Observer design for a nonlinear heat equation: Application to semiconductor wafer processing

In this paper, the problem of observer design for a class of 1D nonlinear heat equations with pointwise in-domain temperature measurements is addressed. A pointwise measurement injection observer is designed and the robust convergence of its estimation error in presence of bounded distributed perturbations is established by verifying input-to-state stability. The obtained convergence conditions express the underlying interplay between heat conduction and radiation and include specific dependencies on the sensor locations which are the main degrees of freedom in the design approach. The theoretical results are experimentally validated on a semiconductor wafer processing unit

Active Disturbance Rejection Control for the Robust Flight of a Passively Tilted Hexarotor

This paper presents a robust control strategy for controlling the flight of a passively (fixed) tilted hexarotor unmanned aerial vehicle (UAV). The proposed controller is based on a robust extended-state observer to estimate and reject internal dynamics and external disturbances at run-time. Both stability and convergence of the observer are proved using Lyapunov-based perturbation theory and an ultimate bound approach. Such a controller is implemented within a highly realistic simulation environment that includes physics motors, devising an almost transparent behaviour with respect to the real UAV. The controller is tested for flying under normal conditions and in the presence of different types of disturbances showing successful results. Furthermore, the proposed control system is compared against another robust control approach, presenting a better performance regarding the attenuation of the error signals

Network Identification for Diffusively-Coupled Systems with Minimal Time Complexity

The theory of network identification, namely identifying the (weighted) interaction topology among a known number of agents, has been widely developed for linear agents. However, the theory for nonlinear agents using probing inputs is less developed and relies on dynamics linearization. We use global convergence properties of the network, which can be assured using passivity theory, to present a network identification method for nonlinear agents. We do so by linearizing the steady-state equations rather than the dynamics, achieving a sub-cubic time algorithm for network identification. We also study the problem of network identification from a complexity theory standpoint, showing that the presented algorithms are optimal in terms of time complexity. We also demonstrate the presented algorithm in two case studies.Comment: 12 pages, 3 figure

Design of Fault Tolerant Control systems

This research designs a Fault Tolerant Control (FTC) approach that compensates for both actuator and sensor faults by using multiple observers. This method is shown to work for both linear time-variant and linear time-invariant systems. This work takes advantage of sensor redundancy to compensate for sensor faults. A method to calculate the rank of available sensor redundancy is developed to determine how many independent sensors can fail without losing observability. This rank is the upper bound on the number of simultaneous sensor failures that the system can tolerate. Based on this rank, a series of reduced order Kalman observers are created to remove sensors presumed faulty from the internal feedback of the estimators. Actuator redundancy is examined as a potential way to compensate for actuator faults. A method to calculate the available actuator redundancy is designed. This redundancy would allow for the correction of partial and full actuator failures, but few systems exhibit sufficient actuator redundancy. Actuator faults are instead tolerated by replacing the Kalman estimators with Augmented State Observers (ASO). The ASO adds estimates of the actuator faults as additional states of the system in order to isolate and estimate the actuator faults. Then a supervisor is designed to select the observer that correctly identifies the sensor fault set. From that observer, the supervisor collects state estimates and calculates estimates of the sensors and faults. These estimates are then used in feedback with a controller that performs pole placement on the original system

Precision Control of a Sensorless Brushless Direct Current Motor System

Sensorless control strategies were first suggested well over a decade ago with the aim of reducing the size, weight and unit cost of electrically actuated servo systems. The resulting algorithms have been successfully applied to the induction and synchronous motor families in applications where control of armature speeds above approximately one hundred revolutions per minute is desired. However, sensorless position control remains problematic. This thesis provides an in depth investigation into sensorless motor control strategies for high precision motion control applications. Specifically, methods of achieving control of position and very low speed thresholds are investigated. The developed grey box identification techniques are shown to perform better than their traditional white or black box counterparts. Further, fuzzy model based sliding mode control is implemented and results demonstrate its improved robustness to certain classes of disturbance. Attempts to reject uncertainty within the developed models using the sliding mode are discussed. Novel controllers, which enhance the performance of the sliding mode are presented. Finally, algorithms that achieve control without a primary feedback sensor are successfully demonstrated. Sensorless position control is achieved with resolutions equivalent to those of existing stepper motor technology. The successful control of armature speeds below sixty revolutions per minute is achieved and problems typically associated with motor starting are circumvented.Research Instruments Ltd

