Self-Adaptive Firefly Algorithm with Pole Zero Cancellation Method for Controlling SMIB Power System

The accurate analysis and controller design for high-order systems are important issues. In this paper, a design of controller is suggested to Single Machine Infinite Bus (SMIB) System in which its order is reduced by the proposed self-adaptive Firefly Algorithm (FA). First, the dynamic adaption to the dominant parameters of the standard FA is proposed for overcoming its disadvantages and improving its ability in searching the global optimum solution with application to reduce the model order of SMIB. The parameters which are proposed to self-adaption are both of the light absorption based on the mean distance of fireflies’ positions and the step setting based on the fitness information to the status of preceding firefly and the current fireflies. Second, proportional–integral–derivative (PID) controller is suggested to be designed by pole zero cancellation method via the step response characteristics of the reduced-order SMIB to be applied to its high order. The efficiency of the proposed methods is tested on high-order SMIB to get its corresponding low order and to control it. The experimental results prove the efficacy of self-adaptive FA compared to the standard FA and the methods in the literature in terms of step response characteristics using error indices. The proposed methods assure the stability of the reduced order and the ability of the designed controller to handle both high and low-order model.

Download Full-text

Reduced Order Modeling of Aeroacoustic Systems for Stability Analyses of Thermoacoustically Non-Compact Gas Turbine Combustors

Volume 4B: Combustion, Fuels and Emissions ◽

10.1115/gt2015-43338 ◽

2015 ◽

Author(s):

Tobias Hummel ◽

Constanze Temmler ◽

Bruno Schuermans ◽

Thomas Sattelmayer

Keyword(s):

Gas Turbine ◽

Time Domain ◽

Order Reduction ◽

High Order ◽

Essential Information ◽

Reduced Order ◽

Stability Analyses ◽

Modal Reduction ◽

Non Linear ◽

Low Order

A methodology is presented to model non-compact thermoacoustic phenomena using Reduced Order Models (ROM) based on the Linearized Navier-Stokes Equations (LNSE). The method is applicable to geometries with a complex flow field as in a gas turbine combustion chamber. The LNSE, and thus the resulting ROM, include coupling effects between acoustics and mean fluid flow, and are hence capable of describing propagation and (e.g. vortical) damping of the acoustic fluctuations within the considered volume. Such a ROM then constitutes the main building block for a novel thermoacoustic stability analysis method via a low-order hybrid approach. This method presents an expansion to state-of-the-art low-order stability tools, and is conceptually based on three core features: Firstly, the multi-dimensional and volumetric nature of the ROM establishes access to account spatial variability and non-compact effects on heat release fluctuations. As a result, it is particularly useful for high frequency phenomena such as screech. Secondly, the LNSE basis grants the ROM the capability to reconstruct complex acoustic performances physically accurate. Thirdly, the formulation of the ROM in state-space allows convenient access to the frequency and time domain. In the time domain, non-linear saturation mechanisms can be included, which reproduce the non-linear stochastic limit cycle behavior of thermoacoustic oscillations. In order to demonstrate and verify the ROM’s underlying methodology, a test case using an orifice-tube geometry as the acoustic volume is performed. The generation of the ROM of the orifice-tube is conducted in a two-step procedure. As the first step, the geometrical domain is aeroacoustically characterized through the LNSE in frequency domain, and discretized via the Finite Element Method (FEM). The second step concerns the actual derivation of the ROM. The high-order dynamical system from the LNSE discretization is subjected to a modal reduction as order reduction technique. Mathematically, this modal reduction is the projection of the high-order (N ∼200,000) system into its truncated left eigenspace. An order reduction of several magnitudes (ROM order: Nr ∼100) is achieved. The resulting ROM contains all essential information about propagation and damping of the acoustic variables, and efficiently reproduces the aeroacoustic performance of the orifice-tube. Validation is achieved by comparing ROM results against numerical and experimental benchmarks from LNSE-FEM simulations and test rig measurements, respectively. Excellent agreement is found, which grants the ROM modeling approach full eligibility for further usage in the context of thermoacoustic stability modeling. This work is concluded by a methodological demonstration of performing stability analyses of non-compact thermoacoustic systems using the herein presented ROMs.

Download Full-text

Reduced-Order Modeling of Aeroacoustic Systems for Stability Analyses of Thermoacoustically Noncompact Gas Turbine Combustors

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4031542 ◽

2015 ◽

Vol 138 (5) ◽

Cited By ~ 6

Author(s):

Tobias Hummel ◽

Constanze Temmler ◽

Bruno Schuermans ◽

Thomas Sattelmayer

Keyword(s):

