Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems

The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems. A general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented. Fundamental properties of stability, dissipation, passivity, and gain for this class of linear quantum models are presented and characterized using complex Lyapunov equations and linear matrix inequalities (LMIs). Coherent $H^\infty$ and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.Comment: 33 pages, 7 figures; accepted for publication in IEEE Transactions on Automatic Control, October 201

Control of multivariable Hammerstein systems by using feedforward passivation

This paper presents a new control method for processes which can be described by Hammerstein models. The control design is based on the concept of passive systems. The proposed method is based on feedforward passivation and thus can be applied to nonminimum phase processes and/or processes of high relative degree. A synthesis technique for marginally stable positive real systems has been developed to achieve offset free control. The new control design can be easily implemented by solving a set of linear matrix inequalities. The proposed approach is illustrated using the example of an acid-base pH control problem

Optimal Output Modification and Robust Control Using Minimum Gain and the Large Gain Theorem

When confronted with a control problem, the input-output properties of the system to be controlled play an important role in determining strategies that can or should be applied, as well as the achievable closed-loop performance. Optimal output modification is a process in which the system output is modified in such a manner that the modified system has a desired input-output property and the modified output is as similar as possible to a specified desired output. The first part of this dissertation develops linear matrix inequality (LMI)-based optimal output modification techniques to render a linear time-invariant (LTI) system minimum phase using parallel feedforward control or strictly positive real by linearly interpolating sensor measurements. H-ininifty-optimal parallel feedforward controller synthesis methods that rely on the input-output system property of minimum gain are derived and tested on a numerical example. The H2- and H-infinity-optimal sensor interpolation techniques are implemented in numerical simulations of noncolocated elastic mechanical systems. All mathematical models of physical systems are, to some degree, uncertain. Robust control can provide a guarantee of closed-loop stability and/or performance of a system subject to uncertainty, and is often performed using the well-known Small Gain Theorem. The second part of this dissertation introduces the lessor-known Large Gain Theorem and establishes its use for robust control. A proof of the Large Gain Theorem for LTI systems using the familiar Nyquist stability criterion is derived, with the goal of drawing parallels to the Small Gain Theorem and increasing the understanding and appreciation of this theorem within the control systems community. LMI-based robust controller synthesis methods using the Large Gain Theorem are presented and tested numerically on a robust control benchmark problem with a comparison to H-infinity robust control. The numerical results demonstrate the practicality of performing robust control with the Large Gain Theorem, including its ability to guarantee an uncertain closed-loop system is minimum phase, which is a robust performance problem that previous robust control techniques could not solve.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143934/1/caverly_1.pd

Robust Scale-Free Synthesis for Frequency Control in Power Systems

The AC frequency in electrical power systems is conventionally regulated by synchronous machines. The gradual replacement of these machines by asynchronous renewable-based generation, which provides little or no frequency control, increases system uncertainty and the risk of instability. This imposes hard limits on the proportion of renewables that can be integrated into the system. In this paper we address this issue by developing a framework for performing frequency control in power systems with arbitrary mixes of conventional and renewable generation. Our approach is based on a robust stability criterion that can be used to guarantee the stability of a full power system model on the basis of a set of decentralised tests, one for each component in the system. It can be applied even when using detailed heterogeneous component models, and can be verified using several standard frequency response, state-space, and circuit theoretic analysis tools. Furthermore the stability guarantees hold independently of the operating point, and remain valid even as components are added to and removed from the grid. By designing decentralised controllers for individual components to meet these decentralised tests, every component can contribute to the regulation of the system frequency in a simple and provable manner. Notably, our framework certifies the stability of several existing (non-passive) power system control schemes and models, and allows for the study of robustness with respect to delays.Comment: 10 pages, submitte

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Quantum Feedback Networks and Control: A Brief Survey

The purpose of this paper is to provide a brief review of some recent developments in quantum feedback networks and control. A quantum feedback network (QFN) is an interconnected system consisting of open quantum systems linked by free fields and/or direct physical couplings. Basic network constructs, including series connections as well as feedback loops, are discussed. The quantum feedback network theory provides a natural framework for analysis and design. Basic properties such as dissipation, stability, passivity and gain of open quantum systems are discussed. Control system design is also discussed, primarily in the context of open linear quantum stochastic systems. The issue of physical realizability is discussed, and explicit criteria for stability, positive real lemma, and bounded real lemma are presented. Finally for linear quantum systems, coherent $H^\infty$ and LQG control are described.Comment: 29 pages, 11 figures. A new reference has been adde