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

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

Relay Feedback and Multivariable Control

This doctoral thesis treats three issues in control engineering related to relay feedback and multivariable control systems. Linear systems with relay feedback is the first topic. Such systems are shown to exhibit several interesting behaviors. It is proved that there exist multiple fast relay switches if and only if the sign of the first non-vanishing Markov parameter of the linear system is positive. It is also shown that these fast switches can appear as part of a stable limit cycle. A linear system with pole excess one or two is demonstrated to be particularly interesting. Stability conditions for these cases are derived. It is also discussed how fast relay switches can be approximated by sliding modes. Performance limitations in linear multivariable control systems is the second topic. It is proved that if the top left submatrices of a stable transfer matrix have no right half-plane zeros and a certain high-frequency condition holds, then there exists a diagonal stabilizing feedback that makes a weighted sensitivity function arbitrarily small. Implications on control structure design and sequential loop-closure are given. A novel multivariable laboratory process is also presented. Its linearized dynamics have a transmission zero that can be located anywhere on the real axis by simply adjusting two valves. This process is well suited to illustrate many issues in multivariable control, for example, control design limitations due to right half-plane zeros. The third topic is a combination of relay feedback and multivariable control. Tuning of individual loops in an existing multivariable control system is discussed. It is shown that a specific relay feedback experiment can be used to obtain process information suitable for performance improvement in a loop, without any prior knowledge of the system dynamics. The influence of the loop retuning on the overall closed-loop performance is derived and interpreted in several ways

Stability analysis and control of DC-DC converters using nonlinear methodologies

PhD ThesisSwitched mode DC-DC converters exhibit a variety of complex behaviours in power electronics systems, such as sudden changes in operating region, bifurcation and chaotic operation. These unexpected random-like behaviours lead the converter to function outside of the normal periodic operation, increasing the potential to generate electromagnetic interference degrading conversion efficiency and in the worst-case scenario a loss of control leading to catastrophic failure. The rapidly growing market for switched mode power DC-DC converters demands more functionality at lower cost. In order to achieve this, DC-DC converters must operate reliably at all load conditions including boundary conditions. Over the last decade researchers have focused on these boundary conditions as well as nonlinear phenomena in power switching converters, leading to different theoretical and analytical approaches. However, the most interesting results are based on abstract mathematical forms, which cannot be directly applied to the design of practical systems for industrial applications. In this thesis, an analytic methodology for DC-DC converters is used to fully determine the inherent nonlinear dynamics. System stability can be indicated by the derived Monodromy matrix which includes comprehensive information concerning converter parameters and the control loop. This methodology can be applied in further stability analysis, such as of the influence of parasitic parameters or the effect of constant power load, and can furthermore be extended to interleaved operating converters to study the interaction effect of switching operations. From this analysis, advanced control algorithms are also developed to guarantee the satisfactory performance of the converter, avoiding nonlinear behaviours such as fast- and slowscale bifurcations. The numerical and analytical results validate the theoretical analysis, and experimental results with an interleaved boost converter verify the effectiveness of the proposed approach.Engineering and Physical Sciences Research Council (EPSRC), China Scholarship Council (CSC), and school of Electrical and Electronic Engineerin

Hysteretic control of grid-side current for a single-phase LCL grid-connected voltage source converter

© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper proposes a new approach to control the grid-side current of LCL-grid connected voltage source converters using hysteretic relay feedback controllers. The closed loop system is stabilized by designing a local feedback around the relay element. The compensator allows the use of relay feedback controllers by making the controlled plant almost strictly positive real. The article proposes the use of the locus of the perturbed relay system as analysis and design tool and studies orbital stability for several plant and controller conditions. The approach is validated by means of simulation testing.Postprint (author's final draft

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue