Control theory

Summary

Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the error signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control

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https://en.wikipedia.org/wiki/Control_theory

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The aim of this work is to set up mathematical models and numerical methods to investigate the mass transfer process occurring during the peritoneal dialysis (PD) therapy. More precisely the final goal is the set up of tools to find for each patient submitted to PD the best therapy profile to purify blood and remove water from the patients. First, we build up specific mathematical models to represent the physical phenomena we are interested in. As discussed in chapter 1, starting from the Kedem-Katchalsky equations, we end up with a systems of nonlinear ordinary differential equations describing the various aspects of the physical problem. Then, we propose a method based on nonlinear programming techniques to solve the inverse problem arising from the need to assess the peritoneal membrane characteristics which are not directly measurable on the patient. Thanks to its flexibility we are able to support the main standard tests nowadays in use to assess the kinetic properties of the peritoneum. We devise a suitable parametrization of the control function (DPD Dynamic Peritoneal Dialysis) that allows to improve the standard PD profiles with a larger set of treatments. Then we propose an optimization algorithm to improve the PD efficiency. Moreover, in the framework of control theory, we devise an algorithm based on the maximum principle of Pontryagin for switched systems to investigate deeply the PD optimal control problem. Afterwards we carry out numerical simulations, investigating the main inputs influencing the peritoneal dialysis efficiency. Specifically we show an extensive comparison between the APD (Automated Peritoneal Dialysis) and DPD (Dynamic Peritoneal Dilaysis) in order to assess the conditions under which DPD allows to improve the PD performance. Then a numerical investigation based on the algorithm devised for switched systems is carried out to assess the adequacy of DPD. Moreover we set up a procedure to reach an efficiency target and minimize the patient's exposure to glucose in order to improve the PD biocompatibility. Finally, we present the validation results of the mathematical model in order to verify its accuracy. A comparison between the APD and DPD is presented. Moreover we carry out a statistical analysis to assess the error distribution related to the most relevant quantities in order to evaluate strengths and weaknesses of this model and to identify the needs for a further improvement.

EPFL2006

Supernumerary Robotic Arm for Three-Handed Surgical Application: Behavioral Study and Design of Human-Machine Interface

Elahe Abdi

In surgical to industrial manipulation, the operator needs assistance for tasks requiring more than two hands. Teamwork may be the source of errors and inefficiency, especially if the assistant is a novice or unfamiliar with the main operator. The need for assistance may become problematic in case of lack of human resources e.g. in emergency surgical cases in the late hours of the night. Our objective is to improve the surgeon's autonomy and dexterity by a robotic arm under his own control. Although a number of robotic instrument holders have been developed, the best way to control such devices is still an open question. No behavioral study has been conducted on the best control strategy and human performance in three-handed tasks. We have selected the foot for commanding the third arm on the basis of a literature review. A series of experiments in virtual environments has been conducted to study the feasibility of this choice. The first experiment compares performance in the same task using two or three hands. Results show that three-handed manipulation is preferred to two-handed manipulation in demanding tasks. The second experiment investigated the type of tasks to be aimed in three-handed manipulation and the learning curve of users. Moving the hands and a foot simultaneously in opposite directions was perceived as difficult compared to a more active task with liberty in choosing the limbs coordination. Limbs were moved in parallel rather than serially. The performance improved within a few minutes of practice. Also, the sense of ownership improved constantly during the experiment. Two other experiments were aimed at handling the endoscope in laparoscopic surgery. Surgeons and medical students participated in these studies. Residents had a more positive approach towards foot usage and performed better compared to more experienced surgeons. This proves that the best training period for surgeons to use a foot controlled robotic arm is during their residency. A realistic virtual abdominal cavity has been developed for the last experiment. This had a positive influence on the participants' performance and emphasizes the importance of using a familiar context for training such a "three-handed surgery". Finally, two different foot interfaces were developed to investigate the most intuitive third arm commanding strategy. A robotic arm is hence controlled by the foot's translation or rotation in one interface (isotonic interface), and by force or torque in the other one (isometric interface). An experimental behavioral study was conducted to compare the two devices. Isometric rate control was preferred to isotonic position control due to the lower physical burden and higher movement accuracy of the robot. It was shown that the proposed device for isometric rate control could be used for intuitive control of four DoFs of a slave robotic arm. This thesis is the first step in a systematic investigation of a three-handed manipulation, two biological hands and a foot controlled robotic assistant. Findings suggest a high potential in using the foot to become more autonomous in surgery as well as other fields. Users can learn the control paradigm in a short period of time with little mental and physical burden. We expect the developed foot interfaces to be the basis of future development of more intuitive control interfaces. We believe that foot controlled robotic arms will be commonly used in various surgical as well as industrial applications.

EPFL2017

Fixed-wing drones for communication networks

Maja Varga

In the last decade, drones became frequently used to provide eye-in-the-sky overview in the outdoor environment. Their main advantage compared to the other types of robots is that they can fly above obstacles and rough terrains and they can quickly cover large areas. These properties also open a new application; drones could provide a multi-hop, line of sight communication for groups of ground users. The aim of this thesis is to develop a drone team that will establish wireless ad-hoc network between users on the ground and distributively adapt links and spatial arrangement to the requirements and motion of the ground users. For this application, we use fixed wing drones. Such platforms can be easily and quickly deployed. Fixed wing drones have higher forward speed and higher battery life than hovering platforms. On the other hand, fixed wing drones have unicycle dynamics with constrained forward speed which makes them unable to hover or perform sharp turns. The first challenge consists in bridging unicycle dynamics of the fixed wing drones. Some control strategies have been proposed and validated in simulations using the average distance between the target and the drone as a performance metric. However, besides the distance metric, energy expenditure of the flight also plays an important role in assessing the overall performance of the flight. We propose a new methodology that introduces a new metric (energy expenditure), we compare existing methods on a large set of target motion patterns and present a comparison between the simulation and field experiments on proposed target motion patterns. The second challenge consists in developing a formation control algorithm that will allow fixed wing robots to provide a wide area coverage and to relay data in a wireless ad-hoc network. In such applications fixed wing drones have to be able to regulate an inter-drone distance. Their reduced maneuverability presents the main challenge to design a formation algorithm that will regulate an inter-drone distance. To address this challenge, we present a distributed control strategy that relies only on local information. Each drone has its own virtual agent, it follows the virtual agent by performing previously evaluated and selected target tracking strategy, and flocking interaction rules are implemented between virtual agents. It is shown in simulation and in field experiments with a team of fixed wing drones that using this distributed formation algorithm, drones can cover an area by creating an equilateral triangular lattice and regulate communication link quality between neighboring drones. The third challenge consists in allowing connectivity between independently moving ground users using fixed wing drone team. We design two distributed control algorithms that change drones' spatial arrangement and interaction topology to maintain the connectivity. We propose a potential field based strategy which adapts distance between drones to shrink and expand the fixed wing drones' formation. In second approach, market-based adaptation, drones distributively delete interaction links to expand the formation graph to a tree graph. In simulations and field experiments we show that our proposed strategies successfully maintain independently moving ground users connected. Overall, this thesis presents synthesis of distributed algorithms for fixed wing drones to establish and maintain wireless ad-hoc communication networks.

EPFL2016