Introductory course on concepts used in predictive control. For more files and MATLAB suporting information go to:
http://controleducation.group.shef.ac.uk/OER_index.htm
This document discusses predictive control, which is a widely used control technique in industry. Predictive control involves using predictions of how a system will behave in the future to determine the best control actions. The key points are:
1. Predictive control is a general approach rather than a specific algorithm, allowing users flexibility to design algorithms for their needs.
2. It is more important for students to understand the concepts behind predictive control, such as how uncertainty is handled, rather than specific algorithm details.
3. Predictive control is logical because humans intuitively use predictions to determine control strategies, such as when driving a car or playing racquet sports. Anticipating the future impacts of different actions allows choosing strategies that
This document provides information about the ME 190M Introduction to Model Predictive Control course taught in fall 2009 at UC Berkeley. The class will be taught on Fridays from 11am to 12pm in room 1165 of Etcheverry Hall. Homework assignments will be given weekly and selected assignments will be graded. Students will need to use MATLAB for assignments, which they can access in room 2109 of Etcheverry Hall. The course will cover modeling, optimization fundamentals, constrained optimal control, predictive control fundamentals and properties, and examples implemented in MATLAB. The goals are for students to design, implement, and tune simple MPC controllers in MATLAB for linear and nonlinear systems.
Model Predictive Control Implementation with LabVIEWyurongwang1
This presentation was presented at National Instruments NIWeek 2007 to demonstrate how to use LabVIEW to implement model predictive control (MPC) strategies to control complicated coax manufacturing processes. Both MatLAB MPC and LabVIEW MPC were implemented in these applications.
Application of a merit function based interior point method to linear model p...Zac Darcy
This paper present
s
robust linear model predictive control (MPC) technique for small scale linear MPC
problems. The quadratic programming (QP) problem arising in linear MPC is solved using primal dual
interior point method
.
We present
a me
rit function based on a path following strategy
to calculate the step
length
α
, which
forces the convergence of feasible iterates
. The algorithm globally converges to the optimal
solution
of the QP p
roblem while strictly following
the
inequality
constraint
s.
The linear system in the QP
problem is solved using LDL
T
factorizatio
n based linear solver which reduces the computational cost of
linear system to a certain extent
.
We implement this method for
a
linear MPC problem of undamped
oscillator. With the help
of a Kalman filter observer, we show that the MPC design is robust to the external
disturbances and integrated white noise.
Design & Analysis of Algorithms Lecture NotesFellowBuddy.com
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
Dynamic Matrix Control (DMC) on jacket tank heater - Rishikesh BagweRishikesh Bagwe
The Dynamic Matrix Control (DMC) method of Model Predictive Control was simulated in MATLAB on Jacketed Tank Heater. The characteristics of the liquid being controlled are height and temperature
This document outlines the course content and structure for a class on Fundamentals of Algorithms. It includes:
1. The prerequisites for the class which include programming experience and familiarity with data structures.
2. An overview of the purpose and evaluation scheme for the class, which focuses on analyzing and designing algorithms rather than programming. Student work will be evaluated through tests, assignments, and other activities.
3. A list of topics to be covered including analysis of algorithms, data structures like trees and graphs, sorting techniques, and others. Reference books are also provided.
This document provides an introduction to algorithms and algorithm analysis. It defines an algorithm as a set of unambiguous instructions to solve a problem in a finite amount of time. The most famous early algorithm is Euclid's algorithm for calculating greatest common divisors. Algorithm analysis involves proving an algorithm's correctness and analyzing its running time and space complexity. Common notations for analyzing complexity include Big-O, which provides upper bounds, Big-Omega, which provides lower bounds, and Big-Theta, which provides tight bounds. The goal of analysis is to determine the most efficient algorithm by evaluating performance as problem size increases.
This document discusses predictive control, which is a widely used control technique in industry. Predictive control involves using predictions of how a system will behave in the future to determine the best control actions. The key points are:
1. Predictive control is a general approach rather than a specific algorithm, allowing users flexibility to design algorithms for their needs.
2. It is more important for students to understand the concepts behind predictive control, such as how uncertainty is handled, rather than specific algorithm details.
