Anshu Narang-Siddarth

Nonlinear Time Scale Systems in Standard and Nonstandard Forms: Analysis and Control

This book introduces key concepts for systematically controlling engineering systems that possess interacting phenomena occurring at widely different speeds. The aim is to present the reader with control techniques that extend the benefits of model reduction of singular perturbation theory to a larger class of nonlinear dynamical systems. New results and relevant background are presented through insightful examples that cover a wide range of applications from different branches of engineering. This book is unique because it presents a new perspective on existing control methods and thus broadens their application to a larger class of nonlinear dynamical systems. It also discusses general rather than problem-specific developments to certain applications or disciplines in order to provide control engineers with useful analytical tools, and it addresses new control problems using singular perturbation methods, including closed-form results for control of nonminimum phase systems. Audience: Nonlinear Time Scale Systems in Standard and Nonstandard Forms: Analysis and Control is intended for researchers and practitioners who use time scale methods to mitigate the curse of dimensionality and higher order controllers. It will be specifically useful to aerospace, mechanical, and electrical engineers, as well as students and researchers in applied mathematics interested in systems and control. It will also be of interest to physicists, biologists, and chemists who use time scale techniques.

Increased Functionality of Continuation-Based Nonlinear System Analysis

The high complexity of modern autonomous aerospace systems has created a need for new, powerful analysis techniques for control design and validation. This paper exploits the capabilities of continuation algorithms to derive a numerical analysis method that provides a systematic way to investigate how system properties local to the equilibrium condition around which the system is operated change throughout the operational envelope. The method is based on computing subsets of the system’s equilibrium manifold with particular properties that are specified by equality constraints. The contribution of this work lies in the derivation of extended systems of equations that enable the definition of constraints on the eigenvalues and eigenvectors of the linearized dynamics, so that sets of equilibrium points with particular characteristics of the local dynamical behavior can be computed. The capabilities of the method are demonstrated through application to a fully nonlinear aircraft model with six degrees of fre...

Continuation Analysis of Nonlinear Systems with Equality Constraints on States, Parameters, and Eigenvalues

The high complexity of modern autonomous aerospace systems has created a need for new, powerful analysis techniques for control design, verification, and validation. This paper exploits the capabilities of continuation methods to analyze system properties of interest along with identification of stability boundaries of parameter-dependent nonlinear systems in the context of numerical bifurcation analysis. Direct inclusion of equality constraints and numerical implementation of continuation methods is discussed. In addition, eigenvalue-based performance metrics are investigated. For this, an extended system of equations for the continuation of equilibrium solutions subject to a specified performance constraint on the eigenvalues of the local linearization is derived. The capabilities of the methods are demonstrated through two applications. Equilibrium points for a range of operating conditions of an axial dual-spin spacecraft are found in the first example and validated with existing results in literature. The second application determines the flight envelope with contours of constant natural frequency, damping ratio, and time-to-double for the Phugoid and Dutch Roll modes of NASA’s Generic Transport Model using the recently published Generic Nonlinear Aerodynamic Model.

Autopilot for a Nonlinear Non-Minimum Phase Tail-Controlled Missile

Acceleration control of highly agile, aerodynamically-controlled missiles is a well-known non-minimum phase control problem. This problem is revisited here for a planar tailcontrolled generic missile, and a globally stable nonlinear autopilot command structure is synthesized to maximize performance. For the rst time the non-minimum phase characteristics of the vehicle are addressed by making no modication to the output denition by inducing an inherent time scale separation in the closed-loop dynamics. Unlike, previous time scale control techniques, results presented here are based on theoretical advancements made in control of nonlinear singularly perturbed systems. Conditions under which the induced time scale separation can be employed for a stable autopilot design are also discussed. The state feedback controller proposed is real-time implementable, independent of operating condition and desired output trajectory. Simulation results presented in the paper show that the approach is able to accomplish perfect tracking while keeping all closed-loop signals bounded.

