Static anti-windup compensator design for locally Lipschitz systems under input and output delays

This paper proposes a static anti-windup compensator (AWC) design methodology for the locally Lipschitz nonlinear systems, containing time-varying interval delays in input and output of the system in the presence of actuator saturation. Static AWC design is proposed for the systems by considering a delay-range-dependent methodology to consider less conservative delay bounds. The approach has been developed by utilizing an improved Lyapunov-Krasovskii functional, locally Lipschitz nonlinearity property, delay-interval, delay derivative upper bound, local sector condition, L2 gain reduction from exogenous input to exogenous output, improved Wirtinger inequality, additive time-varying delays, and convex optimization algorithms to obtain convex conditions for AWC gain calculations. In contrast to the existing results, the present work considers both input and output delays for the AWC design (along with their combined additive effect) and deals with a more generic locally Lipschitz class of nonlinear systems. The effectiveness of the proposed methodology is demonstrated via simulations for a nonlinear DC servo motor system, possessing multiple time-delays, dynamic nonlinearity and actuator constraints

Adaptive Actuator Compensation of Position Tracking for High-Speed Trains with Disturbances

In this paper, the adaptive fault compensation prob-lem is investigated for high-speed trains in the presence of time-varying system parameters, disturbances and actuator failures. To deal with the time-varying system parameters, a new time-varying indicator function instead of commonly used 0-1 function, is proposed to model the train dynamics as a piecewise model with unparameterizable time-varying disturbances, which can cover more time variations and help parametrization for adaptation. A backstepping adaptive controller is designed for the healthy system with unknown piecewise model parameters and known piecewise bounds on disturbances. For both the parameterizable and unparameterizable failures, the backstepping adaptive fail-ure compensation with the adaptive laws are derived to achieve the position tracking under the known bound disturbances. The adaptive failure compensation for unknown bounds on disturbances is also discussed under the parameterizable failure. Through introducing the nonlinear damping in the proposed controller, the failure compensation controller is proposed for the model with unparameterizable system parameters to achieve an arbitrary degree of position tracking accuracy. The stability of the corresponding closed-loop system and asymptotic state tracking are proved via Lyapunov direct method, and validated using a high-speed train model

Disturbance Rejection and Control in Web Servers

An important factor for a user of web sites on the Internet is the duration of time between the request of a web page until an answer has been returned. If this response time is too long, the user is likely to abandon the web site and search for other providers of the service. To avoid this loss of users, it is important for the web site operator to assure that users are treated sufficiently fast. On the other hand, it is also important to minimize the effort to optimize profit. As these objectives often are contradictory, an acceptable target response-time that can be formulated. The resources are allocated in a manner that ensures that long response times do not occur, while, at the same time, using as little resources as possible to not overprovision. The work presented in this doctoral thesis takes a control-theoretic perspective to solve this problem. The resources are considered as the control input, and the response time as the main output. Several disturbances affect the system, such as the arrival rate of requests to the web site. A testbed was designed to allow repeatable experiments with different controller implementations. A server was instrumented with sensors and actuators to handle requests from 12 client computers with capability for changing work loads. On the theoretical side, a model of a web server is presented in this thesis. It explicitly models a specific sensor implementation where buffering occurs in the computer prior to the sensor. As a result, the measurement of the arrival rate becomes state dependent under high load. This property turns out to have some undesirable effects on the controlled system. The model was capable of predicting the behavior of the testbed quite well. Based on the presented model, analysis shows that feed-forward controllers suggested in the literature can lead to instability under certain circumstances at high load. This has not been reported earlier, but is in this doctoral thesis demonstrated by both simulations and experiments. The analysis explains why and when the instability arises. In the attempt to predict future response-times this thesis also presents a feedback based prediction scheme. Comparisons between earlier predictions to the real response-times are used to correct a model based response time prediction. The prediction scheme is applied to a controller to compensate for disturbances before the effect propagates to the response time. The method improves the transient response in the case of sudden changes in the arrival rate of requests. This doctoral thesis also presents work on a control solution for reserving CPU capacity for a given process or a given group of processes on a computer system. The method uses only existing operating-system infrastructure, and achieves the desired CPU capacity in a soft real-time manner

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

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Stochastic Real-time Optimal Control: A Pseudospectral Approach for Bearing-Only Trajectory Optimization

A method is presented to couple and solve the optimal control and the optimal estimation problems simultaneously, allowing systems with bearing-only sensors to maneuver to obtain observability for relative navigation without unnecessarily detracting from a primary mission. A fundamentally new approach to trajectory optimization and the dual control problem is developed, constraining polynomial approximations of the Fisher Information Matrix to provide an information gradient and allow prescription of the level of future estimation certainty required for mission accomplishment. Disturbances, modeling deficiencies, and corrupted measurements are addressed with recursive updating of the target estimate with an Unscented Kalman Filter and the optimal path with Radau pseudospectral collocation methods and sequential quadratic programming. The basic real-time optimal control (RTOC) structure is investigated, specifically addressing limitations of current techniques in this area that lose error integration. The resulting guidance method can be applied to any bearing-only system, such as submarines using passive sonar, anti-radiation missiles, or small UAVs seeking to land on power lines for energy harvesting. Methods and tools required for implementation are developed, including variable calculation timing and tip-tail blending for potential discontinuities. Validation is accomplished with simulation and flight test, autonomously landing a quadrotor helicopter on a wire

An Efficient Navigation-Control System for Small Unmanned Aircraft

Unmanned Aerial Vehicles have been research in the past decade for a broad range of tasks and application domains such as search and rescue, reconnaissance, traffic control, pipe line inspections, surveillance, border patrol, and communication bridging. This work describes the design and implementation of a lightweight Commercial-Off-The-Shelf (COTS) semi-autonomous Fixed-Wing Unmanned Aerial Vehicle (UAV). Presented here is a methodology for System Identification utilizing the Box-Jenkins model estimator on recorded flight data to characterize the system and develop a mathematical model of the aircraft. Additionally, a novel microprocessor, the XMOS, is utilized to navigate and maneuver the aircraft utilizing a PD control system. In this thesis is a description of the aircraft and the sensor suite utilized, as well as the flight data and supporting videos for the benefit of the UAV research community