Design and analysis of robust controllers for directional drilling tools

Directional drilling is a very important tool for the development of oil and gas deposits. Attitude control which enables directional drilling for the efficient placement of the directional drilling tools in petroleum producing zones is reviewed along with the various engineering requirements or constraints. This thesis explores a multivariable attitude governing plant model as formulated in Panchal et al. (2010) which is used for developing robust control techniques. An inherent input and measurement delay which accounts for the plant's dead-time is included in the design of the controllers. A Smith Predictor controller is developed for reducing the effect of this dead-time. The developed controllers are compared for performance and robustness using structured singular value analysis and also for their performance indicated by the transient response of the closed loop models. Results for the transient non-linear simulation of the proposed controllers are also presented. The results obtained indicate that the objectives are satisfactorily achieved

Controller Design for Active Vibration Damping with Inertial Actuators

In the machining industry, there is a constant need to improve productivity while maintaining required dimensional tolerances and surface quality. The self-excited vibration called chatter is one of the main factors limiting machining productivity. Chatter produces unstable cutting conditions during machining and unstable forces will damage and shorten the life of the machine tool. It can also damage the cutting tool, machining components as well as produce a poor surface finish on the workpiece. Researchers have developed various chatter suppression techniques such as changing process parameters, spindle speeds, and using passive dampers. However, many of these methods are not very robust to changing dynamics in the machine tool due to changing machine positioning, cutting setups, etc. Active vibration damping with a force actuator is a robust method of adding damping by due to its bandwidth and variable controller gains. However, the commissioning of the controller design for the actuators is not trivial and requires significant manual tuning to reach optimal productivity. The research presented in this thesis aims to simplify and automate the controller design process for force actuators. A frequency domain, sensitivity based automatic controller tuning method for force actuators has been developed. This method uses the measured actuator dynamics and open-loop system dynamics to develop a prediction tool for closed-loop responses without needing to have the complete system model (model free). By monitoring the predicted closed-loop response of various virtually designed controllers, an optimal controller is found amongst the candidate parameter values. The stability of the system and actuator is monitored during the search to ensure that the system is stable throughout its bandwidth that the actuator does not become saturated. The controller is then experimentally tested to ensure that the predicted output is the same as the real output. In cases where the system has several vibration modes that are in counter-phase and close in frequency, the model-free approach does not perform well. A more complex model-based control law has also been developed and implemented. The method automatically identifies a transfer function model for the measured open-loop system dynamics and synthesizes mixed-sensitivity optimization based controller to damp out the modes in counter-phase. In order to verify that the model-based controllers can reduce vibration modes in counter-phase, a small-scale experimental setup was developed to mimic machine tools with vibration modes in counter-phase. A flexure was designed and fabricated. A shaker from Modal Shop is used as an active damping actuator to reduce the flexure’s vibration modes. It was concluded that while the model-based controller synthesis techniques were able to damp the vibration modes in counter phase, the flexure was too simplistic and the model-free controller was able to achieve similar results

Fixed order controller design via linear programming

Fixed order controllers, such as PD, PI and PID controllers, are the most commonly used in hardware implementations. Therefore, control engineers are often given the task to design fixed order controllers with time domain specifications as the system design requirements. To solve this problem, a systematic fixed order controller design process employing mathematical programming is developed in this thesis. The design process is based on fixed order pole assignment problem. Natural frequencies and minimum damping ratio are the design parameters of the developed controller design process. The design parameters are insightful since damping ratio and frequencies are closely related to time domain specifications. The interval polynomial search algorithm is formulated to maximize the interval characteristic polynomial within the design domain defined by the design parameters on the s-plane. The Edge Theorem is applied to ensure the performance and stability of the interval characteristic polynomial [3]. It is followed by solving the optimal controller, using the linear or non-linear programming with linear constraints technique. This proposed method ensures that the controller will attain the acceptable performance and stability even if the plant dynamic consists of some level of uncertainties. The advantage of this method is the freedom of the choices of design emphasis

