This document summarizes a research paper that proposes using differential evolution optimization to reduce the order of high-order discrete systems and design PID controllers for the reduced-order models. The paper presents a method for:
1) Reducing a high-order discrete system to a lower-order model by minimizing the error between step responses using differential evolution.
2) Designing a PID controller for the reduced-order model by optimizing controller parameters with differential evolution to minimize error.
3) Testing the PID controller on both the reduced and original high-order models. Differential evolution is an evolutionary algorithm that minimizes an objective function by mutating candidate solutions and selecting the best ones to propagate to the next generation.
Acm Tech Talk - Decomposition Paradigms for Large Scale SystemsVinayak Hegde
This document discusses decomposition approaches for solving large-scale systems problems. It begins with an overview of general decomposition strategies and approaches to decomposition. It then discusses specific decomposition paradigms like model coordination and goal coordination. It provides examples of how decomposition can be applied to problems in areas like optimization, identification, and control. The document concludes with some illustrative examples and case studies.
The architecture for the A-7E avionics system utilizes three main architectural structures: a module decomposition structure, a uses structure, and a process structure. The module decomposition structures the system into modules that hide information to achieve qualities like ease of change. It uses a hierarchy with three top-level modules for hardware-hiding, behavior-hiding, and software decisions. The uses structure and process structure also help achieve qualities like modifiability and real-time performance by defining how modules interact and how processes are scheduled. The three structures work together to provide a complete picture of how the avionics system works.
The document discusses the architecture of the Initial Sector Suite System (ISSS), which was intended to upgrade air traffic control systems in the United States. ISSS had ultrahigh availability requirements due to its safety-critical nature. Its architecture used hardware and software redundancy, distributed processing, and layering to achieve high availability and performance. It also employed interface wrapping and standard protocols to support openness, modifiability, and interoperability with other systems.
This document discusses software design principles and processes. It describes key stages of design like problem understanding, identifying solutions, and describing solution abstractions. The design process involves phases like architectural design, interface design, and algorithm design. Good design principles include having linguistic modular units, few interfaces with loose coupling between modules, explicit interfaces, and information hiding. Top-down design and stepwise refinement are common design methods. Cohesion and coupling are important attributes of modular design.
This document discusses software design principles and concepts. It begins by defining software design as translating requirements into a blueprint for constructing software. Key concepts discussed include:
1. Managing complexity through principles like uniformity, accommodating change, and minimizing coupling between modules.
2. Software architecture, which defines the overall structure and interactions between major system elements.
3. Common design techniques like abstraction, modularity, hierarchy, and separation of concerns that help manage complexity.
This document discusses key software design principles:
1. Modularization, abstraction, and encapsulation aim to break down a system into independent and cohesive modules that hide unnecessary details.
2. Coupling and cohesion measure the interdependence between modules - loose coupling and high cohesion where related code is grouped together are ideal.
3. Other principles like separation of interface and implementation, sufficiency, and completeness focus on defining clean interfaces and providing only necessary functionality. The document provides examples and comparisons to explain these fundamental software design concepts.
The document discusses software design, which involves deciding how to implement system requirements using available technology. It covers topics like software architecture, dividing a system into subsystems and interfaces. The key benefits of design are that it makes a project easier to implement, test and maintain. Good design leads to good quality software while bad design can make a project impossible. The phases of design process include architectural design, class design, user interface design, and algorithm design. Design principles discussed aim to divide problems into smaller parts, increase cohesion, reduce coupling, use abstraction, design for flexibility and testability.
The document discusses designing architecture using Attribute-Driven Design (ADD). It describes ADD as a method for designing an architecture to satisfy both functional and quality requirements. The key steps of ADD include choosing architectural drivers from quality scenarios and requirements, selecting an architectural pattern to address the drivers, and instantiating modules and allocating functionality to implement the pattern. As an example, it applies ADD to design a product line architecture for a garage door opener system.
Acm Tech Talk - Decomposition Paradigms for Large Scale SystemsVinayak Hegde
This document discusses decomposition approaches for solving large-scale systems problems. It begins with an overview of general decomposition strategies and approaches to decomposition. It then discusses specific decomposition paradigms like model coordination and goal coordination. It provides examples of how decomposition can be applied to problems in areas like optimization, identification, and control. The document concludes with some illustrative examples and case studies.
The architecture for the A-7E avionics system utilizes three main architectural structures: a module decomposition structure, a uses structure, and a process structure. The module decomposition structures the system into modules that hide information to achieve qualities like ease of change. It uses a hierarchy with three top-level modules for hardware-hiding, behavior-hiding, and software decisions. The uses structure and process structure also help achieve qualities like modifiability and real-time performance by defining how modules interact and how processes are scheduled. The three structures work together to provide a complete picture of how the avionics system works.
The document discusses the architecture of the Initial Sector Suite System (ISSS), which was intended to upgrade air traffic control systems in the United States. ISSS had ultrahigh availability requirements due to its safety-critical nature. Its architecture used hardware and software redundancy, distributed processing, and layering to achieve high availability and performance. It also employed interface wrapping and standard protocols to support openness, modifiability, and interoperability with other systems.
This document discusses software design principles and processes. It describes key stages of design like problem understanding, identifying solutions, and describing solution abstractions. The design process involves phases like architectural design, interface design, and algorithm design. Good design principles include having linguistic modular units, few interfaces with loose coupling between modules, explicit interfaces, and information hiding. Top-down design and stepwise refinement are common design methods. Cohesion and coupling are important attributes of modular design.
This document discusses software design principles and concepts. It begins by defining software design as translating requirements into a blueprint for constructing software. Key concepts discussed include:
1. Managing complexity through principles like uniformity, accommodating change, and minimizing coupling between modules.
2. Software architecture, which defines the overall structure and interactions between major system elements.
3. Common design techniques like abstraction, modularity, hierarchy, and separation of concerns that help manage complexity.
This document discusses key software design principles:
1. Modularization, abstraction, and encapsulation aim to break down a system into independent and cohesive modules that hide unnecessary details.
2. Coupling and cohesion measure the interdependence between modules - loose coupling and high cohesion where related code is grouped together are ideal.
3. Other principles like separation of interface and implementation, sufficiency, and completeness focus on defining clean interfaces and providing only necessary functionality. The document provides examples and comparisons to explain these fundamental software design concepts.
The document discusses software design, which involves deciding how to implement system requirements using available technology. It covers topics like software architecture, dividing a system into subsystems and interfaces. The key benefits of design are that it makes a project easier to implement, test and maintain. Good design leads to good quality software while bad design can make a project impossible. The phases of design process include architectural design, class design, user interface design, and algorithm design. Design principles discussed aim to divide problems into smaller parts, increase cohesion, reduce coupling, use abstraction, design for flexibility and testability.
The document discusses designing architecture using Attribute-Driven Design (ADD). It describes ADD as a method for designing an architecture to satisfy both functional and quality requirements. The key steps of ADD include choosing architectural drivers from quality scenarios and requirements, selecting an architectural pattern to address the drivers, and instantiating modules and allocating functionality to implement the pattern. As an example, it applies ADD to design a product line architecture for a garage door opener system.
