Modeling, Control, and Stability Analysis of Heterogeneous Thermostatically Controlled Load Populations Using Partial Differential Equations

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Azad Ghaffari ◽  
Scott Moura ◽  
Miroslav Krstić
Keyword(s):  
Power Control ◽  
Electricity Consumption ◽  
State Feedback Control ◽  
Seasonal Temperature ◽  
Partial Differential ◽  
Modeling And Control ◽  
Proposed Model ◽  
The Stability ◽  
Utility Managers ◽  
And Control

Thermostatically controlled loads (TCLs) account for more than one-third of the U.S. electricity consumption. Various techniques have been used to model TCL populations. A high-fidelity analytical model of heterogeneous TCL (HrTCL) populations is of special interest for both utility managers and customers (that facilitates the aggregate synthesis of power control in power networks). We present a deterministic hybrid partial differential equation (PDE) model which accounts for HrTCL populations and facilitates analysis of common scenarios like cold load pick up, cycling, and daily and/or seasonal temperature changes to estimate the aggregate performance of the system. The proposed technique is flexible in terms of parameter selection and ease of changing the set-point temperature and deadband width all over the TCL units. We investigate the stability of the proposed model along with presenting guidelines to maintain the numerical stability of the discretized model during computer simulations. Moreover, the proposed model is a close fit to design feedback algorithms for power control purposes. Hence, we present output- and state-feedback control algorithms, designed using the comparison principle and Lyapunov analysis, respectively. We conduct various simulations to verify the effectiveness of the proposed modeling and control techniques.

Analytic Modeling and Integral Control of Heterogeneous Thermostatically Controlled Load Populations

2014 ◽  
Author(s):  
Azad Ghaffari ◽  
Scott Moura ◽  
Miroslav Krstić
Keyword(s):  
Power Control ◽  
Output Feedback ◽  
Electricity Consumption ◽  
Output Feedback Control ◽  
Stability Margin ◽  
Control Technique ◽  
Seasonal Temperature ◽  
Integral Control ◽  
Modeling And Control ◽  
The Stability

Thermostatically controlled loads (TCLs) account for approximately 50% of U.S. electricity consumption. Various techniques have been developed to model TCL populations. A High-fidelity analytical model of heterogeneous TCL populations facilitates the aggregate synthesis of power control in power networks. Such a model assists the utility manager to increase the stability margin of the network. The model, also, assists the customer to schedule his/her tasks in order to reduce his/her energy cost. We present a deterministic hybrid partial differential equation (PDE) model which accounts for heterogeneous populations of TCLs, and facilitates analysis of common scenarios like cold load pick up, cycling, and daily and/or seasonal temperature changes to estimate the aggregate performance of the system. The proposed technique is flexible in terms of parameter selection and ease of changing the set-point temperature and deadband width all over the TCL units. We provide guidelines to maintain the numerical stability of the discretized model during computer simulations. Moreover, the proposed model is a close fit to design output feedback algorithms for power control purposes. Our integral output feedback control, designed using the comparison principle, guarantees fast and efficient power tracking for various real-world scenarios. We present simulation results to verify the effectiveness of the proposed modeling and control technique.

scholarly journals Model Reduction Methods for Complex Network Systems

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
X. Cheng ◽  
J.M.A. Scherpen
Keyword(s):  
Autonomous Systems ◽  
High Dimensional ◽  
Annual Review ◽  
Publication Date ◽  
Network Systems ◽  
Modeling And Control ◽  
Reduced Order ◽  
Reduction Methods ◽  
The Stability ◽  
And Control

Network systems consist of subsystems and their interconnections and provide a powerful framework for the analysis, modeling, and control of complex systems. However, subsystems may have high-dimensional dynamics and a large number of complex interconnections, and it is therefore relevant to study reduction methods for network systems. Here, we provide an overview of reduction methods for both the topological (interconnection) structure of a network and the dynamics of the nodes while preserving structural properties of the network. We first review topological complexity reduction methods based on graph clustering and aggregation, producing a reduced-order network model. Next, we consider reduction of the nodal dynamics using extensions of classical methods while preserving the stability and synchronization properties. Finally, we present a structure-preserving generalized balancing method for simultaneously simplifying the topological structure and the order of the nodal dynamics. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 4 is May 3, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

A Complete Modeling and Control for Wind Turbine Based of a Doubly Fed Induction Generator using Direct Power Control

2017 ◽  
Vol 8 (4) ◽  
pp. 1954 ◽  
Author(s):  
Fawzi Senani
Keyword(s):  
Power Control ◽  
Wind Turbine ◽  
Control Strategy ◽  
Reactive Power ◽  
Maximum Efficiency ◽  
Direct Power ◽  
Direct Power Control ◽  
Modeling And Control ◽  
Doubly Fed ◽  
And Control

<span lang="EN-US">The paper presents the complete modeling and control strategy of variable speed wind turbine system (WTS) driven doubly fed induction generators (DFIG). A back-to-back converter is employed for the power conversion exchanged between DFIG and grid. The wind turbine is operated at the maximum power point tracking (MPPT) mode its maximum efficiency. Direct power control (DPC) based on selecting of the appropriate rotor voltage vectors and the errors of the active and reactive power, the control strategy of rotor side converter combines the technique of MPPT and direct power control. In the control system of the grid side converter the direct power control has been used to maintain a constant DC-Link voltage, and the reactive power is set to 0. Simulations results using MATLAB/SIMULINK are presented and discussed on a 1.5MW DFIG wind generation system demonstrate the effectiveness of the proposed control.</span>

