Nonlinear Time-Frequency Control Theory with Applications

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate

Element and system design for active and passive vibration isolation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, February 2005.Includes bibliographical references (p. 277-294).This thesis focusses on broadband vibration isolation, with an emphasis on control of absolute payload motion for ultra-precision instruments such as the MIT/Caltech Laser-Interferometric Gravitational Wave Observatory (LIGO), which is designed to measure spatial strains on the order of 10-²¹. We develop novel passive elements and control strategies as well as a framework for concurrent design of the passive and active elements of single-stage and multi-stage isolation systems. In many applications, it is difficult to construct passive isolation systems compliant enough to achieve specifications on low-frequency ground transmission without introducing hysteresis as well as high-frequency transmission resonances. We develop and test a compliant support that employs a post-buckled structure in con- junction with a compliant spring to attain a low-frequency, low-static-sag mount in a compact package with a large range of travel and very clean dynamics. Most passive damping techniques increase ground transmission at high frequency, but tuned-mass dampers are decoupled from the ground. We explore the tuned-mass damper as a passive realization of the skyhook damper, obtain the optimal designs for multiple-SDOF systems of dampers, propose the concept of a multi-DOF damper, and show that MDOF dampers that couple translational and rotational motion have the potential to provide performance many times better than that traditional tuned-mass dampers. Active control can be used to improve low-frequency performance, but high-gain control can amplify sensor and actuator noise or cause instability. We study several control strategies for uncertain plants with high-order dynamics.(cont.) In particular, we develop a novel control strategy, "model-reaching" adaptive control, that drives the system onto a dynamic manifold defined directly in terms of the states of the target. The method can be used to robustly increase the apparent compliance of an isolation mount and maintain a -40 dB/decade roll-off above the resulting corner frequency.by Lei Zuo.Ph.D

Design and Optimal Control of a Magnet Assisted Scanning Stage for Precise and Energy Efficient Positioning

Scanning stages are characterized by repeated back and forth motions and are widely used in advanced manufacturing processes like photo-lithography, laser-scribing, inspection, metrology, 3D printing, and precision parts assembly, many of which are closely related to the semiconductor (i.e., integrated circuit) manufacturing industry. In order to deliver more high- performance semiconductor chips, i.e., to keep up with predictions made by Moore’s Law, the scanning stages employed by the industry need to move faster while maintaining nanometer-level precision. Achieving these two goals simultaneously requires extensive use of thermal and vibration-induced error mitigation methods, because the motors, and subsequently the surrounding stage components, become heated and flexible parts of scanning stages are easily excited by their aggressive motions (with high acceleration/deceleration). Most of the available solutions tackle the heat and vibration mitigation problems separately, even though the two problems originate from one source, i.e., the large inertial loads generated by the scanning stage’s actuators. Much benefit (e.g., size and cost reductions) can be achieved by considering the two problems simultaneously by addressing their root cause. This dissertation proposes a design-based approach to simultaneously mitigate thermal and vibration-induced errors of scanning stages. Exploiting the repeated back-and-forth motions of scanning, permanent magnet (PM) based assist devices are designed to provide assist force needed during the motion reversal portions of scanning trajectories. The PM-based assist devices store the kinetic energy of the moving table during deceleration and release the stored energy when the table accelerates. Consequently, the force requirements of the primary actuator decrease, thus lowering its heat generation due to copper (resistive) losses. Moreover, the reaction forces borne by the PM assistive devices are channeled to the ground, bypassing the vibration isolated base upon which the scanning stage rests, thus reducing unwanted vibration. To increase the force density of the PMs, a 2D Halbach arrangement is adopted in a prototype scanning stage. Moreover, an efficient and low-cost servo system, optimized for versatility, is integrated into the scanning stage for automatic positioning of the PMs. The designed magnet assisted scanning stage is an over-actuated system, meaning that it has more control inputs than outputs. For the best utilization of its actuators, a feedforward approach for optimal allocation of control efforts to its actuators is developed. The stage, controlled with the optimal feedforward control inputs, achieves significant reductions of actuator heat and vibration-induced errors when applied to typical scanning motions used in semiconductor manufacturing (silicon wafer processing). To further improve the positioning accuracy of the stage, an Iterative Learning Control (ILC) approach for over-actuated systems is developed, exploiting the repeated motion of scanning stages. The optimal ILC update law is designed, considering model and input force uncertainties, for robust monotonic convergence of tracking errors, and the resultant control force is efficiently allocated to multiple actuators. Applied to the magnet assisted scanning stage, the proposed ILC approach additionally reduces tracking errors arising from the mismatch between the model and actual system, thus significantly improving the positioning accuracy of the stage.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149847/1/yydkyoon_1.pd