This document discusses quality attributes that are important considerations for software architects. It defines key attributes like availability, modifiability, performance, security, and testability. It presents these attributes as general scenarios to help stakeholders communicate and understand them. The document also covers business qualities and architectural qualities that influence design decisions.
Presentation covers all aspects about Software Designing that are followed by Software Engineering Industries. Readers can do detailed study about the Software Design Concepts like (Abstraction, Architecture, Patterns, Modularity, Information Hiding, Refinement, Functional Dependence, Cohesion, Coupling & Refactoring) plus Design Process.
Later then Design Principles are there to understand with Architectural Design, Architectural Styles, Data Centered Architecture, Data Flow Architecture, Call & Return Architecture, Object Oriented Architecture, Layered Architecture with other architectures are named at end of it.
Later then, Component Level Design is discussed. Then after UI Design & Rules of it, UI Design Models, Web Application Design, WebApp Interface Design are discussed at the end.
Comment back if you have any query about it.
An effective frequency domain approach to tuning non-PID controllers for high...ISA Interchange
This document proposes a new method for tuning non-PID controllers to achieve high performance control of complex processes. The method involves 3 stages:
1) Determining an optimal closed-loop transfer function based on the process characteristics and limitations.
2) Deriving an ideal controller from the optimal transfer function, which is usually complex.
3) Applying model reduction to the ideal controller to obtain a simpler, realizable controller form.
Simulation examples are provided to demonstrate the effectiveness of the proposed non-PID controller tuning method for complex processes where PID control is insufficient.
The document discusses key concepts and principles of software design. It begins by defining design as a blueprint for solving problems specified in requirements. Good design implements all requirements, provides a readable guide, and gives a complete picture of the software. The design process has two levels - top-level design of modules and interfaces and detailed design of module internals. The document then covers fundamental design concepts like abstraction, refinement, modularity, architecture, partitioning, data structures, procedures, information hiding, and functional independence. It provides examples and guidelines for applying these concepts to create a high-quality design.
The document discusses key aspects of the software design process including that design is iterative and represented at a high level of abstraction, guidelines for quality design include modularity, information hiding, and functional independence, and architectural design defines system context and archetypes that compose the system.
In the GTU degree engineering, Software engineering is such a subject which is used to explore thinking over designing reliable softwares. In this presentation , Design concepts and principles are mentioned and explained in simplified manner.
This Presentation contains all the topics in design concept of software engineering. This is much more helpful in designing new product. You have to consider some of the design concepts that are given in the ppt
The document provides an overview of software design principles and system models. It discusses the objectives of understanding software design principles and following a structured approach. It describes different system models including data processing, composition, classification, and stimulus-response models. It also covers architectural design, explaining that it is the initial design process that identifies subsystems and establishes a framework for control and communication. It discusses system structuring, control models, and modular decomposition as part of the architectural design process.
SWE-401 - 6. Software Analysis and Design Toolsghayour abbas
The document discusses several software analysis and design tools used by software designers including:
- Data Flow Diagrams (DFDs) which graphically depict the flow of data in a system. DFDs come in logical and physical types.
- Structure Charts which represent the hierarchical structure and functions of system modules in greater detail than DFDs.
- HIPO Diagrams which decompose system functions hierarchically and depict functions performed without data or control flow.
- Additional tools discussed are Structured English, Pseudo-Code, Decision Tables and Entity-Relationship Models.
MINIMIZING THE COMPLEXITY EFFECTS TO MAS ARCHITECTURES DESIGN BASED ON FG4COM...ijseajournal
The efficiency of multi agent system design mainly depends on the quality of a theoretical
architecture of such systems. Therefore, quality issues should be considered at an early stage in
the software development. Large systems such as multi agents systems (MAS) require many
communications and interactions to accomplish their tasks, and this leads to complexity of
architecture design (AD) which have crucial influence on architecture design quality. This work
attempts to introduce approach works on increase the architecture design quality of MAS by
minimizing the effect of complexity
The document describes key components of software design including data design, architectural design, interface design, and procedural design. It discusses the goals of the design process which are to implement requirements, create an understandable guide for code generation and testing, and address implementation from data, functional, and behavioral perspectives. The document also covers concepts like abstraction, refinement, modularity, program structure, data structures, software procedures, information hiding, and cohesion and coupling.
The document discusses techniques for designing software architecture and making good design decisions. It provides principles for dividing a system into components, increasing cohesion and reducing coupling between components. The document emphasizes designing for qualities like flexibility, reusability, portability and testability. Priorities, objectives and cost-benefit analysis can be used to evaluate design alternatives. The architecture is the core of the design and should divide the system into subsystems and define their interactions and interfaces.
The document discusses software design and the software design process. It covers stages of design like problem understanding, identifying solutions, and describing solution abstractions. It also discusses phases in the design process like architectural design, abstract specification, interface design, component design, data structure design, and algorithm design. The document outlines principles for good design like linguistic modular units, few interfaces, small interfaces, explicit interfaces, and information hiding. It discusses concepts like coupling, cohesion, and stepwise refinement in software design.
Design PID controllers for desired time domain or frequency domain responseISA Interchange
The document discusses the design of PID controllers to achieve desired time-domain or frequency-domain responses for a nominal stable process with time delay. It presents an Hρ PID controller derived analytically based on optimal control theory. The controller parameters are derived such that they minimize the worst error resulting from system inputs. The properties of the Hρ PID controller are then investigated and compared to an H2 PID controller and a Maclaurin PID controller. All three controllers are shown to be able to provide quantitative time-domain and frequency-domain responses.
The document discusses key concepts in software design including:
- The main activities in software design are data design, architectural design, procedural design, and sometimes interface design. Preliminary design transforms requirements into architecture while detail design refines the architecture.
- Data design develops data structures to represent information from analysis. Architectural design defines program structure and interfaces. Procedural design represents structural components procedurally using notations like flowcharts.
- Other concepts discussed include modularity, abstraction, software architecture, control hierarchy, data structures, and information hiding. Modular design, abstraction and information hiding help manage complexity. Software architecture and control hierarchy define program organization.
Se 381 - lec 22 - 24 - 12 may15 - modularity - i - couplingbabak danyal
This document discusses modularity and coupling in software engineering. It defines that programs are comprised of components that communicate to achieve program goals. Component size can vary, but should generally be 5-9 statements to fit in human working memory. Modularity partitions a system into components to improve design, maintenance, testing and more. Coupling describes the interaction between components, with loose/weak coupling like data coupling being preferred over tight/strong coupling like content coupling. The document provides examples to illustrate different types of coupling and how modularity improves software engineering.