A flexible mixed-optimization with H∞ control for coupled twin rotor MIMO system based on the method of inequality (MOI)- An Experimental Study

This article introduces a cutting-edge H∞ model-based control method for uncertain Multi Input Multi Output (MIMO) systems, specifically focusing on UAVs, through a flexible mixed-optimization framework using the Method of Inequality (MOI). The proposed approach adaptively addresses crucial challenges such as unmodeled dynamics, noise interference, and parameter variations. Central to the design is a two-step controller development process. The first step involves Nonlinear Dynamic Inversion (NDI) and system decoupling for simplification, while the second step integrates H∞ control with MOI for optimal response tuning. This strategy is distinguished by its adaptability and focus on balancing robust stability and performance, effectively managing the intricate cross-coupling dynamics in UAV systems. The effectiveness of the proposed approach is validated through simulations conducted in MATLAB/Simulink environment. Results demonstrated the efficiency of the proposed robust control approach as evidenced by reduced steady-state error, diminished overshoot, and faster system response times, thus significantly outperforming traditional control methods

Semi-blind robust indentification and robust control approach to personalized anemia management.

The homeostatic blood hemoglobin (Hb) content of a healthy individual varies between the range of 14-18 g/dL for a male and 12-16 g/dL for a female. This quantity provides an estimate of red blood cell (RBC) count in circulation at any given moment. RBC is a protein carrying substance that transports oxygen from the lungs to other tissues in the body and is synthesized by the kidney through a process known as erythropoiesis where erythropoietin is secreted in response to hypoxia. In this regard, the kidneys act not only as a controller but also as a sensor in regulating RBC levels. Patients with chronic kidney diseases (CKD) have dysfunctional kidneys that compromise these fundamental kidney functions. Consequently, anemia is developed. Anemics of CKD have low levels of Hb that must be controlled and properly regulated to the appropriate therapeutic range. Until the discovery of recombinant human erythropoietin (EPO) over three decades ago, treatment procedure of anemia conditions primarily involved repeated blood transfusions–a process known to be associated with several other health related complications. This discovery resulted in a paradigm shift in anemia management from blood transfusions to dosage therapies. The main objective of anemia management with EPO is to increase patients’ hemoglobin level from low to a suitable therapeutic range as defined by the National Kidney Foundation-Kidney Disease Outcomes Quality Initiative (NKF-KDOI) to be in the range of 10 - 12 g/dL while avoiding response values beyond 14 g/dL to prevent other complications associated with EPO medication. It is therefore imperative that clinicians balance dosage efficacy and toxicity in anemia management therapies. At most treatment facilities, protocols are developed to conform to NKF-KDOI recommendations. These protocols are generally based on EPO packet inserts and the expected Hb responses from the average patient. The inevitable variability within the patient group makes this “one-size-fits-all” dosing scheme non-optimal, at best, and potentially dangerous for certain group of patients that do not adhere to the notion of expected “average” response. A dosing strategy that is tailored to the individual patients’ response to EPO medication could provide a better alternative to the current treatment methods. An objective of this work is to develop EPO dosing strategies tailored to the individual patients using robust identification techniques and modern feedback control methods. First, a unique model is developed based on Hb responses and dosage EPO of the individual patients using semi-blind robust identification techniques. This provides a nominal model and a quantitative information on model uncertainty that accounts for other possible patient’s dynamics not considered in the modeling process. This is in the framework of generalized interpolation theory. Then, from the derived nominal model and the associated uncertainty information, robust controller is designed via the =H1-synthesis methods to provide a new dosing strategies for the individual patients. The H1 control theory has a feature of minimizing the influence of some unknown worst case gain disturbance on a system. Finally, a framework is provided to strategize dosing protocols for newly admitted patients

Computationalcost Reduction of Robust Controllers Foractive Magnetic Bearing Systems