3. Predictive control is logical because humans intuitively use predictions to determine control strategies, such as when driving a car or playing racquet sports. Anticipating the future impacts of different actions allows choosing strategies that
This document provides information about the ME 190M Introduction to Model Predictive Control course taught in fall 2009 at UC Berkeley. The class will be taught on Fridays from 11am to 12pm in room 1165 of Etcheverry Hall. Homework assignments will be given weekly and selected assignments will be graded. Students will need to use MATLAB for assignments, which they can access in room 2109 of Etcheverry Hall. The course will cover modeling, optimization fundamentals, constrained optimal control, predictive control fundamentals and properties, and examples implemented in MATLAB. The goals are for students to design, implement, and tune simple MPC controllers in MATLAB for linear and nonlinear systems.
Model Predictive Control Implementation with LabVIEWyurongwang1
This presentation was presented at National Instruments NIWeek 2007 to demonstrate how to use LabVIEW to implement model predictive control (MPC) strategies to control complicated coax manufacturing processes. Both MatLAB MPC and LabVIEW MPC were implemented in these applications.
Application of a merit function based interior point method to linear model p...Zac Darcy
This paper present
s
robust linear model predictive control (MPC) technique for small scale linear MPC
problems. The quadratic programming (QP) problem arising in linear MPC is solved using primal dual
interior point method
.
We present
a me
rit function based on a path following strategy
to calculate the step
length
α
, which
forces the convergence of feasible iterates
. The algorithm globally converges to the optimal
solution
of the QP p
roblem while strictly following
the
inequality
constraint
s.
The linear system in the QP
problem is solved using LDL
T
factorizatio
n based linear solver which reduces the computational cost of
linear system to a certain extent
.
We implement this method for
a
linear MPC problem of undamped
oscillator. With the help
of a Kalman filter observer, we show that the MPC design is robust to the external
disturbances and integrated white noise.
Design & Analysis of Algorithms Lecture NotesFellowBuddy.com
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
Dynamic Matrix Control (DMC) on jacket tank heater - Rishikesh BagweRishikesh Bagwe
The Dynamic Matrix Control (DMC) method of Model Predictive Control was simulated in MATLAB on Jacketed Tank Heater. The characteristics of the liquid being controlled are height and temperature
This document outlines the course content and structure for a class on Fundamentals of Algorithms. It includes:
1. The prerequisites for the class which include programming experience and familiarity with data structures.
2. An overview of the purpose and evaluation scheme for the class, which focuses on analyzing and designing algorithms rather than programming. Student work will be evaluated through tests, assignments, and other activities.
3. A list of topics to be covered including analysis of algorithms, data structures like trees and graphs, sorting techniques, and others. Reference books are also provided.
This document provides an introduction to algorithms and algorithm analysis. It defines an algorithm as a set of unambiguous instructions to solve a problem in a finite amount of time. The most famous early algorithm is Euclid's algorithm for calculating greatest common divisors. Algorithm analysis involves proving an algorithm's correctness and analyzing its running time and space complexity. Common notations for analyzing complexity include Big-O, which provides upper bounds, Big-Omega, which provides lower bounds, and Big-Theta, which provides tight bounds. The goal of analysis is to determine the most efficient algorithm by evaluating performance as problem size increases.
This document summarizes a presentation on introducing algorithms and analyzing their performance. It defines an algorithm as a step-by-step procedure to solve a problem and transform inputs to outputs. There are two ways to analyze performance: space complexity and time complexity. Time complexity depends on the input size and running time of the algorithm. An example compares two algorithms for finding the maximum number in an array: one sorts the array in O(n^2) time while the other compares each element to the first in O(n) time. The conclusion states that analyzing an algorithm's resource usage is more important than just designing it.
This document discusses data structures and algorithms. It defines data structures as how data is organized in memory and algorithms as computational steps to solve problems. The first step to solve a problem is obtaining an abstract model by defining relevant entities and operations. Data structures model static data and algorithms model dynamic changes to data. Properties of good algorithms include being finite, definite, feasible, correct, and efficient. Analyzing algorithms involves determining their time and space complexity using theoretical and empirical methods. Complexity is classified based on how resource needs grow relative to problem size.
Synthesis of analytical methods data driven decision-makingAdam Doyle
This document summarizes Dr. Haitao Li's presentation on synthesizing analytical methods for data-driven decision making. It discusses the three pillars of analytics - descriptive, predictive, and prescriptive. Various data-driven decision support paradigms are presented, including using descriptive/predictive analytics to determine optimization model inputs, sensitivity analysis, integrated simulation-optimization, and stochastic programming. An application example of a project scheduling and resource allocation tool for complex construction projects is provided, with details on its optimization model and software architecture.
This document discusses fundamentals of algorithms including:
- What algorithms are and their evolution from Persian mathematicians.