Se 381 - lec 23 - 28 - 12 may16 - modularity - ii - cohesionbabak danyal
This document discusses the concepts of cohesion and coupling in software engineering. It defines cohesion as a measure of how closely related elements within a module are to each other, and coupling as a measure of the connections between modules. There are seven types of cohesion discussed from weakest to strongest: coincidental, logical, temporal, procedural, communicational, informational, and functional. Functional cohesion, where a module performs a single well-defined task, is considered the ideal. Strong cohesion and loose coupling, where modules are highly independent, leads to better design. The document provides examples and analysis of each cohesion type.
The document discusses component-based software engineering and defines a software component. A component is a modular building block defined by interfaces that can be independently deployed. Components are standardized, independent, composable, deployable, and documented. They communicate through interfaces and are designed to achieve reusability. The document outlines characteristics of components and discusses different views of components, including object-oriented, conventional, and process-related views. It also covers topics like component-level design principles, packaging, cohesion, and coupling.
This document compares the DCT (Discrete Cosine Transform) and DWT (Discrete Wavelet Transform) image compression techniques. It finds that DWT provides higher compression ratios and avoids blocking artifacts compared to DCT. DWT allows for better localization in both spatial and frequency domains. It also has inherent scaling and better identifies visually relevant data, leading to higher compression ratios. However, DCT is faster than DWT. Experimental results on test images show that DWT achieves higher PSNR and lower MSE and BER than DCT, while providing a slightly higher compression ratio and completing compression more quickly.
IRJET- A Design Approach for Basic Telecom OperationIRJET Journal
This document discusses using aspect-oriented programming to handle cross-cutting concerns in telecom operations. It proposes developing cross-cutting concerns like consistency checking as separate aspect modules. This allows cross-cutting concerns to be modularized without impacting the core functionality modules. The document presents class and sequence diagrams to model a basic telecom operation and discusses how aspect-oriented programming can be used to implement consistency checking as a cross-cutting concern in the telecom system.
This document proposes using artificial bee colony (ABC) algorithm to reduce the order of higher order discrete systems and design PID controllers for the reduced order systems. ABC algorithm is used to minimize error between the original and reduced order systems' step responses, obtaining a lower order model. ABC is then used to minimize error between the desired and actual step responses of the reduced order system with a PID controller, tuning the PID parameters. The designed PID controller is then applied to the original higher order system to achieve the desired control objectives. The method is illustrated with a numerical example.
A Hybrid Differential Evolution Method for the Design of IIR Digital FilterIDES Editor
This paper establishes methodology for the robust
and stable design of infinite impulse response (IIR) digital
filters using hybrid differential evolution method. Differential
Evolution (DE) is undertaken as a global search technique
and exploratory search is exploited as a local search technique.
DE is a population based stochastic real parameter
optimization technique relating to evolutionary computation,
whose simple yet powerful and straight forward features make
it very attractive for numerical optimization. Exploratory
search aims to fine tune the solution locally in promising
search area. This proposed DE method augments the capability
to explore and exploit the search space locally as well globally
to achieve the optimal filter design parameters by applying
the opposition learning strategy and random migration. A
multivariable optimization is employed as the design criterion
to obtain the optimal stable IIR filter that minimizes the
magnitude approximation error and ripple magnitude. DE
method is implemented to design low-pass, high-pass, bandpass,
and band-stop digital IIR filters. The achieved design of
IIR digital filters by applying DE method authenticates that
its results are comparable to other algorithms and can be
effectively applied for higher filter design.
This document discusses quality attributes that are important considerations for software architects. It defines key attributes like availability, modifiability, performance, security, and testability. It presents these attributes as general scenarios to help stakeholders communicate and understand them. The document also covers business qualities and architectural qualities that influence design decisions.
Presentation covers all aspects about Software Designing that are followed by Software Engineering Industries. Readers can do detailed study about the Software Design Concepts like (Abstraction, Architecture, Patterns, Modularity, Information Hiding, Refinement, Functional Dependence, Cohesion, Coupling & Refactoring) plus Design Process.
Later then Design Principles are there to understand with Architectural Design, Architectural Styles, Data Centered Architecture, Data Flow Architecture, Call & Return Architecture, Object Oriented Architecture, Layered Architecture with other architectures are named at end of it.
Later then, Component Level Design is discussed. Then after UI Design & Rules of it, UI Design Models, Web Application Design, WebApp Interface Design are discussed at the end.
Comment back if you have any query about it.
An effective frequency domain approach to tuning non-PID controllers for high...ISA Interchange
This document proposes a new method for tuning non-PID controllers to achieve high performance control of complex processes. The method involves 3 stages:
1) Determining an optimal closed-loop transfer function based on the process characteristics and limitations.
2) Deriving an ideal controller from the optimal transfer function, which is usually complex.
3) Applying model reduction to the ideal controller to obtain a simpler, realizable controller form.
Simulation examples are provided to demonstrate the effectiveness of the proposed non-PID controller tuning method for complex processes where PID control is insufficient.
The document discusses key concepts and principles of software design. It begins by defining design as a blueprint for solving problems specified in requirements. Good design implements all requirements, provides a readable guide, and gives a complete picture of the software. The design process has two levels - top-level design of modules and interfaces and detailed design of module internals. The document then covers fundamental design concepts like abstraction, refinement, modularity, architecture, partitioning, data structures, procedures, information hiding, and functional independence. It provides examples and guidelines for applying these concepts to create a high-quality design.
The document discusses key aspects of the software design process including that design is iterative and represented at a high level of abstraction, guidelines for quality design include modularity, information hiding, and functional independence, and architectural design defines system context and archetypes that compose the system.
In the GTU degree engineering, Software engineering is such a subject which is used to explore thinking over designing reliable softwares. In this presentation , Design concepts and principles are mentioned and explained in simplified manner.
This Presentation contains all the topics in design concept of software engineering. This is much more helpful in designing new product. You have to consider some of the design concepts that are given in the ppt
The document provides an overview of software design principles and system models. It discusses the objectives of understanding software design principles and following a structured approach. It describes different system models including data processing, composition, classification, and stimulus-response models. It also covers architectural design, explaining that it is the initial design process that identifies subsystems and establishes a framework for control and communication. It discusses system structuring, control models, and modular decomposition as part of the architectural design process.
SWE-401 - 6. Software Analysis and Design Toolsghayour abbas
The document discusses several software analysis and design tools used by software designers including:
- Data Flow Diagrams (DFDs) which graphically depict the flow of data in a system. DFDs come in logical and physical types.
- Structure Charts which represent the hierarchical structure and functions of system modules in greater detail than DFDs.
- HIPO Diagrams which decompose system functions hierarchically and depict functions performed without data or control flow.
- Additional tools discussed are Structured English, Pseudo-Code, Decision Tables and Entity-Relationship Models.
MINIMIZING THE COMPLEXITY EFFECTS TO MAS ARCHITECTURES DESIGN BASED ON FG4COM...ijseajournal
The efficiency of multi agent system design mainly depends on the quality of a theoretical
architecture of such systems. Therefore, quality issues should be considered at an early stage in
the software development. Large systems such as multi agents systems (MAS) require many
communications and interactions to accomplish their tasks, and this leads to complexity of
architecture design (AD) which have crucial influence on architecture design quality. This work
attempts to introduce approach works on increase the architecture design quality of MAS by
minimizing the effect of complexity
The document describes key components of software design including data design, architectural design, interface design, and procedural design. It discusses the goals of the design process which are to implement requirements, create an understandable guide for code generation and testing, and address implementation from data, functional, and behavioral perspectives. The document also covers concepts like abstraction, refinement, modularity, program structure, data structures, software procedures, information hiding, and cohesion and coupling.
