Feedback Control of Linear Distributed Systems

1967 ◽  
Vol 89 (2) ◽  
pp. 379-383 ◽  
Author(s):  
Donald M. Wiberg
Keyword(s):  
Boundary Condition ◽  
Distributed Systems ◽  
Feedback Control ◽  
Closed Loop ◽  
The State ◽  
Loop System ◽  
Closed Loop System ◽  
Loop Equation ◽  
Control Feedback ◽  
And Control

The optimum feedback control of controllable linear distributed stationary systems is discussed. A linear closed-loop system is assured by restricting the criterion to be the integral of quadratics in the state and control. Feedback is obtained by expansion of the linear closed-loop equation in terms of uncoupled modes. By incorporating symbolic functions into the formulation, one can treat boundary condition control and point observable systems that are null-delta controllable.

scholarly journals Riesz basis property of Timoshenko beams with boundary feedback control

2003 ◽  
Vol 2003 (28) ◽  
pp. 1807-1820 ◽  
Author(s):  
De-Xing Feng ◽  
Gen-Qi Xu ◽  
Siu-Pang Yung
Keyword(s):  
Feedback Control ◽  
Riesz Basis ◽  
Closed Loop ◽  
Loop System ◽  
Beam Equation ◽  
Closed Loop System ◽  
Boundary Feedback Control ◽  
Riesz Basis Property ◽  
Boundary Feedback ◽  
Generalized Eigenvectors

A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the state Hilbert space.

Modeling and Control of an Automotive All-Wheel Drive Clutch as a Piecewise Affine System

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Shiming Duan ◽  
Jun Ni ◽  
A. Galip Ulsoy
Keyword(s):  
Closed Loop ◽  
Open Loop ◽  
Lyapunov Theory ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Modeling And Control ◽  
Piecewise Affine ◽  
Wheel Drive ◽  
And Control

Piecewise affine (PWA) systems belong to a subclass of switched systems and provide good flexibility and traceability for modeling a variety of nonlinear systems. In this paper, application of the PWA system framework to the modeling and control of an automotive all-wheel drive (AWD) clutch system is presented. The open-loop system is first modeled as a PWA system, followed by the design of a piecewise linear (i.e., switched) feedback controller. The stability of the closed-loop system, including model uncertainty and time delays, is examined using linear matrix inequalities based on Lyapunov theory. Finally, the responses of the closed-loop system under step and sine reference signals and temperature disturbance signals are simulated to illustrate the effectiveness of the design.

Global Stabilization for a class of nonlinear fractional-order systems

2019 ◽  
Vol 10 (01) ◽  
pp. 1941009 ◽  
Author(s):  
Taide Liu ◽  
Feng Wang ◽  
Wanchun Lu ◽  
Xuhuan Wang
Keyword(s):  
Lyapunov Function ◽  
Fractional Order ◽  
Closed Loop ◽  
The State ◽  
Loop System ◽  
Global Stabilization ◽  
Fractional Order Systems ◽  
Closed Loop System ◽  
Integer Order ◽  
Backstepping Algorithm

The problem of Mittag–Leffler stabilization (MLS) is studied for a class of nonlinear non-integer order systems. The stabilizer is constructed by using the Lyapunov function and backstepping algorithm. The continuous controller is designed to ensure that the state of the nonlinear fractional-order closed-loop system converges to the equilibrium. Two simulation examples are given to illustrate the effectiveness of the method.

SIMULATION AND CONTROL OF CLOSED-LOOP SYSTEMS WITH INTERNAL RESERVES

2021 ◽  
pp. 7-14
Author(s):  
С.Л. Подвальный ◽  
Д.В. Логунов ◽  
Е.М. Васильев
Keyword(s):  
Closed Loop ◽  
Loop System ◽  
Closed Loop System ◽  
Entire Volume ◽  
Homogeneous Markov Process ◽  
Natural Systems ◽  
Closed Loop Systems ◽  
Recovery Processes ◽  
Proposed Model ◽  
And Control

