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

Adaptive Passivity-Based Pose Tracking Control of Cable-Driven Parallel Robots for Multiple Attitude Parameterizations

The proposed control method uses an adaptive feedforward-based controller to establish a passive input-output mapping for the CDPR that is used alongside a linear time-invariant strictly positive real feedback controller to guarantee robust closed-loop input-output stability and asymptotic pose trajectory tracking via the passivity theorem. A novelty of the proposed controller is its formulation for use with a range of payload attitude parameterizations, including any unconstrained attitude parameterization, the quaternion, or the direction cosine matrix (DCM). The performance and robustness of the proposed controller is demonstrated through numerical simulations of a CDPR with rigid and flexible cables. The results demonstrate the importance of carefully defining the CDPR's pose error, which is performed in multiplicative fashion when using the quaternion and DCM, and in a specific additive fashion when using unconstrained attitude parameters (e.g., an Euler-angle sequence)

Gust-Load Alleviation of a Flexible Aircraft using a Disturbance Observer

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143016/1/6.2017-1718.pd

What works for whom in the management of diabetes in people living with dementia: a realist review

Background Dementia and diabetes mellitus are common long-term conditions and co-exist in a large number of older people. People living with dementia (PLWD) may be less able to manage their diabetes, putting them at increased risk of complications such as hypoglycaemia. The aim of this review was to identify key mechanisms within different interventions that are likely to improve diabetes outcomes in PLWD. Methods This is a realist review involving scoping of the literature and stakeholder interviews to develop theoretical explanations of how interventions might work, systematic searches of the evidence to test and develop the theories and their validation with a purposive sample of stakeholders. Twenty-six stakeholders — user/patient representatives, dementia care providers, clinicians specialising in diabetes or dementia and researchers — took part in interviews, and 24 participated in a consensus conference. Results We included 89 papers. Ten focused on PLWD and diabetes, and the remainder related to people with either dementia, diabetes or other long-term conditions. We identified six context-mechanism-outcome configurations which provide an explanatory account of how interventions might work to improve the management of diabetes in PLWD. This includes embedding positive attitudes towards PLWD, person-centred approaches to care planning, developing skills to provide tailored and flexible care, regular contact, family engagement and usability of assistive devices. An overarching contingency emerged concerning the synergy between an intervention strategy, the dementia trajectory and social and environmental factors, especially family involvement. Conclusions Evidence highlighted the need for personalised care, continuity and family-centred approaches, although there was limited evidence that this happens routinely. This review suggests there is a need for a flexible service model that prioritises quality of life, independence and patient and carer priorities. Future research on the management of diabetes in older people with complex health needs, including those with dementia, needs to look at how organisational structures and workforce development can be better aligned to their needs. Trial registration PROSPERO, CRD42015020625. Registered on 18 May 2015

MIMO Nyquist interpretation of the large gain theorem

The Large Gain Theorem is an input-output stability result with intriguing applications in the field of control systems. This paper aims to increase understanding and appreciation of the Large Gain Theorem by presenting an interpretation of it for linear time-invariant systems using the well-known Nyquist stability criterion and illustrative examples of its use. The Large Gain Theorem is complementary in nature to the Small Gain Theorem, as it uses a lower bound on the gain of the open-loop system to guarantee closed-loop stability, rather than an upper bound on the gain of the open-loop system. It is shown that the stipulations of the Large Gain Theorem ensure that the multi-input multi-output Nyquist stability criterion is satisfied. Numerical examples of minimum gain and systems that satisfy the Large Gain Theorem are presented, along with examples that make use of the Large Gain Theorem to guarantee robust closed-loop stability