The document discusses techniques for designing software architecture and making good design decisions. It provides principles for dividing a system into components, increasing cohesion and reducing coupling between components. The document emphasizes designing for qualities like flexibility, reusability, portability and testability. Priorities, objectives and cost-benefit analysis can be used to evaluate design alternatives. The architecture is the core of the design and should divide the system into subsystems and define their interactions and interfaces.
The document discusses software design and the software design process. It covers stages of design like problem understanding, identifying solutions, and describing solution abstractions. It also discusses phases in the design process like architectural design, abstract specification, interface design, component design, data structure design, and algorithm design. The document outlines principles for good design like linguistic modular units, few interfaces, small interfaces, explicit interfaces, and information hiding. It discusses concepts like coupling, cohesion, and stepwise refinement in software design.
Design PID controllers for desired time domain or frequency domain responseISA Interchange
The document discusses the design of PID controllers to achieve desired time-domain or frequency-domain responses for a nominal stable process with time delay. It presents an Hρ PID controller derived analytically based on optimal control theory. The controller parameters are derived such that they minimize the worst error resulting from system inputs. The properties of the Hρ PID controller are then investigated and compared to an H2 PID controller and a Maclaurin PID controller. All three controllers are shown to be able to provide quantitative time-domain and frequency-domain responses.
The document discusses key concepts in software design including:
- The main activities in software design are data design, architectural design, procedural design, and sometimes interface design. Preliminary design transforms requirements into architecture while detail design refines the architecture.
- Data design develops data structures to represent information from analysis. Architectural design defines program structure and interfaces. Procedural design represents structural components procedurally using notations like flowcharts.
- Other concepts discussed include modularity, abstraction, software architecture, control hierarchy, data structures, and information hiding. Modular design, abstraction and information hiding help manage complexity. Software architecture and control hierarchy define program organization.
Se 381 - lec 22 - 24 - 12 may15 - modularity - i - couplingbabak danyal
This document discusses modularity and coupling in software engineering. It defines that programs are comprised of components that communicate to achieve program goals. Component size can vary, but should generally be 5-9 statements to fit in human working memory. Modularity partitions a system into components to improve design, maintenance, testing and more. Coupling describes the interaction between components, with loose/weak coupling like data coupling being preferred over tight/strong coupling like content coupling. The document provides examples to illustrate different types of coupling and how modularity improves software engineering.
Se 381 - lec 23 - 28 - 12 may16 - modularity - ii - cohesionbabak danyal
This document discusses the concepts of cohesion and coupling in software engineering. It defines cohesion as a measure of how closely related elements within a module are to each other, and coupling as a measure of the connections between modules. There are seven types of cohesion discussed from weakest to strongest: coincidental, logical, temporal, procedural, communicational, informational, and functional. Functional cohesion, where a module performs a single well-defined task, is considered the ideal. Strong cohesion and loose coupling, where modules are highly independent, leads to better design. The document provides examples and analysis of each cohesion type.
The document discusses component-based software engineering and defines a software component. A component is a modular building block defined by interfaces that can be independently deployed. Components are standardized, independent, composable, deployable, and documented. They communicate through interfaces and are designed to achieve reusability. The document outlines characteristics of components and discusses different views of components, including object-oriented, conventional, and process-related views. It also covers topics like component-level design principles, packaging, cohesion, and coupling.
This document compares the DCT (Discrete Cosine Transform) and DWT (Discrete Wavelet Transform) image compression techniques. It finds that DWT provides higher compression ratios and avoids blocking artifacts compared to DCT. DWT allows for better localization in both spatial and frequency domains. It also has inherent scaling and better identifies visually relevant data, leading to higher compression ratios. However, DCT is faster than DWT. Experimental results on test images show that DWT achieves higher PSNR and lower MSE and BER than DCT, while providing a slightly higher compression ratio and completing compression more quickly.
IRJET- A Design Approach for Basic Telecom OperationIRJET Journal
This document discusses using aspect-oriented programming to handle cross-cutting concerns in telecom operations. It proposes developing cross-cutting concerns like consistency checking as separate aspect modules. This allows cross-cutting concerns to be modularized without impacting the core functionality modules. The document presents class and sequence diagrams to model a basic telecom operation and discusses how aspect-oriented programming can be used to implement consistency checking as a cross-cutting concern in the telecom system.
This document proposes using artificial bee colony (ABC) algorithm to reduce the order of higher order discrete systems and design PID controllers for the reduced order systems. ABC algorithm is used to minimize error between the original and reduced order systems' step responses, obtaining a lower order model. ABC is then used to minimize error between the desired and actual step responses of the reduced order system with a PID controller, tuning the PID parameters. The designed PID controller is then applied to the original higher order system to achieve the desired control objectives. The method is illustrated with a numerical example.
A Hybrid Differential Evolution Method for the Design of IIR Digital FilterIDES Editor
This paper establishes methodology for the robust
and stable design of infinite impulse response (IIR) digital
filters using hybrid differential evolution method. Differential
Evolution (DE) is undertaken as a global search technique
and exploratory search is exploited as a local search technique.
DE is a population based stochastic real parameter
optimization technique relating to evolutionary computation,
whose simple yet powerful and straight forward features make
it very attractive for numerical optimization. Exploratory
search aims to fine tune the solution locally in promising
search area. This proposed DE method augments the capability
to explore and exploit the search space locally as well globally
to achieve the optimal filter design parameters by applying
the opposition learning strategy and random migration. A
multivariable optimization is employed as the design criterion
to obtain the optimal stable IIR filter that minimizes the
magnitude approximation error and ripple magnitude. DE
method is implemented to design low-pass, high-pass, bandpass,
and band-stop digital IIR filters. The achieved design of
IIR digital filters by applying DE method authenticates that
its results are comparable to other algorithms and can be
effectively applied for higher filter design.
This document discusses several software design techniques: stepwise refinement, levels of abstraction, structured design, integrated top-down development, and Jackson structured programming. Stepwise refinement is a top-down technique that decomposes a system into more elementary levels. Levels of abstraction designs systems as layers with each level performing services for the next higher level. Structured design converts data flow diagrams into structure charts using design heuristics. Integrated top-down development integrates design, implementation, and testing with a hierarchical structure. Jackson structured programming maps a problem's input/output structures and operations into a program structure to solve the problem.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
COMPARATIVE ANALYSIS OF CONVENTIONAL PID CONTROLLER AND FUZZY CONTROLLER WIT...IJITCA Journal
All the real systems exhibits non-linear nature,conventional controllers are not always able to provide good and accurate results. Fuzzy Logic Control is used to obtain better response. A model for simulation is designed and all the assumptions are made before the development of the model. An attempt has been made to analyze the efficiency of a fuzzy controller over a conventional PID controller for a three tank level control system using fuzzification & defuzzification methods and their responses are compared. Analysis is done through computer simulation using Matlab/Simulink toolbox. This study shows that the application of Fuzzy Logic Controller (FLC) gives the best response with triangular membership function and centroid defuzzification method.