Рассматривается задача воспроизведения в искусственных объектах способности естественных систем к самовосстановлению вследствие существования в них замкнутого круговорота вещества и энергии. Показано, что создание замкнутого жизненного цикла в системе предполагает реализацию в ней процессов восстановления ресурсов и их накопления в виде внутренних резервов, расходуемых системой в неблагоприятных условиях существования. Получена функциональная схема системы с замкнутым циклом и предложена математическая модель её функционирования в виде дискретного однородного марковского процесса без последействия. Обнаружено, что введение в систему внутреннего резервирования требует рассмотрения двух альтернативных вариантов модели системы: варианта для случая, в котором объём резервов ограничен возможностями каналов восстановления в системе, и варианта, в котором указанное ограничение отсутствует. Составлены графы состояний системы для указанных режимов функционирования и получены выражения для финальных вероятностей этих состояний. На основе полученных финальных вероятностей составлены аналитические расчётные соотношения для характеристик эффективности системы с замкнутым циклом. В качестве основной характеристики эффективности такого рода систем предлагается использовать вероятность полного функционирования системы, т.е. вероятность её работы с использованием всего объёма активных ресурсов. Представлен числовой пример, подтверждающий работоспособность предложенной модели, и проведён сопоставительный анализ вариантов управления эффективностью замкнутой системы путём изменения объёма резервов, количества процессов восстановления и интенсивности этих процессов. Выявлено доминирующее значение внутренних резервов при обеспечении заданных показателей эффективности системы с замкнутым циклом Here we consider the problem of reproduction of the ability of natural systems to self-repair in artificial objects due to the existence of a closed loop of matter and energy in them. We show that the creation of a closed life cycle in the system presupposes the implementation of the process of restoring resources and their accumulation in the form of internal reserves consumed by the system in unfavorable conditions of existence. We obtained a functional diagram of a closed-loop system and proposed a mathematical model of its functioning in the form of a discrete homogeneous Markov process without aftereffect. We found that the introduction of internal redundancy into the system requires consideration of two alternative options for the system model: the option for the case in which the volume of reserves is limited by the capabilities of the recovery channels in the system, and the option in which the specified limitation is absent. We compiled the graphs of the states of the system for the specified modes of operation and obtained expressions for the final probabilities of these states. On the basis of the obtained final probabilities, we got analytical design ratios for the characteristics of the efficiency of a system with a closed loop. As the main characteristic of the efficiency of such systems, we propose to use the probability of the complete functioning of the system, i.e. the probability of its work using the entire volume of active resources. We present a numerical example that confirms the performance of the proposed model, and carried out a comparative analysis of options for managing the efficiency of a closed-loop system by changing the volume of reserves, the number of recovery processes and the intensity of these processes. We revealed the dominant value of internal reserves while ensuring the specified performance indicators of a closed-loop system

Continuous Post-operative Blood Glucose Monitoring and Control Using a Closed-loop System in Patients Undergoing Hepatic Resection

2007 ◽  
Vol 53 (5) ◽  
pp. 1405-1410 ◽  
Author(s):  
Takehiro Okabayashi ◽  
Kazuhiro Hnazaki ◽  
Isao Nishimori ◽  
Takeki Sugimoto ◽  
Hiromichi Maeda ◽  
...  
Keyword(s):  
Blood Glucose ◽  
Hepatic Resection ◽  
Closed Loop ◽  
Glucose Monitoring ◽  
Loop System ◽  
Blood Glucose Monitoring ◽  
Monitoring And Control ◽  
Closed Loop System ◽  
And Control

On the Determination of the Worst Allowable Persistent Bounded Disturbance for a System With Constraints

1995 ◽  
Vol 117 (2) ◽  
pp. 126-133 ◽  
Author(s):  
Suhada Jayasuriya
Keyword(s):  
Closed Loop ◽  
Specific Impulse ◽  
Loop System ◽  
Exact Nature ◽  
Impulse Responses ◽  
Closed Loop System ◽  
Input Disturbance ◽  
Bounded Disturbances ◽  
And Control ◽  
Bounded Disturbance

The problem of explicitly determining the worst persistent input disturbance that a closed-loop system can tolerate under prespecified state and control constraints is studied. Verification of designs specifically aimed at maximizing the size of persistent bounded disturbances while satisfying system constraints, typically requires extensive simulations because the exact nature of the worst input is not known. In this paper the exact nature of the worst input is completely characterized for both SISO and MIMO cases. A finite number of specific impulse responses of the closed-loop system determines the worst persistent input disturbance. In the case of a SISO with n state constraints (|xi| ≤ βi), a control constraint (|u| ≤ βu) and an output constraint (|y| ≤ βo), n + 2 impulse responses are generally needed. With this new result the large number of simulations that is typically needed for design verification can be significantly reduced. Two examples illustrate how the new characterization can be utilized.

scholarly journals PANDEMIC POLICY DESIGN VIA FEEDBACK: A MODELLING STUDY

2021 ◽  
Author(s):  
Klaske Van Heusden ◽  
Greg Stewart ◽  
Sarah Otto ◽  
Guy Dumont
Keyword(s):  
Public Health ◽  
Decision Making ◽  
Feedback Control ◽  
Human Health ◽  
Closed Loop ◽  
Policy Design ◽  
Loop System ◽  
Model Parameters ◽  
Closed Loop System ◽  
Hospital Occupancy

