Quasilinear Control of Systems with Time-Delays and Nonlinear Actuators and Sensors

This thesis investigates Quasilinear Control (QLC) of time-delay systems with nonlinear actuators and sensors and analyzes the accuracy of stochastic linearization for these systems. QLC leverages the method of stochastic linearization to replace each nonlinearity with an equivalent gain, which is obtained by solving a transcendental equation. The idea of QLC is to stochastically linearize the system in order to analyze and design controllers using classical linear control theory. In this thesis, the existence of the equivalent gain for a closed-loop time-delay system is discussed. To compute the equivalent gain, two methods are explored. The first method uses an explicit but complex algorithm based on delay Lyapunov equation to study the time-delay, while the second method uses Pade approximant. It is shown that, under a suitable criterion, Pade approximant can be effectively applied for QLC of time-delay systems. Furthermore, the method of Saturated-Root Locus (S-RL) is extended to nonlinear time-delay systems. It turns out that, in a time-delay system, S-RL always terminates prematurely as opposed to a delay-free system, which may or may not terminate prematurely. Statistical experiments are performed to investigate the accuracy of stochastic linearization compared to a system without time-delay. The impact of increasing the time-delay in the approach of stochastic linearization is also investigated. Results show that stochastic linearization effectively linearizes a nonlinear time-delay system, even though delays generally degrade accuracy. Overall, the accuracy remains relatively high over the selected parameters. Finally, this approach is applied to pitch control in a wind turbine system as a practical example of a nonlinear time-delay system, and its performance is analyzed to demonstrate the efficacy of the approach

Quasilinear Control Theory for Systems with Asymmetric Actuators and Sensors.

Quasilinear Control (QLC) theory provides a set of methods for analysis and design of systems with nonlinear actuators and sensors. In practice, actuators always saturate and sensors often have deadzone or quantization. One limitation of the current QLC theory is that it is applicable only to systems with symmetric nonlinearities. In many situations, however, nonlinearities are asymmetric. Examples of such systems abound: air-conditioning/heating systems, automotive torque and idle speed control, wind turbine control, etc. In this work, we provide an extension of the QLC theory to the asymmetric case. Similar to the symmetric case, the approach is based on the method of stochastic linearization, which replaces nonlinear systems by quasilinear ones. Unlike the symmetric case, however, stochastic linearization in the asymmetric case replaces each nonlinearity not only by an equivalent gain, but also by an equivalent bias. The latter leads to steady state errors incompatible with the usual error coefficients predicted by linear systems theory. For this reason, the extension to the asymmetric case is non-trivial. Specific problems addressed in this dissertation with regards to asymmetric systems are: (i) Introduction and investigation of the notion of asymmetry. (ii) Development of a formalism of stochastic linearization for systems at hand. (iii) Analysis of tracking and disturbance rejection performance. (iv) Introduction and investigation of performance loci, i.e., root locus and tracking error locus. (v) Utilization of the performance loci for random reference and step reference tracking controller design. (vi) Recovery of linear performance in nonlinear systems. (vii) Disturbance rejection controller design using an LQR-type approach. (viii) Application of the methods developed to a wind farm controller design. In addition, a Matlab-based toolbox that implements most of the QLC methods has been developed and is available at www.QuasilinearControl.com.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99805/1/hamido_1.pd