An Implementation on Effective Robot Mission under Critical Environemental Co...IJERA Editor
Software engineering is a field of engineering, for designing and writing programs for computers or other electronic devices. A software engineer, or programmer, writes software (or changes existing software) and compiles software using methods that make it better quality. Is the application of engineering to the design, development, implementation, testingand main tenance of software in a systematic method. Now a days the robotics are also plays an important role in present automation concepts. But we have several challenges in that robots when they are operated in some critical environments. Motion planning and task planning are two fundamental problems in robotics that have been addressed from different perspectives. For resolve this there are Temporal logic based approaches that automatically generate controllers have been shown to be useful for mission level planning of motion, surveillance and navigation, among others. These approaches critically rely on the validity of the environment models used for synthesis. Yet simplifying assumptions are inevitable to reduce complexity and provide mission-level guarantees; no plan can guarantee results in a model of a world in which everything can go wrong. In this paper, we show how our approach, which reduces reliance on a single model by introducing a stack of models, can endow systems with incremental guarantees based on increasingly strengthened assumptions, supporting graceful degradation when the environment does not behave as expected, and progressive enhancement when it does.
Computer aided design of electrical machineAsif Jamadar
This document discusses computer aided design of electrical machines. It introduces the topic and outlines some key advantages of CAD, such as performing millions of computations quickly, enabling the study of wide parameter variations to find optimal designs, and eliminating tedious calculations. It then describes two main methods of computer aided design - the analysis method and the synthesis method. The analysis method determines machine performance from initial parameters, while the synthesis method uses numerical techniques and iteration to modify variable values to meet desired performance characteristics and find an optimal design.
This document discusses software re-engineering, reverse engineering, and configuration management activities. It defines software re-engineering as examining and altering a system to improve understandability or functionality. Reverse engineering aims to understand how a system works by analyzing its code or components. Configuration management systematically controls changes to a system's configuration throughout its lifecycle.
FPGA based Efficient Interpolator design using DALUT Algorithmcscpconf
The document describes the design and implementation of an efficient interpolator for wireless communication systems using FPGA. It proposes a multiplier-less technique using distributed arithmetic look-up tables (DALUT) that replaces multiply-accumulate operations with LUT accesses. A 66th-order half-band polyphase FIR structure is implemented using the DALUT approach on Spartan-3E and Virtex2Pro FPGAs. Results show the proposed design achieves maximum frequencies of 92.859MHz on Virtex Pro and 61.6MHz on Spartan 3E while consuming fewer resources than a traditional MAC-based design.
FPGA based Efficient Interpolator design using DALUT Algorithmcscpconf
Interpolator is an important sampling device used for multirate filtering to
provide signal processing in wireless communication system. There are many
applications in which sampling rate must be changed. Interpolators and decimators are
utilized to increase or decrease the sampling rate. In this paper an efficient method has
been presented to implement high speed and area efficient interpolator for wireless
communication systems. A multiplier less technique is used which substitutes multiplyand-accumulate
operations with look up table (LUT) accesses. Interpolator has been
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technique. This technique has been used to take an optimal advantage of embedded
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Reduced order in discrete domain
1. International Journal of Information and Mathematical Sciences 6:1 2010
Controller Design of Discrete Systems by Order
Reduction Technique Employing Differential
Evolution Optimization Algorithm
J. S. Yadav, N. P. Patidar, and J. Singhai
high order systems can be reduced in continuous as well as in
Abstract—One of the main objectives of order reduction is to discrete domain [3-5]. There are two approaches for the
design a controller of lower order which can effectively control the reduction of discrete system, namely the indirect method and
original high order system so that the overall system is of lower direct method. The indirect method uses some transformation
order and easy to understand. In this paper, a simple method is and then reduction is carried out in the transformed domain.
presented for controller design of a higher order discrete system. First the z- domain transfer functions are converted into
First the original higher order discrete system in reduced to a lower
s-domain by the bilinear transformation and then after
order model. Then a Proportional Integral Derivative (PID)
controller is designed for lower order model. An error minimization
reducing them in s-domain, suitably, they are converted back
technique is employed for both order reduction and controller into z-domain. In the direct method the higher order z-
design. For the error minimization purpose, Differential Evolution domain transfer functions are reduced to a lower order
(DE) optimization algorithm has been employed. DE method is transfer function in the same domain without any
based on the minimization of the Integral Squared Error (ISE) transformation [6].
between the desired response and actual response pertaining to a There are two common approaches for controller design.
unit step input. Finally the designed PID controller is connected to First approach is to obtain the controller on the basis of
the original higher order discrete system to get the desired reduced order model called process reduction [7]. In the
specification. The validity of the proposed method is illustrated second approach, the controller is designed for the original
through a numerical example.
higher order system and then the closed loop response of
higher order controller with original system is reduced
Keywords—Discrete System, Model Order Reduction, PID
pertaining to unity feedback called controller reduction [8].
Controller, Integral Squared Error, Differential Evolution.
Both the approaches have their own advantages and
disadvantages. The process reduction approach is
I. INTRODUCTION
computationally simpler as it deals with lower order models
T HE mathematical procedure of system modeling often
leads to detailed description of a process in the form of
high order differential equations. These equations in the
and controller but at the same time errors are introduced in
the design process as the reduction is carried out at the early
stages of design. In the controller reduction approach error
frequency domain lead to a high order transfer function. propagation is minimized as the design process is carried out
Therefore, it is desirable to reduce higher order transfer at the final stages of reduction but the approaches deals with
functions to lower order systems for analysis and design higher order models and thus introduces computational
purposes. Reduction of high order systems to lower order complexity.