The COVID-19 pandemic has had an enormous toll on human health and well-being and led to major social and economic disruptions. Public health interventions in response to burgeoning case numbers and hospitalizations have repeatedly bent down the epidemic curve in many jurisdictions, effectively creating a closed-loop dynamic system. We aim to formalize and illustrate how to incorporate principles of feedback control into pandemic projections and decision making. Starting with a SEEIQR epidemiological model, we illustrate how feedback control can be incorporated into pandemic management using a simple design (proportional-integral or PI control), which couples recent changes in case numbers or hospital occupancy with explicit policy restrictions. We then analyse a closed-loop system between the SEEIQR model and the designed feedback controller to illustrate the potential benefits of pandemic policy design that incorporates feedback. We first explored a feedback design that responded to hospital measured infections, demonstrating robust ability to control a pandemic despite simulating large uncertainty in reproduction number R0 (range: 1.04-5.18) and average time to hospital admission (range: 4-28 days). The second design compared responding to hospital occupancy to responding to case counts, showing that shorter delays reduced both the cumulative case count and the average level of interventions. Finally, we show that feedback is robust to changing public compliance to public health directives, and to systemic changes associated with new variants of concern and with the introduction of a vaccination program. The negative impact of a pandemic on human health and societal disruption can be reduced by coupling models of disease propagation with models of the decision-making process. This creates a closed-loop system that better represents the coupled dynamics of a disease and public health responses. Importantly, we show that feedback control is robust to delays in both measurements and responses, and to uncertainty in model parameters and the efficacy of control measures.

scholarly journals Control of vibrational field in a cyber-physical vibration unit

2018 ◽  
pp. 144-151 ◽  
Author(s):  
Olga P. Tomchina
Keyword(s):  
Feedback Control ◽  
Phase Shift ◽  
Closed Loop ◽  
Loop System ◽  
Closed Loop System ◽  
Rotor Vibration

The problem of feedback control of vibrational fields in a vibration unit is posed. The algorithms for control of the vibration fields by means of the control of the phase shift between rotors are proposed. The performance of the closed loop system is examined by simulation for the two-rotor vibration unit SV-2M.

A Biological Feedback Control System with Electronic Input: The Artificially Closed Femur-Tibia Control System of Stick Insects

1986 ◽  
Vol 120 (1) ◽  
pp. 369-385 ◽  
Author(s):  
G. WEILAND ◽  
U. BÄSSLER ◽  
M. BRUNNER
Keyword(s):  
Control System ◽  
Feedback Control ◽  
Closed Loop ◽  
Stick Insect ◽  
Open Loop ◽  
Loop System ◽  
Chordotonal Organ ◽  
Closed Loop System ◽  
Open Loop System ◽  
Stick Insects

An experimental arrangement was constructed which is based on the open-loop femur-tibia control system of two stick insect species (Carausius morosus and Cuniculina impigra). It could be artificially closed in the following way: the position of the tibia was measured by an optical device and this value was used to drive a penmotor which moved the receptor apodeme of the femoral chordotonal organ in the same way as in intact animals. This arrangement allows direct comparison of the behaviour of the open-loop and the closed-loop system as well as introducing an additional delay. The Carausius system has a phase reserve of only 30°-50° and the factor of feedback control approaches 1 between 1 and 2 Hz. This agrees with the observation that an additional delay of 70–200 ms produces long-lasting oscillations of 1–2 Hz. The Cuniculina system has a larger phase reserve and consequently a delay of 200 ms produced no oscillations. All experiments show that extrapolation from the open-loop system to the closed-loop system is valid, despite the non-linear characteristics of the loop. Consequences for servo-mechanisms during walking and rocking movements are discussed.

Plant-Input-Mapping Discretization Method for a Feedback System in the State-Space Form

2021 ◽  
Author(s):  
Keisuke Yagi ◽  
Hiroaki Muto ◽  
Yoshikazu Mori
Keyword(s):  
Transfer Function ◽  
State Space ◽  
State Feedback ◽  
Closed Loop ◽  
Space Form ◽  
Feedback System ◽  
The State ◽  
Loop System ◽  
Closed Loop System ◽  
Digital Redesign

Abstract The paper proposes the digital redesign technique called plant-input-mapping (PIM) method for a feedback system described in the state-space form. The PIM method, which was originally presented in the transfer function form, focuses on the plant input signal via the plant input transfer function and discretizes it so as to satisfy the control zero principle in the resulting discrete-time closed-loop system, which leads to guaranteeing the closed-loop stability for any non-pathological sampling interval. In accordance with this approach, the proposed PIM method focuses on the control zeros included in the plant input signal. The paper proves that the matched-pole-zero discrete-time model of the plant input state-equation satisfies the control zero principle with the step-invariant model of the plant. Then, when the matched-pole-zero model is set as the target of model matching, the parameters of the state-space PIM controller employing the observer-based dynamic state-feedback can systematically be determined from the underlying continuous-time closed-loop system with guaranteed stability. This discretization process can immediately be applied to a state-feedback system and a class of multi-input multi-output systems without any modification, which cannot be discretized by the conventional PIM methods. The discretization performance of the proposed PIM method is evaluated through illustrative examples with comparable digital redesign methods, which reveal that the proposed method performs a good reproduction of the characteristics of the underlying closed-loop system.

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