Towards verifiable adaptive control for safety critical applications

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.Includes bibliographical references (p. 97-101).To be implementable in safety critical applications, adaptive controllers must be shown to behave strictly according to predetermined specifications. This thesis presents two tools for verifying specifications relevant to practical direct-adaptive control systems. The first tool is derived from an asymptotic analysis of the error dynamics of a direct adaptive controller and uncertain linear plant. The analysis yields a so called Reduced Linear Asymptotic System, which can be used for designing adaptive systems to meet transient specifications. The tool is demonstrated in two design examples from flight mechanics, and verified in numerical simulation. The second tool developed is an algorithm for direct-adaptive control of plants with magnitude saturation constraints on multiple inputs. The algorithm is a non-trivial extension of an existing technique for single input systems with saturation. Boundeness of all signals is proved for initial conditions in a compact region. In addition, the notion of a class of multi-dimensional saturation functions is introduced. The saturation compensation technique is demonstrated in numerical simulation. Finally, these tools are applied to design a direct-adaptive controller for a realistic multi-input aircraft model to accomplish control reconfiguration in the case of unforeseen failure, damage, or disturbances. A novel control design for incorporating control allocation and reconfiguration is introduced. The adaptive system is shown in numerical simulation to have favorable transient qualities and to give a stable response with input saturation constraints.by Mac Schwager.S.M

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Magnetic Actuators and Suspension for Space Vibration Control

The research on microgravity vibration isolation performed at the University of Virginia is summarized. This research on microgravity vibration isolation was focused in three areas: (1) the development of new actuators for use in microgravity isolation; (2) the design of controllers for multiple-degree-of-freedom active isolation; and (3) the construction of a single-degree-of-freedom test rig with umbilicals. Described are the design and testing of a large stroke linear actuator; the conceptual design and analysis of a redundant coarse-fine six-degree-of-freedom actuator; an investigation of the control issues of active microgravity isolation; a methodology for the design of multiple-degree-of-freedom isolation control systems using modern control theory; and the design and testing of a single-degree-of-freedom test rig with umbilicals

Development of automatic and manual flight director landing systems for the XV-15 tilt rotor aircraft in helicopter mode

The objective of this effort is to determine IFR approach path and touchdown dispersions for manual and automatic XV-15 tilt rotor landings, and to develop missed approach criteria. Only helicopter mode XV-15 operation is considered. The analysis and design sections develop the automatic and flight director guidance equations for decelerating curved and straight-in approaches into a typical VTOL landing site equipped with an MLS navigation aid. These system designs satisfy all known pilot-centered, guidance and control requirements for this flying task. Performance data, obtained from nonstationary covariance propagation dispersion analysis for the system, are used to develop the approach monitoring criteria. The autoland and flight director guidance equations are programmed for the VSTOLAND 1819B digital computer. The system design dispersion data developed through analysis and the 1819B digital computer program are verified and refined using the fixed-base, man-in-the-loop XV-15 VSTOLAND simulation

THE DEVELOPMENT OF A NOVEL SUSPENSION ARM WITH 2-DIMENSIONAL ACTUATION, FOR USE IN ADVANCED HARD DISK DRIVES

As magnetic computer disks are developed to ever-greater data storage densities, the accuracy required for head positioning is moving beyond the accuracy provided by present technology using single-stage voice-coil motors in hard disk drives. This thesis details work to develop a novel active suspension arm with 2-dimensional actuation for use in advanced hard disk drives. The arm developed is capable of high-bandwidth data tracking as well as precision head flying height control motion. High-bandwidth data tracking is facilitated by the use of piezoelectric stack actuator, positioned closer to the head. The suspension arm is also capable of motion in the orthogonal axis. This motion represents active flying height control to maintain the correct altitude during drive operation. To characterise the suspension arm's structural dynamics, a high-resolution measurement system based on the optical beam deflection technique has been developed. This has enabled the accurate measurement of minute end-deflections of the suspension arm in 2-dimensions, to sub-nanometre resolution above noise. The design process of the suspension arm has led into the development of novel piezoelectric-actuated arms. In the work involving lead zirconate titanate (PZT) thick films as actuators, work in this thesis shows that reinforcing the films with fibre improves the overall actuation characteristics of the thick films. This discovery benefits applications such as structural health monitoring. The final suspension arm design has been adopted because it is simple in design, easier to integrate within current hard disk drive environment and easier to fabricate in mass. Closed-loop control algorithms based on proportional, integral and derivative (PID) controller techniques have been developed and implemented to demonstrate high bandwidths that have been achieved. The suspension arm developed presents an important solution in head-positioning technology in that it offers much higher bandwidths for data tracking and flying height control; both very essential in achieving even higher data storage densities on magnetic disks at much reduced head flying heights, compared to those in existing hard disk drives