- The process of designing algorithms including defining inputs, outputs, and order of instructions.
- The need for algorithms to be correct according to their specifications and methods for confirming correctness.
- Iterative design issues such as use of loops, efficiency considerations, and estimating execution time.
- Algorithmic strategies like divide and conquer, backtracking, dynamic programming, and heuristics.
This document provides an introduction to algorithms and their design and analysis. It discusses what algorithms are, their key characteristics, and the steps to develop an algorithm to solve a problem. These steps include defining the problem, developing a model, specifying and designing the algorithm, checking correctness, analyzing efficiency, implementing, testing, and documenting. Common algorithm design techniques like top-down design and recursion are explained. Factors that impact algorithm efficiency like use of loops, initial conditions, invariants, and termination conditions are covered. Finally, common control structures for algorithms like if/else, loops, and branching are defined.
The document discusses the topic of designing and analyzing algorithms. It states that algorithm design and analysis is an important topic that is frequently covered in exams. It defines an algorithm as a set of unambiguous instructions that takes inputs and produces outputs within a finite amount of time. The key aspects of designing an algorithm are understanding the problem, choosing a data structure and strategy, specifying and verifying the algorithm, analyzing its efficiency, and implementing it in a programming language. Algorithm analysis involves measuring the time and space complexity.
This document outlines the requirements for the capstone term project in ME 3012 Systems Analysis & Control. Students will work individually or in pairs to design a feedback controller to improve the performance of a real-world system. They must choose a system, perform open-loop modeling and analysis, design at least three feedback controllers, compare closed-loop performance, and present results. An interim status report is due on February 23rd and the final written report and oral presentation are due on April 14th. The project aims to provide hands-on experience with feedback controller design for real-world applications.
The document discusses randomized algorithms. Randomized algorithms employ randomness as part of their logic, using random bits to guide their behavior. This allows them to achieve good average performance over many trials. The output or running time of a randomized algorithm is a random variable. Advantages include simplicity, efficiency through testing many possibilities, and better complexity bounds than deterministic algorithms. Disadvantages include potential for hardware failures from long runtimes, high memory usage for repeated processes, and longer runtimes as operations split into many parts.
Fpga implementation of optimal step size nlms algorithm and its performance a...eSAT Publishing House
This document discusses the implementation of an optimal step size normalized least mean square (NLMS) adaptive filtering algorithm on an FPGA. It begins with background on LMS and NLMS algorithms. It then derives the optimal step size NLMS algorithm and discusses its theoretical performance advantages over fixed step size LMS. The paper presents the FPGA implementation of the optimal step size NLMS algorithm for audio noise cancellation. Simulation results show the proposed algorithm has faster convergence, lower error rates, and superior noise cancellation performance compared to LMS and variable step size LMS algorithms. Area utilization and maximum operating frequency are also compared for the different implementations on an Altera Cyclone III FPGA.
Fpga implementation of optimal step size nlms algorithm and its performance a...eSAT Journals
Abstract The Normalized Least Mean Square error (NLMS) algorithm is most popular due to its simplicity. The conflicts of fast convergence and low excess mean square error associated with a fixed step size NLMS are solved by using an optimal step size NLMS algorithm. The main objective of this paper is to derive a new nonparametric algorithm to control the step size and also the theoretical performance analysis of the steady state behavior is presented in the paper. The simulation experiments are performed in Matlab. The simulation results show that the proposed algorithm as superior performance in Fast convergence rate, low error rate, and has superior performance in noise cancellation. Index Terms: Least Mean square algorithm (LMS), Normalized least mean square algorithm (NLMS)
On the Performance of the Pareto Set Pursuing (PSP) Method for Mixed-Variable...Amir Ziai
This document describes a study on modifying the Pareto Set Pursuing (PSP) method to solve multi-objective optimization problems with mixed continuous and discrete variables. The PSP method was originally developed for problems with only continuous variables. The modifications allow it to handle mixed variable problems. The performance of the modified PSP method is compared to other multi-objective algorithms based on metrics like efficiency, robustness, and closeness to the true Pareto front with a limited number of function evaluations. Preliminary results on benchmark problems and two engineering design examples show that the modified PSP is competitive when the number of function evaluations is limited, but its performance decreases as the number of design variables increases.