models has also been an important subject area in control In recent years, one of the most promising research
engineering for many years [1,2]. One of the main objectives fields has been “Evolutionary Techniques”, an area utilizing
of order reduction is to design a controller of lower order analogies with nature or social systems. Evolutionary
which can effectively control the original high order system. techniques are finding popularity within research community
The conventional methods of reduction, developed so as design tools and problem solvers because of their
far, are mostly available in continuous domain. However, the versatility and ability to optimize in complex multimodal
search spaces applied to non-differentiable objective
functions. Differential evolution (DE) is a branch of
J. S. Yadav is working as an Associate Professor in Electronics and
Communication Engg. Department, MANIT Bhopal, India (e- evolutionary algorithms developed by Rainer Stron and
mail:jsy1@rediffmail.com). Kenneth Price in 1995 for optimization problems [9]. It is a
N. P. Patidar is working as an Associate professor in Electrical population-based direct search algorithm for global
Engineering Department, MANIT, Bhopal, India. (e-mail: optimization capable of handling non-differentiable, non-
nppatidar@yahoo.com)
J. Singhai is working as Associate Professor in Electronics and linear and multi-modal objective functions, with few, easily
Communication Engineering Department, MANIT Bhopal, India. chosen, control parameters. It has demonstrated its usefulness
( j_singhai@manit.ac.in) and robustness in a variety of applications such as, Neural
43
2. International Journal of Information and Mathematical Sciences 6:1 2010
network learning, Filter design and the optimization of The polynomial D(z ) is stable, that is all its zeros reside
aerodynamics shapes. DE differs from other evolutionary
algorithms (EA) in the mutation and recombination phases. inside the unit circle z =1. Where, a i ( 0 ≤ i ≤ n − 1 ) ,
DE uses weighted differences between solution vectors to b i ( 0 ≤ i ≤ n ) , c i ( 0 ≤ i ≤ r − 1) and d i ( 0 ≤ i ≤ r ) are
change the population whereas in other stochastic techniques scalar constants.
such as genetic algorithm (GA) and expert systems (ES), The numerator order is given as being one less than that of
perturbation occurs in accordance with a random quantity.
DE employs a greedy selection process with inherent elitist the denominator, as for the original system. The R (z )
features. Also it has a minimum number of EA control approximates G0 ( z ) in some sense and retains the important
parameters, which can be tuned effectively [10]. In view of
the above, this paper proposes to use DE optimization characteristics of G0 ( z ) and the transient responses of
technique for both model reduction and controller design. R(z ) should be as close as possible to that of G0 ( z ) for
In this paper, controller design of a higher order discrete
system is presented employing process reduction approach. similar inputs.
The original higher order discrete system in reduced to a B. Controller design
lower order model employing DE technique. DE technique is
All The proposed method of design of a controller by
based on the minimization of the Integral Squared Error
process reduction technique involves the following steps:
(ISE) between the transient responses of original higher order
Step-1
model and the reduced order model pertaining to a unit step
Reduce the given higher order discrete system to a lower
input. Then a Proportional Integral Derivative (PID)
order model by error minimization technique.
controller is designed for lower order model. The parameters
The objective function J is defined as an integral squared
of the PID controller are tuned by using the same error
error of difference between the responses given by the
minimization technique employing DE. The performance of
expression:
the designed PID controller is verified by connecting the t∞
designed PID controller with the original higher order J = ∫ [ y 0 (t ) − y r (t )]2 dt (3)
discrete system to get the desired specification. 0
Despite significant strides in the development of advanced
control schemes over the past two decades, the conventional
Where y 0 (t ) and y r (t ) are the unit step responses of
lead-lag (LL) structure controller as well as the classical original and reduced order systems.
proportional-integral-derivative (PID) controller and its Step-2
variants, remain the controllers of choice in many industrial Design a PID controller for the reduced order system.
applications. These controller structures remain an engineer’s The parameters of the PID controller are optimized using
preferred choice because of their structural simplicity, the same error same error minimization technique
employing DE.
reliability, and the favorable ratio between performance and
Step-3
cost. Beyond these benefits, these controllers also offer
Test the designed PID controller for the reduced order
simplified dynamic modeling, lower user-skill requirements,
model for which the PID controller has been designed.
and minimal development effort, which are issues of Step-4
substantial importance to engineering practice. Test the designed PID controller for the original higher
order model.
II. PROBLEM STATEMENT
III. PROPORTIONAL INTEGRAL DERIVATIVE (PID)
A. Model order reduction CONTROLLER
Please Given a high order discrete time stable system of PID controller is basic type of feedback controller. The
order ‘ n ’ that is described by the z -transfer function:
basic structure of conventional feedback control systems is
shown in Fig. 1, using a block diagram representation. In this
N (z) a 0 + a 1 z + ......... + a n −1 z n −1 (1) figure, the process is the object to be controlled. In this
GO ( z) = =
D ( z ) b 0 + b1 z + ......... + b n −1 z n −1 + b n z n figure, the object to be controlled is the process. To make the
process variable y follow the set-point value r is the main
The objective is to find a reduced r order model that objective of control. To achieve this purpose, the
th
has a transfer function ( r < n ): manipulated variable u is changed at the authority of the
controller. The “disturbance d” is any factor, other than the
N (z) c 0 + c 1 z + ......... + c r − 1 z r − 1 manipulated variable, that influences the process variable.
R(z) = r = Fig.1 assumes that only one disturbance is added to the
D r ( z ) d 0 + d 1 z + ......... + d r − 1 z r − 1 + d r z r
manipulated variable. In some applications, however, a major
(2) disturbance enters the process in a different way, or plural
44
3. International Journal of Information and Mathematical Sciences 6:1 2010
disturbances need to be considered. The error e is defined by the controller to an error, the degree to which the controller
e = r – y. overshoot signal overshoots the set point and the degree of
d system oscillation.
Some applications may require using only one or two
r + ∑ e C (s) u + ∑ y modes to provide the appropriate system control. This is
P(s )
_ + achieved by setting the gain of undesired control outputs to
zero. A PID controller will be called a PI, PD, P or I
Controller Process
controller in the absence of the respective control actions. PI
controllers are fairly common, since derivative action is
Fig. 1. Block diagram of basic feedback controller sensitive to measurement noise, whereas the absence of an
integral value may prevent the system from reaching its
PID control is the method of feedback control that uses target value due to the control action.
the PID controller as the main tool. PID controller is most In application, engineers have independence of
widely used in industrial control applications because of its implementing the three functional elements (P, I, and D) of
structural simplicity, reliability, and the favorable ratio the PID controller in whatsoever grouping they consider
between performance and cost. Beyond these benefits, these most suitable for their problems. The combination of
controllers also offer simplified dynamic modeling, lower element(s) used is called the action mode of the PID
user-skill requirements, and minimal development effort, controller. Tuning a control loop is the adjustment of its
which are issues of substantial importance to engineering control parameters (gain/proportional band, integral
practice. A PID controller calculates an error value as the gain/reset, derivative gain/rate) to the optimum values for the
difference between a measured process variable and a desired desired control response. Stability (bounded oscillation) is a
set point. The controller attempts to minimize the error by basic requirement, but beyond that, different systems have
adjusting the process control inputs. In the absence of different behavior, different applications have different
knowledge of the underlying process, PID controllers are the requirements, and some desiderata conflict. Further, some
best controllers. However, for best performance, the PID processes have a degree of non-linearity and so parameters
parameters used in the calculation must be according to the that work well at full-load conditions don't work when the
nature of the system – while the design is generic, the process is starting up from no-load; this can be corrected by
parameters depend on the specific system. The structure of a gain scheduling (using different parameters in different
PID controller is shown in Fig. 2. operating regions). PID controllers often provide acceptable
control even in the absence of tuning, but performance can
K P e(t ) generally be improved by careful tuning, and performance
P may be unacceptable with poor tuning.