Gas Turbine ◽

Time Domain ◽

Stokes Equations ◽

Order Reduction ◽

High Order ◽

Essential Information ◽

Reduced Order ◽

Stability Analyses ◽

Modal Reduction ◽

Low Order

A methodology is presented to model noncompact thermoacoustic phenomena using reduced-order models (ROMs) based on the linearized Navier–Stokes equations (LNSEs). The method is applicable to geometries with a complex flow field as in a gas turbine combustion chamber. The LNSEs, and thus the resulting ROM, include coupling effects between acoustics and mean fluid flow and are hence capable of describing propagation and (e.g., vortical) damping of the acoustic fluctuations within the considered volume. Such an ROM then constitutes the main building block for a novel thermoacoustic stability analysis method via a low-order hybrid approach. This method presents an expansion to state-of-the-art low-order stability tools and is conceptually based on three core features: First, the multidimensional and volumetric nature of the ROM establishes access to account spatial variability and noncompact effects on heat-release fluctuations. As a result, it is particularly useful for high-frequency phenomena such as screech. Second, the LNSE basis grants the ROM the capability to reconstruct complex acoustic performances physically accurate. Third, the formulation of the ROM in state-space allows convenient access to the frequency and time domain. In the time domain, nonlinear saturation mechanisms can be included, which reproduce the nonlinear stochastic limit cycle behavior of thermoacoustic oscillations. In order to demonstrate and verify the ROM's underlying methodology, a test case using an orifice-tube geometry as the acoustic volume is performed. The generation of the ROM of the orifice tube is conducted in a two-step procedure. As the first step, the geometrical domain is aeroacoustically characterized through the LNSE in frequency domain and discretized via the finite element method (FEM). The second step concerns the actual derivation of the ROM. The high-order dynamical system from the LNSE discretization is subjected to a modal reduction as order reduction technique. Mathematically, this modal reduction is the projection of the high-order (N∼ 200,000) system into its truncated left eigenspace. An order reduction of several magnitudes (ROM order: Nr∼ 100) is achieved. The resulting ROM contains all essential information about propagation and damping of the acoustic variables, and efficiently reproduces the aeroacoustic performance of the orifice tube. Validation is achieved by comparing ROM results against numerical and experimental benchmarks from LNSE–FEM simulations and test rig measurements, respectively. Excellent agreement is found, which grants the ROM modeling approach full eligibility for further usage in the context of thermoacoustic stability modeling. This work is concluded by a methodological demonstration of performing stability analyses of noncompact thermoacoustic systems using the herein presented ROMs.

Download Full-text

CONTINUOUS FIREFLY ALGORITHM FOR OPTIMAL TUNING OF PID CONTROLLER IN AVR SYSTEM

Journal of Electrical Engineering ◽

10.2478/jee-2014-0006 ◽

2014 ◽

Vol 65 (1) ◽

pp. 44-49 ◽

Cited By ~ 15

Author(s):

Omar Bendjeghaba

Keyword(s):

Pid Controller ◽

Firefly Algorithm ◽

Step Response ◽

Voltage Regulator ◽

Proportional Integral Derivative ◽

Swarm Optimization ◽

Response Characteristics ◽

Tuning Method ◽

Point Tracking ◽

Avr System

Abstract This paper presents a tuning approach based on Continuous firefly algorithm (CFA) to obtain the proportional-integral- derivative (PID) controller parameters in Automatic Voltage Regulator system (AVR). In the tuning processes the CFA is iterated to reach the optimal or the near optimal of PID controller parameters when the main goal is to improve the AVR step response characteristics. Conducted simulations show the effectiveness and the efficiency of the proposed approach. Furthermore the proposed approach can improve the dynamic of the AVR system. Compared with particle swarm optimization (PSO), the new CFA tuning method has better control system performance in terms of time domain specifications and set-point tracking.

Download Full-text

A Novel Mixed Method Using MM-SE with Change in Routhain Array for Model Order Reduction

10.21203/rs.3.rs-705686/v1 ◽

2021 ◽

Author(s):

Aswant Kumar Sharma ◽

Dhanesh Kumar Sambariya

Keyword(s):

Mixed Method ◽

Model Order Reduction ◽

Order Reduction ◽

Step Response ◽

System Modelling ◽

Stability Equation ◽

Model Order ◽

Reduced Order ◽

Response Characteristics ◽

Higher Order Differential Equations

Abstract The system modelling leads towards the higher-order differential equations. These systems are difficult to analyse. Therefore, for ease and understanding, the conversion of higher to lower order is required. The model order reduction(MOR) is a systematic procedure to tackle these kinds of situations. This paper offers a mixed method for MOR using the modified moment matching (MM) and stability equation (SE). The modification is applied in the routhain array of MM. The approach has been verified by examining the error between the original, proposed and compared with reduced order available in the literature. The obtained result has been compared on the basis of step response characteristics and the response indices error.

Download Full-text

Design and Simulation of Low Order Control Laws for High Order Thermal Models

Volume 2: Automotive Systems; Bioengineering and Biomedical Technology; Computational Mechanics; Controls; Dynamical Systems ◽

10.1115/esda2008-59215 ◽

2008 ◽

Author(s):

Ziv Brand ◽

Nadav Berman ◽

Guy Rodnay

Keyword(s):

Control Theory ◽

Model Reduction ◽

Real Time ◽

Controller Design ◽

High Order ◽

Optimal Controller ◽

Small Scale ◽

Balanced Truncation ◽

Control Laws ◽

Low Order

A method for designing small scale control laws for large scale thermal systems is proposed. For high order models, traditional control theory produces high order control laws, which are impractical to implement. Here, Balanced Truncation is used to reduce the order of the model, while preserving as much as possible the dynamical properties that are important for controller design. Then, a low order controller is designed by applying a standard linear quadratic optimal control design procedure on the reduced model. The small scale controller performance is tested by incorporating it in a simulation with the full scale model. A geometric approach is used, in order to propose that the norms that are defined on the input and output spaces of the system should be the same in the model reduction phase and in the optimal controller design phase. This way, the cost function of the optimal controller is taken into account during the model reduction phase. A reduced order observer which allows real time estimation of process values that cannot be directly measured can be easily designed. The input signals that are computed during closed loop simulation can be also used in real time open loop operation. Hence, the work has a pure computational aspect: calculate the heat fluxes that are required in order to track a temperature profile that is given for a set of output points. Integrating standard computational methods with standard control theory via the Balanced Truncation algorithm is proved to be a powerful tool.

Download Full-text