Predictive Control for Alleviation of Gust Loads on Very Flexible Aircraft

In this work the dynamics of very flexible aircraft are described by a set of non-linear, multi-disciplinary equations of motion. Primary structural components are represented by a geometrically-exact composite beam model which captures the large dynamic deformations of the aircraft and the interaction between rigid-body and elastic degrees-of-freedom. In addition, an implementation of the unsteady vortex-lattice method capable of handling arbitrary kinematics is used to capture the unsteady, three-dimensional flow-eld around the aircraft as it deforms. Linearization of this coupled nonlinear description, which can in general be about a nonlinear reference state, is performed to yield relatively high-order linear time-invariant state-space models. Subsequent reduction of these models using standard balanced truncation results in low-order models suitable for the synthesis of online, optimization-based control schemes that incorporate actuator constraints. Predictive controllers are synthesized using these reduced-order models and applied to nonlinear simulations of the plant dynamics where they are shown to be superior to equivalent optimal linear controllers (LQR) for problems in which constraints are active

Balanced Truncation of Linear Time-Invariant Systems over Finite-frequency Ranges

This paper discusses model order reduction of LTI systems over limited frequency intervals within the framework of balanced truncation. Two new \emph{frequency-dependent balanced truncation} methods were developed, one is \emph{SF-type frequency-dependent balanced truncation} to copy with the cases that only a single dominating point of the operating frequency interval is pre-known, the other is \emph{interval-type frequency-dependent balanced truncation} to deal with the cases that both of the upper and lower bound of frequency interval are known \emph{a priori}. SF-type error bound and interval-type error bound are derived for the first time to estimate the desired approximation error over pre-specified frequency interval. We show that the new methods generally lead to good in-band approximation performance, at the same time, provide accurate error bounds under certain conditions. Examples are included for illustration.Comment: prepared to submit for International Journal of Contro

Model Reduction Using Semidefinite Programming

In this thesis model reduction methods for linear time invariant systems are investigated. The reduced models are computed using semidefinite programming. Two ways of imposing the stability constraint are considered. However, both approaches add a positivity constraint to the program. The input to the algorithms is a number of frequency response samples of the original model. This makes the computational complexity relatively low for large-scale models. Extra properties on a reduced model can also be enforced, as long as the properties can be expressed as convex conditions. Semidefinite program are solved using the interior point methods which are well developed, making the implementation simpler. A number of extensions to the proposed methods were studied, for example, passive model reduction, frequency-weighted model reduction. An interesting extension is reduction of parameterized linear time invariant models, i.e. models with state-space matrices dependent on parameters. It is assumed, that parameters do not depend on state variables nor time. This extension is valuable in modeling, when a set of parameters has to be chosen to fit the required specifications. A good illustration of such a problem is modeling of a spiral radio frequency inductor. The physical model depends nonlinearly on two parameters: wire width and wire separation. To chose optimally both parameters a low-order model is usually created. The inductor modeling is considered as a case study in this thesis