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An efficient nonlinear equivalent beam finite-element method for the application of a full state feedback design is described, which is robust to plant uncertainties to a beamlike truss structure with nonlinear elements. The method may be extended to model nonlinear structures with other types of control systems, such as model-based compensators.
This report attempts to document the broad scope of issues that must be satisfactorily resolved before one can expect to methodically obtain, with a reasonable confidence, a near-optimal robust closed loop performance in physical applications. These include elements of signal processing, noise identification, system identification, model validation, and uncertainty modeling. Based on a recently developed methodology involving a parameterization of all model validating uncertainty sets for a given linear fractional transformation (LFT) structure and noise allowance, a new software, Uncertainty Bound Identification (UBID) toolbox, which conveniently executes model validation tests and determine uncertainty bounds from data, has been designed and is currently available. This toolbox also serves to benchmark the current state-of-the-art in uncertainty bound determination and in turn facilitate benchmarking of robust control technology. To help clarify the methodology and use of the new software, two tutorial examples are provided. The first involves the uncertainty characterization of a flexible structure dynamics, and the second example involves a closed loop performance validation of a ducted fan based on an uncertainty bound from data. These examples, along with other simulation and experimental results, also help describe the many factors and assumptions that determine the degree of success in applying robust control theory to practical problems.
Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.
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A strategy that calculates an explicit state feedback policy to regulate constrained uncertain discrete‐time uncertain linear systems is presented. We consider uncertain processes, affected by box‐bounded multiplicative uncertainty as well as bounded additive uncertainty with linear state and inputs constraints. The proposed method includes (i) the calculation of a terminal set constraint and (ii) the robust reformulation of state constraints in the prediction horizon. These features allow the derivation of the desired policy by solving a single multiparametric quadratic programming problem that guarantees feasible operation in the presence of uncertainty. Additionally, we employ variable and constraint elimination approaches to enhance the computational performance of the strategy. We demonstrate the steps and benefits of these developments with a numerical example and a chemical engineering case study.
Motivated by the recent explosive development of results in the area of parametric robust control, a new technique to identify a family of uncertain systems is identified. The new technique takes the frequency domain input and output data obtained from experimental test signals and produces an 'interval transfer function' that contains the complete frequency domain behavior with respect to the test signals. This interval transfer function is one of the key concepts in the parametric robust control approach and identification with such an interval model allows one to predict the worst case performance and stability margins using recent results on interval systems. The algorithm is illustrated by applying it to an 18 bay Mini-Mast truss structure.
Abstract On‐orbit close proximity operations involve robotic spacecraft maneuvering and making decisions for a growing number of mission scenarios demanding autonomy, including on‐orbit assembly, repair, and astronaut assistance. Of these scenarios, on‐orbit assembly is an enabling technology that will allow large space structures to be built in situ, using smaller building block modules. However, like many of these scenarios, robotic on‐orbit assembly involves several technical hurdles, such as changing system models. For instance, grappled modules moved by a free‐flying “assembler” robot can cause significant changes in the combined system inertia, which have cascading impacts on motion planning and control portions of the autonomy stack. Further, on‐orbit assembly and other scenarios require collision‐avoiding motion planning, particularly when operating in a “construction site” scenario of multiple assembler robots and structures. Multiple key technologies that address these complicating factors for autonomous microgravity close proximity operations are detailed in this work, in particular: (1) application of global long‐horizon planning, accomplished using offline and online sampling‐based planner options that consider the system dynamics; (2) adaptation of the recently proposed RATTLE information‐aware planning framework for on‐orbit reconfiguration model learning; and (3) connection with robust control tools to provide low‐level control robustness using current system knowledge. These approaches were demonstrated for an autonomous on‐orbit assembly use case by the RElative Satellite sWarming and Robotic Maneuvering (ReSWARM) experiments using NASA's Astrobee robots on the International Space Station. Results of the ReSWARM experiments are provided along with significant operational and implementation detail discussing the practicalities of hardware implementation and unique aspects of working with the Astrobee free‐flyer robots in microgravity. ReSWARM provides a base set of planning and control tools for robotic close proximity operations, demonstrates them in microgravity, and outlines some of the important hardware aspects that future autonomous free‐flyers will need to consider.
Abstract The majority of literature on robust control assumes that a design model is available and that the uncertainty model bounds the actual variations about the nominal model. However, methods for generating accurate design models have not received as much attention in the literature. The influence of the level of accuracy of the uncertainty model on closed loop performance has received even less attention. The research reported herein is an initial step in applying and extending the concept of model validation to the problem of obtaining practical uncertainty models for robust control analysis and design applications. An extension of model validation called 'sequential validation' is presented and applied to a simple spring-mass-damper system to establish the feasibility of the approach and demonstrate the benefits of the new developments.
A frequency domain method is developed for plant set estimation. The estimation of a plant 'set' rather than a point estimate is required to support many methods of modern robust control design. The approach here is based on using a Schroeder-phased multisinusoid input design which has the special property of placing input energy only at the discrete frequency points used in the computation. A detailed analysis of the statistical properties of the frequency domain estimator is given, leading to exact expressions for the probability distribution of the estimation error, and many important properties. It is shown that, for any nominal parametric plant estimate, one can use these results to construct an overbound on the additive uncertainty to any prescribed statistical confidence. The 'soft' bound thus obtained can be used to replace 'hard' bounds presently used in many robust control analysis and synthesis methods.
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Universal control of multimode bosonic modes typically relies on a dispersively coupled transmon ancilla. However, its frequency undergoes a Stark shift that depends on the state of each coupled bosonic mode, leading to a frequency mismatch in the ancilla drive and ultimately reducing the fidelity of multimode gates
Variables control charts based on sample means for determining in-control probability properties
In-control probability properties of variables control charts for mean population surveillance
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An approach to the control of elastic robotic systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law, u sub d, is derived such that in the closed loop system, independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law, u sub s, is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that, in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u sub d + u sub s.