This work developed strategies for reducing the computational complexity of implementing robust controllers for active magnetic bearing (AMB) systems and investigated the use of a novel add-on controller for gyroscopic effect compensation to improve achievable performance with robust controllers. AMB systems are multi-input multi-output (MIMO) systems with many interacting mechanisms that needs to fulfill conflicting performance criteria. That is why robust control techniques are a perfect application for AMB systems as they provide systematic methods to address both robustness and performance objectives. However, robust control techniques generally result in high order controllers that require high-end control hardware for implementation. Such controllers are not desirable by industrial AMB vendors since their hardware is based on embedded systems with limited bandwidths. That is why the computational cost is a major obstacle towards industry adaptation of robust controllers. Two novel strategies are developed to reduce the computational complexity of singlerate robust controllers while preserving robust performance. The first strategy identifies a dual-rate configuration of the controller for implementation. The selection of the dualrate configuration uses the worst-case plant analysis and a novel approach that identifies the largest tolerable perturbations to the controller. The second strategy aims to redesign iv the controller by identifying and removing negligible channels in the context of robust performance via the largest tolerable perturbations to the controller. The developed methods are demonstrated both in simulation and experiment using three different AMB systems, where significant computational savings are achieved without degrading the performance. To improve the achievable performance with robust controllers, a novel add-on controller is developed to compensate the gyroscopic effects in flexible rotor-AMB systems via modal feedback control. The compensation allows for relaxing the robustness requirements in the control problem formulation, potentially enabling better performance. The effectiveness of the developed add-on controller is demonstrated experimentally on two AMB systems with different rotor configurations. The effects of the presence of the add-on controller on the performance controller design is investigated for one of the AMB systems. Slight performance improvements are observed at the cost of increased power consumption and increased computational complexity

Design and verification of Guidance, Navigation and Control systems for space applications

