. This results in a closed loop lens surfacing control system, which has a surfacing rate and accuracy with orders-of-magnitude improvement with respect to the current practice in the lens manufacturing industry.
While the control algorithm development for the dual-stage actuation will primarily rely on the sliding mode approach, alternative control designs can also be deployed these include various MIMO control strategies can be applied and tested, which include LQG, H∞, and μ-synthesis. The formulations of these control algorithms are standard. The LQG design minimizes the H2 norm of the controlled system, the H∞ design minimizes the H∞ norm of the controlled system, and the μ-synthesis is based on the H∞ norm and accounts for the plant model uncertainties during the controller synthesis process with guaranteed robustness. Other alternative control designs may also be used with the principles of the invention.
Although the invention has been described in conjunction with specific embodiments, many alternatives and variations can be apparent to those skilled in the art in light of this description and the annexed drawings. Accordingly, the invention is intended to embrace all of the alternatives and variations that fall within the spirit and the scope of the appended claims.
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/US08/77637 | 9/25/2008 | WO | 00 | 12/13/2010 |
| Number | Date | Country | |
|---|---|---|---|
| 60975390 | Sep 2007 | US |
