Disturbance decoupling for singulars systems by proportional and derivate feedback and proportional and derivate outputm injection

We study the disturbance decoupling problem for linear time invariant singular systems. We give necessary and su±cient conditions for the existence of a solution to the disturbance decoupling problem with or without stability via a proportional and derivative feedback and proportional and derivative output injection that also makes the resulting closed-loop system regular and/or of index at most one. All results are based on canonical reduced forms that can be computed using a complete system of invariants that can be implemented in a numerically stable way.Postprint (published version

Solving disturbance decoupling for singular systems by p&d-feedback and p&d-output injection

Singular systems are an important class of systems from both point of view theoretical and practical. In this paper we analyze the problem of constructing feedbacks and/or output injections that suppress this disturbance in the sense that it does not affect the inputoutput behavior of the system and makes the resulting closed-loop system regular and of index at most one. All results are based on the canonical reduced forms that they can be computed using a complete system of invariants and can be implemented in a numerically stable way.Peer ReviewedPostprint (published version

A Small-Gain Theorem with Applications to Input/Output Systems, Incremental Stability, Detectability, and Interconnections

A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form. In addition, we highlight applications to incrementally stable systems, detectable systems, and to interconnections of stable systems.Comment: 16 pages, no figure

H2H_2 optimal controllers with observer based architecture for continuous-time systems : separation principle

For a general H2 optimal control problem, at first all Hz optimal measurement feedback controllers are characterized and parameterized, and then attention is focused on controllers with observer based architecture. Both full order as well as reduced order observer based H2 optimal controllers are characterized and parameterized. Also, systematic methods ofdesigning them are presented. An important problem that can be coined as an H2 optimal control problem with simultaneous pole placement, is formulated and solved. That is, since in general there exist many H2 optimal measurement feedback controllers, utilizing such flexibility and freedom, we can solve the problem of simultaneously placing the closed-loop poles at desirable locations whenever possible while still preserving H2 optimality. All the design algorithms developed here are easily computer implementable

A geometric theory for 2-D systems including notions of stabilisability

In this paper we consider the problem of internally and externally stabilising controlled invariant and output-nulling subspaces for two-dimensional (2-D) Fornasini–Marchesini models, via static feedback. A numerically tractable procedure for computing a stabilising feedback matrix is developed via linear matrix inequality techniques. This is subsequently applied to solve, for the first time, various 2-D disturbance decoupling problems subject to a closed-loop stability constraint

Controls design with crossfeeds for hovering rotorcraft using quantitative feedback theory

A multi-input, multi-output controls design with dynamic crossfeed pre-compensation is presented for rotorcraft in near-hovering flight using Quantitative Feedback Theory (QFT). The resulting closed-loop control system bandwidth allows the rotorcraft to be considered for use as an inflight simulator. The use of dynamic, robust crossfeeds prior to the QFT design reduces the magnitude of required feedback gain and results in performance that meets most handling qualities specifications relative to the decoupling of off-axis responses. Handling qualities are Level 1 for both low-gain tasks and high-gain tasks in the roll, pitch, and yaw axes except for the 10 deg/sec moderate-amplitude yaw command where the rotorcraft exhibits Level 2 handling qualities in the yaw axis caused by phase lag. The combined effect of the QFT feedback design following the implementation of low-order, dynamic crossfeed compensators successfully decouples ten of twelve off-axis channels. For the other two channels it was not possible to find a single, low-order crossfeed that was effective. This is an area to be investigated in future research

The statistical properties of stars and their dependence on metallicity: the effects of opacity (article)

The author has deposited data related to this article in ORE on open access. See: http://hdl.handle.net/10871/14881We report the statistical properties of stars and brown dwarfs obtained from four radiation hydrodynamical simulations of star cluster formation that resolve masses down to the opacity limit for fragmentation. The calculations are identical except for their dust and gas opacities. Assuming dust opacity is proportional to metallicity, the calculations span a range of metallicities from 1/100 to 3 times solar, although we emphasize that changing the metallicity has other thermodynamic effects that the calculations do not capture (e.g. on the thermal coupling between gas and dust). All four calculations produce stellar populations whose statistical properties are difficult to distinguish from observed stellar systems, and we find no significant dependence of stellar properties on opacity. The mass functions and properties of multiple stellar systems are consistent with each other. However, we find that protostellar mergers are more common with lower opacities. Combining the results from the three calculations with the highest opacities, we obtain a stellar population consisting of more than 500 stars and brown dwarfs. Many of the statistical properties of this population are in good agreement with those observed in our Galaxy, implying that gravity, hydrodynamics, and radiative feedback may be the primary ingredients for determining the statistical properties of low-mass stars. However, we do find indications that the calculations may be slightly too dissipative. Although further calculations will be required to understand all of the effects of metallicity on stellar properties, we conclude that stellar properties are surprisingly resilient to variations of the dust and gas opacities