Robust fractional order PI control for cardiac output stabilisation

Drug regulatory paradigms are dependent on the hemodynamic system as it serves to distribute and clear the drug in/from the body. While focusing on the objective of the drug paradigm at hand, it is important to maintain stable hemodynamic variables. In this work, a biomedical application requiring robust control properties has been used to illustrate the potential of an autotuning method, referred to as the fractional order robust autotuner. The method is an extension of a previously presented autotuning principle and produces controllers which are robust to system gain variations. The feature of automatic tuning of controller parameters can be of great use for data-driven adaptation during intra-patient variability conditions. Fractional order PI/PD controllers are generalizations of the well-known PI/PD controllers that exhibit an extra parameter usually used to enhance the robustness of the closed loop system. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved

On reduced-order interval observers for time-delay systems

International audienceThe estimation problem for uncertain time-delay systems is addressed. A design method of reduced-order interval observers is proposed. The observer estimates the set of admissi-ble values (the interval) for the state at each instant of time. The cases of known fixed delays and uncertain time-varying delays are analyzed. The proposed approach can be applied to linear delay systems and nonlinear time-delay systems in the output canonical form. The framework efficiency is demonstrated on examples of nonlinear systems

Mathematical model of non-basal testosterone regulation in the male by pulse modulated feedback

A parsimonious mathematical model of pulse modulated regulation of non-basal testosterone secretion in the male is developed. The model is of third differential order, reflecting the three most significant hormones in the regulation loop, but is yet shown to be capable of sustaining periodic solutions with one or two pulses of gonadotropin-releasing hormone (GnRH) on each period. Lack of stable periodic solutions is otherwise a main shortcoming of existing low-order hormone regulation models. Existence and stability of periodic solutions are studied. The periodic mode with two GnRH pulses on the least period has not been described in medical literature but is found to explain experimental data well

상태변수 영역 접합을 통한 하이브리드 시스템의 상태변수 추정 및 추종 제어

학위논문 (박사)-- 서울대학교 대학원 공과대학 전기·컴퓨터공학부, 2017. 8. 서진헌.In this dissertation, we propose a new observer and tracking controller design approach for a class of hybrid dynamical systems with state jumps. The hybrid dynamical system exhibits characteristics typical of both continuous-time dynamical system and discrete-time dynamical system. Therefore, it can be modeled as differential equation of the continuous-time dynamics, difference equation of the discrete-time dynamics, the interaction between them. Since the interaction of continuous-time and discrete-time dynamics in a hybrid system leads to rich dynamical behavior and unfamiliar phenomena, several challenges are encountered when we deal with this system. The observer design considered in this dissertation is to construct a dynamical system called an observer that estimates the state of a given hybrid dynamical system (without any input), from an output of the given system. In addition, the tracking controller design is to construct a dynamical system called a tracking controller that makes an input for a given hybrid dynamical system (with an input) such that the state of the given system tracks a given reference. There many results of the observer and tracking controller designs for the continuous-time and discrete-time dynamical systems, but the results for the hybrid dynamical systems are insufficient. Moreover, the results are applied to some classes of hybrid systems (switched systems, hormone systems, powertrain systems, and so on) rather than general hybrid dynamical systems. The proposed idea dealing with the hybrid dynamical system is to "glue" the jump set (a part of the domain where the jumps take place) onto its image. Then, on the "glued" domain, the hybrid dynamical system becomes a continuous-time dynamical system without any jumps. Especially, for some class of the system, the continuous-time dynamical system has a smooth vector field via some notion, "smoothing". Furthermore, we specify this concept of gluing as a map and investigate the essential conditions of the map. By this map, we obtain the "glued" hybrid dynamical system (which is a continuous-time dynamical system) and it may be possible to construct an observer and/or a tracking controller through conventional methods for continuous-time dynamical systems. From these constructions, we obtain the observer and tracking controller for the hybrid system. Especially, the proposed observer does not require any detection of the state jumps while many previous results does. Furthermore, the proposed tracking controller does not need to make the state jump whenever the jumps of the reference happen. Simulation results for examples including mechanical system with impacts and ripple generator in AC/DC converter illustrate the effectiveness of the proposed approach.1 Introduction 1 1.1 Research Background 1 1.2 Organization and Contributions of the Dissertation 4 2 Mathematical Preliminaries 9 2.1 Calculus in Rn 9 2.2 Differential Geometry 11 2.3 Viability Theorems for Ordinary Differential Equations 23 3 Reviews of Related Previous Works 27 3.1 Gluing Manifolds and Vector Fields 27 3.2 Viability Condition 36 3.3 State Estimation 38 3.4 Tracking Control 42 4 Gluing Domain of Hybrid System 45 4.1 Frameworks 45 4.2 Gluing and Smoothing 48 4.3 Frameworks in Rn and Gluing Function 53 5 State Estimation Strategy 71 5.1 Standing Assumptions 71 5.2 State Estimation 75 5.3 Observer with Linearized Error Dynamics 83 5.4 Observer for Lipschitz Continuous Systems 88 6 Tracking Control Strategy 99 6.1 Standing Assumptions 99 6.2 Tracking Control 101 6.3 Using Discontinuous Feedback to Counteract Dynamics Jumps 108 6.4 Output Tracking Controller for Normal Form 119 7 Conclusions 129 BIBLIOGRAPHY 133 국문초록 139Docto

From classical absolute stability tests towards a comprehensive robustness analysis

In this thesis, we are concerned with the stability and performance analysis of feedback interconnections comprising a linear (time-invariant) system and an uncertain component subject to external disturbances. Building on the framework of integral quadratic constraints (IQCs), we aim at verifying stability of the interconnection using only coarse information about the input-output behavior of the uncertainty