Modeling and Control of a Thermoelastic Beam

2013 ◽  
Author(s):  
Ilhan Tuzcu ◽  
Javier Gonzalez-Rocha
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Elastic Displacement ◽  
Linear Quadratic ◽  
Partial Differential ◽  
Numerical Application ◽  
Modeling And Control ◽  
Thermoelastic Beam ◽  
And Control

The objective of this paper is to model a thermoelastic beam and use thermoelectric heat actuators dispersed over the beam to control not only its vibration, but also its temperature. The model is represented by two coupled partial differential equations governing the elastic bending displacement and temperature variation over the length of the beam. The partial differential equations are replaced by a set of ordinary differential equations through discretization. The first-order ordinary differential equations are cast in the compact state-space form to be used in the thermoelastic analysis and control. The Linear Quadratic Gaussian (LQG) is used for control design. An numerical application to a uniform cantilever beam demonstrates the coupling between the temperature and the elastic displacement and feasibility of using thermoelectric actuators in controlling the vibration and temperature simultaneously.

BIOMECHANICAL STABILITY ANALYSIS OF THE λ-MODEL CONTROLLING ONE JOINT

2007 ◽  
Vol 17 (03) ◽  
pp. 193-206 ◽  
Author(s):  
L. LAN ◽  
K. Y. ZHU
Keyword(s):  
Equilibrium Point ◽  
Motor System ◽  
Jacobian Matrix ◽  
System Modeling ◽  
Neuromuscular Disorders ◽  
Biomechanical Stability ◽  
Modeling And Control ◽  
Human Motor ◽  
The Stability ◽  
And Control

Computer modeling and control of the human motor system might be helpful for understanding the mechanism of human motor system and for the diagnosis and treatment of neuromuscular disorders. In this paper, a brief view of the equilibrium point hypothesis for human motor system modeling is given, and the λ-model derived from this hypothesis is studied. The stability of the λ-model based on equilibrium and Jacobian matrix is investigated. The results obtained in this paper suggest that the λ-model is stable and has a unique equilibrium point under certain conditions.

scholarly journals Analysis of Hysteresis-Free Creep of the Stack Piezoelectric Actuator

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xueliang Zhao ◽  
Chengjin Zhang ◽  
Hongbo Liu ◽  
Guilin Zhang ◽  
Kang Li
Keyword(s):  
Fixed Point ◽  
Piezoelectric Actuator ◽  
High Speed ◽  
Creep Model ◽  
Modeling And Control ◽  
Creep Effect ◽  
Proposed Model ◽  
Series Of Experiments ◽  
Creep Models ◽  
And Control

A modified log-type creep model without hysteresis of the stack piezoelectric actuator is presented. For high-speed micro-/nanopositioning system, the time scale should be less than one second for creep modeling and control in the stack piezoelectric actuator. But creep effect was studied in the frame of minutes in previous works. Meanwhile, parameters of the classical creep models are hard to be determined. By the proposed model, the hysteresis and the creep effect can be separated. A series of experiments have been performed, where different staircase voltages have been applied to the actuator. There are two clear rules to follow in small duration and different heights to determine parameters. Firstly,L0starts from fixed point either in ascending stage or in descending stage and rotates clockwise. Secondly,γconverges to a small vicinity of a constant when the duration is small enough.

scholarly journals Fuzzy Modeling and Control of HIV Infection

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hassan Zarei ◽  
Ali Vahidian Kamyad ◽  
Ali Akbar Heydari
Keyword(s):  
Viral Load ◽  
Fuzzy Control ◽  
Hiv Infection ◽  
Immune Cells ◽  
Control Function ◽  
Drug Dosage ◽  
Modeling And Control ◽  
Proposed Model ◽  
Linear Fuzzy Differential Equations ◽  
And Control

The present study proposes a fuzzy mathematical model of HIV infection consisting of a linear fuzzy differential equations (FDEs) system describing the ambiguous immune cells level and the viral load which are due to the intrinsic fuzziness of the immune system's strength in HIV-infected patients. The immune cells in question are considered CD4+ T-cells and cytotoxic T-lymphocytes (CTLs). The dynamic behavior of the immune cells level and the viral load within the three groups of patients with weak, moderate, and strong immune systems are analyzed and compared. Moreover, the approximate explicit solutions of the proposed model are derived using a fitting-based method. In particular, a fuzzy control function indicating the drug dosage is incorporated into the proposed model and a fuzzy optimal control problem (FOCP) minimizing both the viral load and the drug costs is constructed. An optimality condition is achieved as a fuzzy boundary value problem (FBVP). In addition, the optimal fuzzy control function is completely characterized and a numerical solution for the optimality system is computed.

Modeling and Control of Flexible Transporter System With Arbitrarily Time-Varying Cable Lengths

2003 ◽  
Author(s):  
Yuhong Zhang ◽  
Sunil K. Agrawal ◽  
Peter Hagedorn
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ritz Method ◽  
Nonlinear Partial Differential Equations ◽  
Time Varying ◽  
Governing Equations ◽  
Partial Differential ◽  
Modeling And Control ◽  
Lyapunov Controller ◽  
And Control

A systematic procedure for deriving the system model of a cable transporter system with arbitrarily time-varying lengths is presented. Two different approaches are used to develop the model, namely, Newton’s Law and Hamilton’s Principle. The derived governing equations are nonlinear partial differential equations. The same results are obtained using the two methods. The Rayleigh-Ritz method is used to obtain an approximate numerical solution of the governing equations by transforming the infinite order partial differential equations into a finite order discretized system. A Lyapunov controller which can both dissipate the vibratory energy and assure the attainment of the desired goal is derived. The validity of the proposed controller is verified by numerical simulation.

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