The investigation and design of a piezoelectric active vibration control system for vertical machining centres

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Nonlinear Time-Frequency Control Theory with Applications

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate

Structural-acoustic design and control of an integrally actuated composite panel

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.Includes bibliographical references (p. 165-170).The need for structural based acoustic control is evident in aircraft, aerospace, and naval systems. A promising approach utilizes active materials to intelligently control the dynamic response of light-weight, modally dense structures suppressing the radiated acoustic power. The basic representative structural element of a single panel offers an analytically tractable basis for examining various control methodologies for mitigating the acoustic response. An electro-mechanical Rayleigh-Ritz structural model is combined with an expression of the acoustic power radiated from a rectangular panel to yield a fully coupled structural-acoustic model. The insight afforded by this model is used to design the sensor and actuator architecture of the active structure for optimal closed-loop acoustic performance. The manufacturing of a composite panel with eight embedded active fiber composite (AFC) actuators and collocated strain sensors is presented in detail. The geometry of the test article is designed to represent the dynamics of the target applications, and the active elements are embedded in the composite panel to demonstrate the capabilities of the technology. Active control methods are explored through simulations and experiments to compare the applicability to active structural-acoustic control (ASAC). To quantify the comparison, designs based on classical low-authority feedback, optimal feedback, and x-filtered LMS feedforward techniques are presented. The results lend insight into the inherent limitations and advantages of each approach to the problem of broadband control. The investigation is application motivated in that the sensing and piezoelectric actuation occur solely at the structure while the performance is measured in the acoustic field. The conclusions consider the analytically predicted performance along with the corresponding experimental achievement to develop an understanding of the key issues necessary to apply the technology to the active structural-acoustic control of complex systems.by Brian S. Bingham.S.M

Towards the Development of a Wearable Tremor Suppression Glove

Patients diagnosed with Parkinson’s disease (PD) often associate with tremor. Among other symptoms of PD, tremor is the most aggressive symptom and it is difficult to control with traditional treatments. This thesis presents the assessment of Parkinsonian hand tremor in both the time domain and the frequency domain, the performance of a tremor estimator using different tremor models, and the development of a novel mechatronic transmission system for a wearable tremor suppression device. This transmission system functions as a mechatronic splitter that allows a single power source to support multiple independent applications. Unique features of this transmission system include low power consumption and adjustability in size and weight. Tremor assessment results showed that the hand tremor signal often presents a multi-harmonics pattern. The use of a multi-harmonics tremor model produced a better estimation result than using a monoharmonic tremor model

On The Dynamics and Control Strategy of Time-Delayed Vibro-Impact Oscillators

Being able to control nonlinear oscillators, which are ubiquitous, has significant engineering implications in process development and product sustainability design. The fundamental characteristics of a vibro-impact oscillator, a non-autonomous time-delayed feedback oscillator, and a time-delayed vibro-impact oscillator are studied. Their being stochastic, nonstationary, non-smooth, and dynamically complex render the mitigation of their behaviors in response to linear and stationary inputs very difficult if not entirely impossible. A novel nonlinear control concept featuring simultaneous control of vibration amplitude in the time-domain and spectral response in the frequency-domain is developed and subsequently incorporated to maintain dynamic stability in these nonlinear oscillators by denying bifurcation and route-to-chaos from coming to pass. Convergence of the controller is formulated to be inherently unconditional with the optimization step size being self-adaptive to system identification and control force input. Optimal initial filter weights are also derived to warrant fast convergence rate and short response time. These novel features impart adaptivity, intelligence, and universal applicability to the wavelet based nonlinear time-frequency control methodology. The validity of the controller design is demonstrated by evaluating its performance against PID and fuzzy logic controllers in controlling the aperiodic, broad bandwidth, discontinuous responses characteristic of the time-delayed, vibro-impact oscillator