Setpoint Error t + Output The analysis for designing a digital implementation of a
∑ K I ∫ e(t ) dt + ∑
Process
PID controller requires the standard form of the PID
+
_
I o +
D controller to be discretised. Approximations for first-order
de(t )
KD derivatives are made by backward finite differences. The
dt
integral term is discretised, with a sampling Δt time, as
follows:
Fig. 2. Structure of PID controller
t k
The PID controller involves three separate parameters,
and is accordingly sometimes called three-term control: the
∫ e(τ )dτ = ∑ e(ti )Δt
0 i =1
(4)
Proportionality, the integral and derivative values, denoted
by P, I, and D. The proportional value determines the The derivative term is approximated as,
reaction to the current error, the integral value determines the
reaction based on the sum of recent errors, and the derivative de(t k ) e(t k ) − e(t k −1 )
= (5)
d (t )
value determines the reaction based on the rate at which the
Δt
error has been changing. The weighted sum of these three
actions is used to adjust the process via a control element.
Heuristically, these values can be interpreted in terms of IV. DIFFERENTIAL EVOLUTION
time: P depends on the present error, I on the accumulation of Differential Evolution (DE) algorithm is a stochastic,
past errors, and D is a prediction of future errors, based on population-based optimization algorithm recently introduced
current rate of change. [9]. DE works with two populations; old generation and new
By tuning the three constants in the PID controller generation of the same population. The size of the population
algorithm, the controller can provide control action designed is adjusted by the parameter NP. The population consists of
for specific process requirements. The response of the real valued vectors with dimension D that equals the number
controller can be described in terms of the responsiveness of of design parameters/control variables. The population is
45
4. International Journal of Information and Mathematical Sciences 6:1 2010
randomly initialized within the initial parameter bounds. The C. Crossover
optimization process is conducted by means of three main Three parents are selected for crossover and the child is a
operations: mutation, crossover and selection. In each perturbation of one of them. The trial vector U i,G +1 is
generation, individuals of the current population become
developed from the elements of the target vector ( X i ,G ) and
target vectors. For each target vector, the mutation operation
produces a mutant vector, by adding the weighted difference the elements of the donor vector ( X i ,G ).Elements of the
between two randomly chosen vectors to a third vector. The donor vector enter the trial vector with probability CR as:
crossover operation generates a new vector, called trial
vector, by mixing the parameters of the mutant vector with ⎧V j , i , G +1 if rand j ,i ≤ CR or j = I rand
⎪
those of the target vector. If the trial vector obtains a better U j , i , G +1 = ⎨
⎪ X j , i , G +1 if rand j ,i > CR or j ≠ I rand
⎩
fitness value than the target vector, then the trial vector
replaces the target vector in the next generation. The (7)
evolutionary operators are described below [9, 10]. With rand j , i ~ U (0,1), Irand is a random integer from
(1,2,….D) where D is the solution’s dimension i.e number of
X r1,G control variables. Irand ensures that Vi , G +1 ≠ X i ,G .
Difference Vector
D. Selectionn
F . ( X r 2 ,G − X r 3 ,G )
The target vector X i ,G is compared with the trial vector
Vi , G +1 and the one with the better fitness value is admitted
Vi,G+1 = X r1,G + F. ( X r 2,G − X r3,G ) to the next generation. The selection operation in DE can be
represented by the following equation:
X r 2 ,G ⎧U i ,G +1 if f (U i ,G +1 ) < f ( X i ,G )
⎪ (8)
X i ,G +1 = ⎨
⎪ X i ,G
⎩ otherwise.
X r 2 , G − X r 3, G
where i ∈ [1, N P ] .
X r 3, G V. NUMERICAL EXAMPLE
Consider the transfer function of the plant from
Fig. 3 Vector addition and subtraction in differential evolution references [11, 12] as:
N (z)
G (z) = =
A. Initialization D(z)
For each parameter j with lower bound X L and upper ( 0 .1625 z 7 + 0 .125 z 6 − 0 .0025 z 5 + 0 .00525 z 4 −
j
0 .02263 z 3 − 0 .00088 z 2 + 0 .003 z − 0.000413 )
bound X U , initial parameter values are usually randomly
j ( z 8 − 0 .6307 z 7 − 0 .4185 z 6 + 0 .078 z 5 − 0.057 z 4 −
selected uniformly in the interval [ X L , X U ].
j j 0 .1935 z 3 + 0 .09825 z 2 − 0 .0165 z + 0 .00225 )
(9)
B. Mutation For which a controller is to be designed to get the desired
output.
For a given parameter vector X i ,G , three vectors
A. Application of DE for Model Order Reduction
( X r1,G X r 2,G X r 3,G ) are randomly selected such that To reduce the higher order model in to a lower order
the indices i, r1, r2 and r3 are distinct. A donor vector model DE is employed. The objective function J defined as
Vi ,G +1 is created by adding the weighted difference an integral squaredequation difference between the responses
given by the
error of
(3) is minimized by DE.
between the two vectors to the third vector as: Implementation of DE requires the determination of six
fundamental issues: DE step size function, crossover
Vi,G +1 = X r1,G + F .( X r 2,G − X r 3,G ) (6) probability, the number of population, initialization,
termination and evaluation function. Generally DE step size
Where F is a constant from (0, 2). (F) varies in the interval (0, 2). A good initial guess to F is in
the interval (0.5, 1). Crossover probability (CR) constants are
generally chosen from the interval (0.5, 1). If the parameter is
co-related, then high value of CR work better, the reverse is
46
5. International Journal of Information and Mathematical Sciences 6:1 2010
true for no correlation [10]. In the present study, a population 0.004821z − 0.002508
size of NP=20, generation number G=200, step size F=0.8 R2 ( z ) = (15)
and crossover probability of CR =0.8 have been used. 0.030465 z 2 − 0.053953 z + 0.025634
Optimization is terminated by the pre-specified number of
generations for DE. One more important factor that affects The unit step responses of original and reduced systems are
the optimal solution more or less is the range for unknowns. shown in Fig. 6. It can be seen that the steady state responses
For the very first execution of the program, a wider solution of proposed reduced order models is exactly matching with
space can be given and after getting the solution one can that of the original model. Also, the transient response of
shorten the solution space nearer to the values obtained in the proposed reduced model by DE is very close to that of
previous iteration. The flow chart of the DE algorithm original model. It can be seen from Fig. 6 that both the
employed in the present study is given in Fig. 4. One more original model and the reduced model settle at a value of 1.07
important point that affects the optimal solution more or less for a input of 1.0 (unit step input). Now, to get the desired
is the range for unknowns. For the very first execution of the out put i.e. 1.0, a PID controller is designed.
program, more wide solution space can be given and after
getting the solution one can shorten the solution space nearer
to the values obtained in the previous iteration. Optimization 12
was performed with the total number of generations set to
100. Simulations were conducted on a Pentium 4, 3 GHz, 10
504 MB RAM computer, in the MATLAB 7.0.1
environment. A typical convergence
8
I S E E rro r
6
Start
4
Specify the DE parameters
Initialize the population
2
Gen.=1
Evalute the population 0
0 10 20 30 40 50 60 70 80 90 100
Generation
Create offsprings and evalute their fitness
Fig. 5. Convergence of fitness function
No
Is fitness of offspring better than B. Application of DE for PID Controller Design
fitness of parents ?