In the last decades, systems have strongly increased their complexity in terms of number of functions that can be performed and quantity of relationships between functions and hardware as well as interactions of elements and disciplines concurring to the definition of the system. The growing complexity remarks the importance of defining methods and tools that improve the design, verification and validation of the system process: effectiveness and costs reduction without loss of confidence in the final product are the objectives that have to be pursued. Within the System Engineering context, the modern Model and Simulation based approach seems to be a promising strategy to meet the goals, because it reduces the wasted resources with respect to the traditional methods, saving money and tedious works. Model Based System Engineering (MBSE) starts from the idea that it is possible at any moment to verify, through simulation sessions and according to the phase of the life cycle, the feasibility, the capabilities and the performances of the system. Simulation is used during the engineering process and can be classified from fully numerical (i.e. all the equipment and conditions are reproduced as virtual model) to fully integrated hardware simulation (where the system is represented by real hardware and software modules in their operational environment). Within this range of simulations, a few important stages can be defined: algorithm in the loop (AIL), software in the loop (SIL), controller in the loop (CIL), hardware in the loop (HIL), and hybrid configurations among those. The research activity, in which this thesis is inserted, aims at defining and validating an iterative methodology (based on Model and Simulation approach) in support of engineering teams and devoted to improve the effectiveness of the design and verification of a space system with particular interest in Guidance Navigation and Control (GNC) subsystem. The choice of focusing on GNC derives from the common interest and background of the groups involved in this research program (ASSET at Politecnico di Torino and AvioSpace, an EADS company). Moreover, GNC system is sufficiently complex (demanding both specialist knowledge and system engineer skills) and vital for whatever spacecraft and, last but not least the verification of its behavior is difficult on ground because strong limitations on dynamics and environment reproduction arise. Considering that the verification should be performed along the entire product life cycle, a tool and a facility, a simulator, independent from the complexity level of the test and the stage of the project, is needed. This thesis deals with the design of the simulator, called StarSim, which is the real heart of the proposed methodology. It has been entirely designed and developed from the requirements definition to the software implementation and hardware construction, up to the assembly, integration and verification of the first simulator release. In addition, the development of this technology met the modern standards on software development and project management. StarSim is a unique and self-contained platform: this feature allows to mitigate the risk of incompatibility, misunderstandings and loss of information that may arise using different software, simulation tools and facilities along the various phases. Modularity, flexibility, speed, connectivity, real time operation, fidelity with real world, ease of data management, effectiveness and congruence of the outputs with respect to the inputs are the sought-after features in the StarSim design. For every iteration of the methodology, StarSim guarantees the possibility to verify the behavior of the system under test thanks to the permanent availability of virtual models, that substitute all those elements not yet available and all the non-reproducible dynamics and environmental conditions. StarSim provides a furnished and user friendly database of models and interfaces that cover different levels of detail and fidelity, and supports the updating of the database allowing the user to create custom models (following few, simple rules). Progressively, pieces of the on board software and hardware can be introduced without stopping the process of design and verification, avoiding delays and loss of resources. StarSim has been used for the first time with the CubeSats belonging to the e-st@r program. It is an educational project carried out by students and researchers of the “CubeSat Team Polito” in which StarSim has been mainly used for the payload development, an Active Attitude Determination and Control System, but StarSim’s capabilities have also been updated to evaluate functionalities, operations and performances of the entire satellite. AIL, SIL, CIL, HIL simulations have been performed along all the phases of the project, successfully verifying a great number of functional and operational requirements. In particular, attitude determination algorithms, control laws, modes of operation have been selected and verified; software has been developed step by step and the bugs-free executable files have been loaded on the micro-controller. All the interfaces and protocols as well as data and commands handling have been verified. Actuators, logic and electrical circuits have been designed, built and tested and sensors calibration has been performed. Problems such as real time and synchronization have been solved and a complete hardware in the loop simulation test campaign both for A-ADCS standalone and for the entire satellite has been performed, verifying the satisfaction of a great number of CubeSat functional and operational requirements. The case study represents the first validation of the methodology with the first release of StarSim. It has been proven that the methodology is effective in demonstrating that improving the design and verification activities is a key point to increase the confidence level in the success of a space mission

Highly redundant and fault tolerant actuator system: control, condition monitoring and experimental validation

This thesis is concerned with developing a control and condition monitoring system for a class of fault tolerant actuators with high levels of redundancy. The High Redundancy Actuator (HRA) is a concept inspired by biomimetics that aims to provide fault tolerance using relatively large numbers of actuation elements which are assembled in parallel and series configurations to form a single actuator. Each actuation element provides a small contribution to the overall force and displacement of the system. Since the capability of each actuation element is small, the effect of faults within the individual element of the overall system is also small. Hence, the HRA will gracefully degrade instead of going from fully functional to total failure in the presence of faults. Previous research on HRA using electromechanical technology has focused on a relatively low number of actuation elements (i.e. 4 elements), which were controlled with multiple loop control methods. The objective of this thesis is to expand upon this, by considering an HRA with a larger number of actuation elements (i.e. 12 elements). First, a mathematical model of a general n-by-m HRA is derived from first principles. This method can be used to represent any size of electromechanical HRA with actuation elements arranged in a matrix form. Then, a mathematical model of a 4-by-3 HRA is obtained from the general n-by-m model and verified experimentally using the HRA test rig. This actuator model is then used as a foundation for the controller design and condition monitoring development. For control design, two classical and control method-based controllers are compared with an H_infinity approach. The objective for the control design is to make the HRA track a position demand signal in both health and faulty conditions. For the classical PI controller design, the first approach uses twelve local controllers (1 per actuator) and the second uses only a single global controller. For the H_infinity control design, a mixed sensitivity functions is used to obtain good tracking performance and robustness to modelling uncertainties. Both of these methods demonstrate good tracking performance, with a slower response in the presence of faults. As expected, the H_infinity control method's robustness to modelling uncertainties, results in a smaller performance degradation in the presence of faults, compared with the classical designs. Unlike previous work, the thesis also makes a novel contribution to the condition monitoring of HRA. The proposed algorithm does not require the use of multiple sensors. The condition monitoring scheme is based on least-squares parameter estimation and fuzzy logic inference. The least-squares parameter estimation estimates the physical parameters of the electromechanical actuator based on input-output data collected from real-time experiments, while the fuzzy logic inference determines the health condition of the actuator based on the estimated physical parameters. Hence, overall, a new approach to both control and monitoring of an HRA is proposed and demonstrated on a twelve elements HRA test rig