Observer-based Fault Diagnosis: Applications to Exothermic Continuous Stirred Tank Reactors

For chemical engineering dynamic systems, there is an increasing demand for better process performance, high product quality, absolute reliability & safety, maximum cost efficiency and less environmental impact. Improved individual process components and advanced automatic control techniques have brought significant benefits to the chemical industry. However, fault-free operation of processes cannot be guaranteed. Timely fault diagnosis and proper management can help to avoid or at least minimize the undesirable consequences. There are many techniques for fault diagnosis, and observer-based methods have been widely studied and have proved to be efficient for fault diagnosis. The basic idea of an observer-based approach is to generate a specific residual signal which carries the information of specific faults, as well as the information of process disturbances, model uncertainties, other faults and measurement noises. For fault diagnosis, the residual should be sensitive to faults and insensitive to other unknown inputs. With this feature, faults can be easily detected and may be isolated and identified. This thesis applied an observer-based fault diagnosis method to three exothermic CSTR case studies. In order to improve the operational safety of exothermic CSTRs with risks of runaway reactions and explosion, fault diagnostic observers are built for fault detection, isolation and identification. For this purpose, different types of most common faults have been studied in different reaction systems. For each fault, a specific observer and the corresponding residual is built, which works as an indicator of that fault and is robust to other unknown inputs. For designing linear observers, the original nonlinear system is linearized at steady state, and the observer is designed based on the linearized system. However, in the simulations, the observer is tested on the nonlinear system instead of the linearized system. In addition, an efficient & effective general MATLAB program has been developed for fault diagnosis observer design. Extensive simulation studies have been performed to test the fault diagnostic observer on exothermic CSTRs. The results show that the proposed fault diagnosis scheme can be directly implemented and it works well for diagnosing faults in exothermic chemical reactors

Contraction Theory for Robust Learning-Based Control: Toward Aerospace and Robotic Autonomy

Machine learning and AI have been used for achieving autonomy in various aerospace and robotic systems. In next-generation research tasks, which could involve highly nonlinear, complicated, and large-scale decision-making problems in safety-critical situations, however, the existing performance guarantees of black-box AI approaches may not be sufficiently powerful. This thesis gives a mathematical overview of contraction theory, with some practical examples drawn from joint projects with NASA JPL, for enjoying formal guarantees of nonlinear control theory even with the use of machine learning-based and data-driven methods. This is not to argue that these methods are always better than conventional approaches, but to provide formal tools to investigate their performance for further discussion, so we can design and operate truly autonomous aerospace and robotic systems safely, robustly, adaptively, and intelligently in real-time. Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution trajectories with respect to each other. Its nonlinear stability analysis boils down to finding a suitable contraction metric that satisfies a stability condition expressed as a linear matrix inequality, resulting in many parallels drawn between linear systems theory and contraction theory for nonlinear systems. This yields much-needed safety and stability guarantees for neural network-based control and estimation schemes, without resorting to a more involved method of using uniform asymptotic stability for input-to-state stability. Such distinctive features permit the systematic construction of a contraction metric via convex optimization, thereby obtaining an explicit exponential bound on the distance between a time-varying target trajectory and solution trajectories perturbed externally due to disturbances and learning errors. The first two parts of this thesis are about a theoretical overview of contraction theory and its advantages, with an emphasis on deriving formal robustness and stability guarantees for deep learning-based 1) feedback control, 2) state estimation, 3) motion planning, 4) multi-agent collision avoidance and robust tracking augmentation, 5) adaptive control, 6) neural net-based system identification and control, for nonlinear systems perturbed externally by deterministic and stochastic disturbances. In particular, we provide a detailed review of techniques for finding contraction metrics and associated control and estimation laws using deep neural networks. In the third part of the thesis, we present several numerical simulations and empirical validation of our proposed approaches to assess the impact of our findings on realizing aerospace and robotic autonomy. We mainly focus on the two joint projects with NASA JPL: 1) Science-Infused Spacecraft Autonomy for Interstellar Object Exploration and 2) Constellation Autonomous Space Technology Demonstration of Orbital Reconfiguration (CASTOR), where we also perform hardware demonstrations of our methods using our thruster-based spacecraft simulators (M-STAR) and in high-conflict, distributed, intelligent UAV swarm reconfiguration with up to 20 UAVs (crazyflies).</p