Quantitative Feedback Theory (QFT) is a control system design methodology founded on the premise that feedback is necessary only because of system uncertainty. Articulating flexible structures, such as flexible manipulators, present a difficult closed-loop control problem. In such servo systems, the coupling of the rigid and flexible modes and the non-minimum phase dynamics severely limit system stability and performance. The difficulties in controlling these structures is exacerbated by the denumerably infinite number of flexible modes and associated difficulties in developing accurate dynamic models for controller design. As such, the control of articulating flexible structures presents a non-trivial testbed for the design of QFT based robust control systems. This dissertation examines the multi-input multi-output (MIMO) QFT based control of an articulating flexible structure and presents an enhancement of the theoretical basis for the MIMO QFT design methodologies. The control problem under consideration is the active vibration control of an articulating single-link flexible manipulator. This is facilitated by an actuation scheme comprised of a combination of spatially discrete actuation, in the form of a DC motor to perform articulation, and spatially distributed actuation, in the form of a piezoelectric transducer for active vibration control. In the process of developing and experimentally validating the QFT based control system, shortcomings in the theoretical basis for the MIMO QFT design methodologies are addressed. Robust stability theorems are developed for the two main MIMO QFT design methodologies, namely the sequential and non-sequential MIMO QFT design methodologies. The theorems complement and extend the existing theoretical basis for the MIMO QFT design methodologies. The dissertation results expose salient features of the MIMO QFT design methodologies and provide connections to other multivariable design methodologies.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 152-158).

Thesis (M.S.)--Ohio University, August, 2001. / Title from PDF t.p.

Thesis (M.S.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Electrical and Computer Engineering, 2009. / Includes bibliographical references.

Includes bibliographical references (p. 35-38).

Thesis (M.S.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Electrical and Computer Engineering, 2008. / Includes bibliographical references.

Thesis (Ph.D.(Electronic engineering))--University of Pretoria, 2008. / Summary in English. Includes bibliographical references.

Thesis (Ph.D.)--University of Melbourne, Dept. of Computer Science and Software Engineering, 2010. / Typescript. Includes bibliographical references (p. 153-167)

State dependent Riccati equation (SDRE) plays an important role in nonlinear controller design. For autonomous nonlinear systems that can be expressed in linear form with state-dependent coefficients (SDC), SDRE-based controllers guarantee local asymptotic stability of the closed-loop system, under pointwise stabilizability and detectability conditions. Moreover, the optimal control for a quadratic cost function, when it exists, corresponds to an SDRE-based control design for a specific SDC parameterization of the associated nonlinear system. Unfortunately, the implementation of the SDRE-based controllers is computationally expensive. Various techniques have been developed for solving the SDRE, which are either computationally expensive or lack acceptable precision. In this dissertation, a modified state-dependent differential Riccati equation (MSDDRE) is proposed for approximating the solution of the SDRE, which is easy to implement with moderate computation power and its solution can be made arbitrarily close to that of the SDRE. Therefore, it can be used for real-time implementation of near-optimal controllers for nonlinear systems in state-dependent linear form. The proposed technique is then extended to SDRE-based filter design and its application to SDRE-based output feedback control technique. The proposed technique is also extended to state-dependent H-inf; robust control design for a constant noise attenuation bound, when the solution exists. To reduce the design conservativeness, the technique is further extended to state-dependent H-inf; robust control design with adaptive noise attenuation bound, using gain-scheduling technique and linear matrix inequality (LMI) optimization, to approximate H-inf; optimal control with state-dependent noise-attenuation bound. Local asymptotic stability of the closed-loop system is proven for all proposed techniques. Simulation results further confirm the validity of the development and demonstrate the efficiency of the proposed techniques.

Space missions increasingly require sophisticated guidance, navigation and control algorithms, the development of which is reliant on verification and validation (V&V) techniques to ensure mission safety and success. A crucial element of V&V is the assessment of control system robust performance in the presence of uncertainty. In addition to estimating average performance under uncertainty, it is critical to determine the worst case performance. Industrial V&V approaches typically employ mu-analysis in the early control design stages, and Monte Carlo simulations on high-fidelity full engineering simulators at advanced stages of the design cycle. While highly capable, such techniques present a critical gap between pessimistic worst case estimates found using analytical methods, and the optimistic outlook often presented by Monte Carlo runs. Conservative worst case estimates are problematic because they can demand a controller redesign procedure, which is not justified if the poor performance is unlikely to occur. Gaining insight into the probability associated with the worst case performance is valuable in bridging this gap. It should be noted that due to the complexity of industrial-scale systems, V&V techniques are required to be capable of efficiently analysing non-linear models in the presence of significant uncertainty. As well, they must be computationally tractable. It is desirable that such techniques demand little engineering effort before each analysis, to be applied widely in industrial systems. Motivated by these factors, this thesis proposes and develops an efficient algorithm, based on the cross entropy simulation method. The proposed algorithm efficiently estimates the probabilities associated with various performance levels, from nominal performance up to degraded performance values, resulting in a curve of probabilities associated with various performance values. Such a curve is termed the probability profile of performance (PPoP), and is introduced as a tool that offers insight into a control system's performance, principally the probability associated with the worst case performance. The cross entropy-based robust performance analysis is implemented here on various industrial systems in European Space Agency-funded research projects. The implementation on autonomous rendezvous and docking models for the Mars Sample Return mission constitutes the core of the thesis. The proposed technique is implemented on high-fidelity models of the Vega launcher, as well as on a generic long coasting launcher upper stage. In summary, this thesis (a) develops an algorithm based on the cross entropy simulation method to estimate the probability associated with the worst case, (b) proposes the cross entropy-based PPoP tool to gain insight into system performance, (c) presents results of the robust performance analysis of three space industry systems using the proposed technique in conjunction with existing methods, and (d) proposes an integrated template for conducting robust performance analysis of linearised aerospace systems.