A Foot Placement Strategy for Robust Bipedal Gait Control

This thesis introduces a new measure of balance for bipedal robotics called the foot placement estimator (FPE). To develop this measure, stability first is defined for a simple biped. A proof of the stability of a simple biped in a controls sense is shown to exist using classical methods for nonlinear systems. With the addition of a contact model, an analytical solution is provided to define the bounds of the region of stability. This provides the basis for the FPE which estimates where the biped must step in order to be stable. By using the FPE in combination with a state machine, complete gait cycles are created without any precalculated trajectories. This includes gait initiation and termination. The bipedal model is then advanced to include more realistic mechanical and environmental models and the FPE approach is verified in a dynamic simulation. From these results, a 5-link, point-foot robot is designed and constructed to provide the final validation that the FPE can be used to provide closed-loop gait control. In addition, this approach is shown to demonstrate significant robustness to external disturbances. Finally, the FPE is shown in experimental results to be an unprecedented estimate of where humans place their feet for walking and jumping, and for stepping in response to an external disturbance

Commande Robuste et Contraintes d'Optimisation

This thesis presents an overview of my research activities carried out since my PhD in 2001. In the first section, description of the projects, my different contributions to robust control applied to the spatial field and underwater robotics, are highlighted. My research project for the coming years is then presented; I propose an original and efficient methodology to compute simple control laws by combining \textit{robust control} and \textit{global optimization}. The second part of this thesis is dedicated to the scientific aspects that will help clarify the proposed research project. As a starting point, Youla parametrization is presented as a tool to \textit{render convex} the control problem, and the subsequent work is used as a foundation to establish specifications based on the constraints related to optimization. This theme has served as a driving thread in illustrating how industrial requirements could lead to a control problem. Parallel to this, the question also arose as to the practical realization of results from these methodologies, that is, how they might be implemented in an embedded system. Ariane 5 launcher control is taken as an example for research on the structured control and validation.Ce mémoire présente un panorama des activités de recherche menées depuis ma thèse de doctorat en 2001. Dans une première partie, à travers la description des projets, sont mises en avant les différentes contributions à la commande robuste appliquée au monde spatial et au monde de la robotique sous-marine. On montre alors comment s'est construit le projet de recherche proposé pour les années à venir. Il s'agit de proposer une méthodologie originale et efficace pour régler des lois de commande simple à implémenter en combinant \textit{commande robuste} et \textit{optimisation globale}. La seconde partie de ce mémoire est consacrée à quelques aspects scientifiques qui aident à comprendre le projet de recherche proposé. On y trouve comme point de départ la paramétrisation de Youla en tant qu'outil pour \textit{convexifier} le problème de commande et les travaux qui en ont découlés pour traduire un cahier des charges en terme de contrainte dans un problème d'optimisation. Cette thématique a été un fil conducteur important pour faire le lien avec la demande industrielle de savoir comment les exigences étaient traduites dans le problème de commande. En parallèle, s'est posée la question de la réalisation pratique des résultats issues de ces méthodologies, c'est-à-dire leur implémentation sur un système embarqué. On prendra comme exemple les activités de recherche sur la structuration de correcteur et leur qualification pour les lois de pilotage des lanceurs Ariane 5