Sistema Didáctico para el Diseño de Compensadores Utilizando LabVIEW

En el presente trabajo se describe un sistema para el diseño de compensadores implementado en un instrumento virtual (IV). Los compensadores que se utilizan son compensadores en cascada, para su diseño se emplea una técnica de control clásico llamada “Lugar Geométrico de las Raíces” (LGDR).El IV se realizó en LabVIEW utilizando un lenguaje de programación gráfico, este software ofrece la ventaja de poder realizar cálculos de manera concurrente. El IV cuenta con un sistema resistivo – capacitivo (RC) de segundo orden donde es posibleelegir los valores de las resistencias y capacitancias, obteniendo la función de transferencia en lazo abierto que se utilizará como proceso. En el IV se puede analizar gráficamente el comportamiento del sistema en lazo abierto ante diferentes entradas de posición.El proceso se puede compensar utilizando sistemas de control: Proporcional, Proporcional -  Integral (PI), Proporcional – Derivativo (PD), Proporcional – Integral – Derivativo (PID), compensador en atraso, compensador en adelanto y compensador en atraso – adelanto.Todos los resultados obtenidos en cada una de las compensaciones se pueden analizar gráficamente en simulación y en línea, además de observar los nuevos LGDR (Lugar geométrico de la raíz) de los sistemas compensados

Quasilinear Control: Multivariate Nonlinearities, Robustness and Numerical Properties, and Applications

Quasilinear Control (QLC) is a theory with a set of tools used for the analysis and design of controllers for nonlinear feedback systems driven by stochastic inputs. It is based on the concept of Stochastic Linearization (SL), which is a method of linearizing a nonlinear function that, unlike traditional Jacobian linearization, uses statistical properties of the input to the nonlinearity to linearize it. Until now in the literature of QLC, SL was applied only to feedback systems with single-variable nonlinearities that appear only in actuators and/or sensors. In this dissertation, my recent contributions to the literature of QLC are summarized. First, the QLC theory is extended to feedback systems with isolated multivariate nonlinearities that can appear anywhere in the loop and applied to optimal controller design problems, including systems with state-multiplicative noise. Second, the numerical properties of SL, particularly, the accuracy, robustness, and computation of SL, are investigated. Upper bounds are provided for the open-loop relative accuracy and, consequently, the closed-loop accuracy of SL. A comparison of the computational costs of several common numerical algorithms in solving the SL equations is provided, and a coordinate transformation proposed to improve most of their success rates. A numerical investigation is carried out to determine the relative sensitivities of SL coefficients to system parameters. Finally, QLC is applied to the optimal primary frequency control of power systems with generator saturation, and control of virtual batteries in distribution feeders. The expected impacts of this work are far-reaching. On the technical front, this work provides: i) a new set of theoretical and algorithmic tools that can improve and simplify control of complex systems affected by noise, ii) information to control engineers on accuracy guarantees, choice of solvers, and relative sensitivities of SL coefficients to system parameters to guide the analysis and design of nonlinear stochastic systems in the context of QLC, iii) a new computationally efficient method of addressing saturation in generators or virtual batteries in modern electric power systems, resulting in efficient utilization of resources in providing grid services. On the societal front, this work: i) enables technologies that rely on computationally-efficient algorithms for automation of complex systems, e.g., control of soil temperature for agriculture, which depends on multiple factors like soil moisture and net radiation, ii) allows effective coordination of controllable smart devices in people’s homes, so as not to hamper their quality of service, and iii) provides a stepping stone towards key societal challenges like combating climate change by facilitating reliable operation of the grid with significant renewable penetration