Discard the
In this study, the PID controller has been designed
Yes
offspring in employing process reduction approach. The original higher
Replace the parents by offsprings new population order discrete system given by equation (14) is reduced to a
in the new population
lower order model employing DE technique given by
equation (15). Then the PID controller is designed for lower
Yes order model. The parameters of the PID controller are tuned
Size of new population <
Old population ? by using the same error minimization technique employing
Gen. = Gen+1
No
DE as explained in section 5.1. The optimized PID controller
parameters are:
No
Gen. > Max. Gen ?
K P = 6.7105 , K I = 14.9726 , K D = 0.5089
Yes
Stop
The unit step response of the reduced system with DE
optimized PID controller and original system with DE
Fig. 4 Flow chart of proposed DE optimization approach
optimized PID controller are shown in Fig. 7 and 8. It is clear
from Fig. 8 that the design of PID controller using the
of objective function with the number of generation is shown
proposed DE optimization technique helps to obtain the
in Fig.5. The optimization processes is run 20 times and best
designer’s specifications in transient as well as in steady state
among the 20 runs are taken as the final result.
nd responses for the original system.
The reduced 2 order model employing DE technique is
obtained as given in equation (15):
47
6. International Journal of Information and Mathematical Sciences 6:1 2010
1.6
1.4
1.2
1
Amplitude
0.8
0.6
0.4
0.2 Original 8th order discrete model
Reduced 2nd order discrete model by DE
0
0 10 20 30 40 50 60 70 80 90 100
Time in sec
Fig. 6. Step Responses of original system and reduced model
1.5
1
Amplitude
0.5
Reduced 2nd order model without PID controller
Reduced 2nd order model with PID controller
0
0 10 20 30 40 50 60 70 80 90 100
Time in sec
Fig. 7. Step response of reduced model with PID Controller
1.5
1
Amplitude
0.5
Original 8th order model without PID controller
Original 8th order model with PID controller
0
0 10 20 30 40 50 60 70 80 90 100
Time in sec
Fig. 8. Step response of original model with PID Controller
48
7. International Journal of Information and Mathematical Sciences 6:1 2010
[6] J.S. Yadav, N.P. Patidar and J. Singhai, S. Panda, “Differential Evolution
VI. CONCLUSION Algorithm for Model Reduction of SISO Discrete Systems”, Proceedings
of World Congress on Nature & Biologically Inspired Computing
The proposed model reduction method uses the modern (NaBIC 2009) 2009, pp. 1053-1058.
heuristic optimization technique in its procedure to derive the [7] D.A. Wilson and R.N. Mishra, “Design of low order estimators using
stable reduced order model for the discrete system. The reduced models”, Int. J. Control, Vol. 29, pp. 267-278, 1979.
algorithm has also been extended to the design of controller for [8] J.A. Davis and R.E. Skelton, “Another balanced controller reduction
algorithm” Systems and Controller Letters, Vol. 4, pp. 79-83, 1884.
the original discrete system. The algorithm is simple to [9] R Stron. And K. Price, “Differential Evolution – A simple and efficient
implement and computer oriented. The matching of the step adaptive scheme for Global Optimization over continuous spaces, Journal
response is assured reasonably well in this proposed method. of Global Optimization, Vol. 11, pp. 341-359, 1995.
Algorithm preserves more stability and avoids any error [10] Sidhartha Panda, “Differential Evolutionary Algorithm for TCSC-based
Controller Design”, Simulation Modelling Practice and Theory, Vol. 17,
between the initial or final values of the responses of original
pp. 1618-1634, 2009.
and reduced model. This approach minimizes the complexity [11] S. Mukhrjee and R.N. Mishra, “Optimal order reduction of discrete
involved in direct design of PID Controller. The values for systems”, Journal of Institution of Engineers, Vol. 68, pp. 142-149, 1988.
PID Controller are optimized using the reduced model and to [12] K. Ramesh, A. Nirmalkumar and G. Gurusamy, “Design of discrete
meet the required performance specifications. The tuned controller via a novel model order reduction technique”, International
Journal of Electrical Power and Engineering, Vol. 3, pp. 163-168, 2009.
values of the PID controller parameters are tested with the
original system and its closed loop response for a unit step
input is found to be satisfactory with the response of reduced J S Yadav is working as Associate Professor in Electronics and
order model. Communication Engineering Department, MANIT, Bhopal, India. He received
the B.Tech.degree from GEC Jabalpur in Electronics and Communication
Engineering in 1995 and M.Tech. degree from MANIT, Bhopal in Digital
Communication in 2002. Presently he is persuing Ph.D. His area of interest
REFERENCES includes Optimization techniques, Model Order Reduction, Digital
Communication, Signal and System and Control System.
[1] J. S. Yadav, N. P. Patidar, J. Singhai, S. Panda, and C. Ardil “A
Combined Conventional and Differential Evolution Method for Model Narayana Prasad Patidar is working as Associate Professor in Electrical
Order Reduction”, International Journal of Computational Intelligence, Engineering Department, MANIT, Bhopal, India. He received his PhD. degree
Vol. 5, No. 2, pp. 111-118, 2009. from Indian Institute of Technology, Roorkee, in 2008, M.Tech. degree from
[2] S. Panda, J. S. Yadav, N. P. Patidar and C. Ardil, “Evolutionary Visvesvaraya National Institute of Technology Nagpur in Integrated Power
Techniques for Model Order Reduction of Large Scale Linear Systems”, System in 1995 and B.Tech. degree from SGSITS Indore in Electrical
International Journal of Applied Science, Engineering and Technology, Engineering in 1993. His area of research includes voltage stability, security
Vol. 5, No. 1, pp. 22-28, 2009. analysis, power system stability and intelligent techniques. Optimization
[3] Y. Shamash, “Continued fraction methods for the reduction of discrete techniques, Model Order Reduction, and Control System.
time dynamic systems”, Int. Journal of Control, Vol. 20, pages 267-268,
1974. Jyoti Singhai is working as Associate Professor in Electronics and
[4] C.P. Therapos, “A direct method for model reduction of discrete system”, Communication Engineering Department, MANIT Bhopal, India. She received
Journal of Franklin Institute, Vol. 318, pp. 243-251, 1984. the PhD. degree from MANIT Bhopal in 2005, M.Tech. degree from MANIT,
[5] J.P. Tiwari, and S.K. Bhagat, “Simplification of discrete time systems by Bhopal in Digital Communication in 1997 and B.Tech. degree from MANIT
improved Routh stability criterion via p-domain”, Journal of IE (India), Bhopal in Electronics and Communication Engineering in 1991. Her area of
Vol. 85, pp. 89-192, 2004. research includes Optimization techniques, Model Order Reduction, Digital
Communication, Signal and System and Control System.
49