Analysis and Control of Non-Affine, Non-Standard, Singularly Perturbed Systems

This dissertation addresses the control problem for the general class of control non-affine, non-standard singularly perturbed continuous-time systems. The problem of control for nonlinear multiple time scale systems is addressed here for the first time in a systematic manner. Toward this end, this dissertation develops the theory of feedback passivation for non-affine systems. This is done by generalizing the Kalman-Yakubovich-Popov lemma for non-affine systems. This generalization is used to identify conditions under which non-affine systems can be rendered passive. Asymptotic stabilization for non-affine systems is guaranteed by using these conditions along with well-known passivity-based control methods. Unlike previous non-affine control approaches, the constructive static compensation technique derived here does not make any assumptions regarding the control influence on the nonlinear dynamical model. Along with these control laws, this dissertation presents novel hierarchical control design procedures to address the two major difficulties in control of multiple time scale systems: lack of an explicit small parameter that models the time scale separation and the complexity of constructing the slow manifold. These research issues are addressed by using insights from geometric singular perturbation theory and control laws are designed without making any assumptions regarding the construction of the slow manifold. The control schemes synthesized accomplish asymptotic slow state tracking for multiple time scale systems and simultaneous slow and fast state trajectory tracking for two time scale systems. The control laws are independent of the scalar perturbation parameter and an upper bound for it is determined such that closed-loop system stability is guaranteed. Performance of these methods is validated in simulation for several problems from science and engineering including the continuously stirred tank reactor, magnetic levitation, six degrees-of-freedom F-18/A Hornet model, non-minimum phase helicopter and conventional take-off and landing aircraft models. Results show that the proposed technique applies both to standard and non-standard forms of singularly perturbed systems and provides asymptotic tracking irrespective of the reference trajectory. This dissertation also shows that some benchmark non-minimum phase aerospace control problems can be posed as slow state tracking for multiple time scale systems and techniques developed here provide an alternate method for exact output tracking

Investigation of a Verification and Validation Tool with a Turbofan Aircraft Engine Application

The development of more advanced control architectures for turbofan aircraft engines can yield gains in performance and efficiency over the lifetime of an engine. However, the implementation of these increasingly complex controllers is contingent on their ability to provide safe, reliable engine operation. Therefore, having the means to verify the safety of new control algorithms is crucial. As a step towards this goal, CoCoSim, a publicly available verification tool for Simulink, is used to analyze C-MAPSS40k, a 40,000 lbf class turbo-fan engine model developed at NASA for testing new control algorithms. Due to current limitations of the verification software, several modifications are made to C-MAPSS40k to achieve compatibility with CoCoSim. Some of these modifications sacrifice fidelity to the original model. Several safety and performance requirements typical for turbofan engines are identified and constructed into a verification framework. Preliminary results using an industry standard baseline controller for these requirements are presented. While verification capabilities are demonstrated, a truly comprehensive analysis will require further development of the verification tool

The attributes, ontology terms and their relationship within (A) Variation and (B) Interaction level.

<p>The attributes, ontology terms and their relationship within (A) Variation and (B) Interaction level.</p

(A) The screenshot of FROG Interface displaying ontology terms and associated fingerprints (B) The search tool interface to query the DNA variation using ontology (C) Sample output of the search tool.

<p>(A) The screenshot of FROG Interface displaying ontology terms and associated fingerprints (B) The search tool interface to query the DNA variation using ontology (C) Sample output of the search tool.</p

(A) Summary of the fingerprints designed to represent ontology terms in the six levels (B) As an example, the 15 attributes of the Variation level are listed along with their bit annotation (C) Example in Table 2 is explained with help of color coded bits.

<p>(A) Summary of the fingerprints designed to represent ontology terms in the six levels (B) As an example, the 15 attributes of the Variation level are listed along with their bit annotation (C) Example in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0134693#pone.0134693.t002" target="_blank">Table 2</a> is explained with help of color coded bits.</p

The attributes, ontology terms and their relationship within (A) RNA and (B) Protein level.

<p>The attributes, ontology terms and their relationship within (A) RNA and (B) Protein level.</p

(A) Scope of FROG (B) Number of attributes and terms in six levels.

<p>(A) Scope of FROG (B) Number of attributes and terms in six levels.</p

Properties in FROG and their source.

<p>Properties in FROG and their source.</p

The attributes, ontology terms and their relationship within (A) Chromosome and (B) DNA level.

<p>The attributes, ontology terms and their relationship within (A) Chromosome and (B) DNA level.</p