The Method of Multiple Scales for Orbit Propagation with Atmospheric Drag

E cient space situational awareness requires trajectory propagation techniques that give direct insight into how atmospheric drag related uncertainties manifest in position and velocity errors over time. This paper uses the method of multiple scales to develop a new semi-analytic trajectory propagation technique for drag-perturbed objects that gives this necessary insight for the rst time. As opposed to other approaches, the approximate trajectories generated using this method are shown to have known error properties that directly depend on the drag parameters. These properties are essential for e ective object tracking and catalog maintenance. Simulations demonstrate the e ectiveness of the technique for several representative orbit families.

Time-scale separation on networks: Consensus, tracking, and state-dependent interactions

This paper studies the coupling between dynamics that span multiple time-scales in distributed networked systems. In particular, we consider the evolution of the consensus dynamics interacting with fast nonlinear vehicle dynamics as well as its progress over a state-dependent graphs with slow-varying weight dynamics. Graph-based guarantees are provided that certify the existence of a separation principle across time-scales. Further, we quantify the role of the networks structure in ensuring stability of the composite multi-time-scale system. Graph spectral measures are calculated providing designers a network structure approach to improve performance and/or stability of the coupled system. Examples are presented illustrating the results.

A constructive stabilization approach for open-loop unstable non-affine systems

This paper focuses on the stabilization of non-affine-in-control systems that are open-loop unstable. The main result of the paper is a general method for constructing feedback stabilization of all non-affine systems. The synthesis procedure is based on concepts of feedback passivation, and is extended for non-affine systems by deriving sufficient conditions for passivity. The developments and essential ideas of the proposed technique are validated via simulation.

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

The development of new capabilities in system intelligence and autonomy will require new means of verification and validation (V&V) to ensure safety and performance requirements are satisfied. As a step towards this goal, CoCoSim, a publicly available V&V tool, is being developed to analyze the validity of user-defined assertions on MATLAB/Simulink models. This paper demonstrates CoCoSim’s capabilities by applying it to C-MAPSS40k, a 40,000 lbf class turbofan engine model developed at NASA for testing new control algorithms. Due to the current limitations of the CoCoSim V&V software, several modifications are made to C-MAPSS40k to achieve compatibility with CoCoSim. Some of these modifications sacrifice fidelity of the original model, but the analysis is still useful even with that limitation. Several safety and performance requirements typical of turbofan engines are identified and constructed into a series of assertions to be tested as part of the V&V framework. Preliminary results for these requirements using C-MAPSS40k’s industry standard turbofan engine controller are presented. While CoCoSim’s capabilities are demonstrated, a truly comprehensive analysis will require further development of the tool.

Autonomously Blended Passive and Active control for a CubeSat-class science mission

One challenge facing CubeSat-class spacecraft undertaking science operations is that the volume constraints associated with this form factor impose strict limitations on control authority. In particular, it can be difficult to complete traditional reorientation maneuvers in a timely manner due to the comparatively low saturation limits of these actuators. This paper demonstrates the use of a new approach to spacecraft attitude control known as Autonomously Blended Passive and Active (ABPA) control. This control strategy treats the space environment as an asset and seeks to simultaneously regulate both passive and active attitude control elements in flight in accordance with a set of desired guidance commands. Applied to a six-unit (6U) CubeSat performing a reorientation maneuver typical of scientific spacecraft, a controller designed using techniques in autonomous blending of active and passive controls is demonstrated through simulation to offer significant thruster propellant savings without sacrificing time domain performance when compared to traditional control methods.

Pseudo-arclength method convergence for continuous, piecewise-differentiable systems

Continuation algorithms such as the pseudo-arclength method are frequently used to analyze nonlinear dynamical systems and to solve optimal control problems. They require continuous differentiability of the equations to be solved and may stall if this assumption is violated. This paper analyzes the conditions under which the pseudo-arclength method succeeds or fails when applied to a system of equations that is continuous but only piecewise differentiable. A strategy to alleviate this problem is derived based on the insights gained.