This document discusses algorithm design and provides information on various algorithm design techniques. It begins with definitions of an algorithm and algorithm design. It then discusses the importance of algorithm design and some common algorithm design techniques including dynamic programming, graph algorithms, divide and conquer, backtracking, greedy algorithms, and using flowcharts. It also provides brief descriptions and examples of each technique. The document concludes by listing some advantages of designing algorithms such as ease of use, performance, scalability, and stability.
This document provides an overview of the randomized algorithms course. It defines randomized algorithms as algorithms whose output or running time depends on both the input and random bits chosen. Two types are described: Las Vegas algorithms always produce the correct output but have random running time, and Monte Carlo algorithms may produce incorrect output with some probability but have deterministic running time. Randomized algorithms are often simpler and more efficient than deterministic ones. Examples of problems solved more easily with randomized algorithms include sorting, finding the smallest enclosing circle, computing minimum cuts, and primality testing. The course will cover programming assignments, midterm and final exams, with passing criteria outlined. Office hours and contact details are provided.
This document discusses different types of randomized algorithms. It begins by defining randomized algorithms as algorithms that can access random bits during execution. It then discusses reasons for using randomized algorithms, including simplicity and speed advantages over deterministic algorithms. It describes Las Vegas algorithms as randomized algorithms that always produce the correct output or indicate failure. As an example, it summarizes the randomized quicksort algorithm and how it makes random choices during partitioning. It also briefly discusses Monte Carlo algorithms that can produce incorrect outputs with bounded error probabilities for decision problems. Finally, it provides an overview of the min-cut algorithm for finding the minimum cut in a graph by randomly contracting edges.
MiL Testing of Highly Configurable Continuous ControllersLionel Briand
This document describes research on model-in-the-loop (MiL) testing of highly configurable continuous controllers. The researchers developed an approach using dimensionality reduction, surrogate modeling, and search-based techniques to efficiently test controllers across large configuration spaces. They applied their approach to an industrial conveyor belt controller case study. Evaluation results showed that their technique could find stability, smoothness, and responsiveness violations that previous approaches had missed. It provided a scalable way to thoroughly test continuous controller models over varied parameter configurations.
This document discusses the process of algorithm design and analysis. It outlines 9 key techniques for solving problems algorithmically: 1) Understanding the problem, 2) Ascertaining computational capabilities, 3) Determining exact or approximate solutions, 4) Choosing appropriate data structures, 5) Using algorithm design techniques, 6) Specifying the algorithm, 7) Proving correctness, 8) Analyzing efficiency, and 9) Coding the algorithm. These techniques provide a systematic approach to developing procedural solutions to problems through specific instructions to obtain answers.
The document discusses clock-driven scheduling for real-time systems. It covers key concepts like static schedules, cyclic executives, frame size constraints, job slicing, and algorithms for constructing static schedules. Notations are introduced to represent periodic tasks, and assumptions made for clock-driven scheduling are explained. Methods to improve the average response time of aperiodic jobs through slack stealing are also summarized.
This document introduces algorithms and their characteristics. It discusses the two phases of programming as problem solving and implementation. It covers understanding the problem, designing the algorithm, proving correctness, analyzing complexity, and coding the algorithm. Common algorithm design techniques like divide-and-conquer, greedy methods, and dynamic programming are presented. The document also discusses representing algorithms in pseudocode and natural language, and analyzing worst-case, average-case, and best-case complexity.
This presentation discusses code optimization and performance tuning. It covers identifying time and space complexity of algorithms, examining programming constructs like loops and functions, and using performance libraries. Some key points include defining time complexity as the time taken by algorithm steps, optimizing loops by techniques like unrolling and reducing work inside loops, and the advantages of using pre-existing performance libraries like reducing errors and development time.
The document presents a methodology for modeling and compensating for friction in motion control systems using support vector regression (SVR). It discusses how friction is a nonlinear phenomenon that affects precision in motion control. It then describes developing an SVR model to identify and compensate for friction without requiring an explicit parametric friction model. The SVR model was able to significantly reduce position error in point-to-point and tracking motion control tests compared to not having compensation.
4 modeling and control of distillation column in a petroleum processnazir1988
This document describes the modeling and simulation of a condensate distillation column in a petroleum process. It presents a calculation procedure to model the column based on an energy balance structure using reflux rate and boilup rate as inputs to control distillate purity and bottom product impurity. A nonlinear dynamic model of the column is developed and simulated in MATLAB. The simulation shows the column can maintain product quality under normal operations but quality decreases with disturbances like changes in feed rate. A reduced-order linear model is then developed for use in model-reference adaptive control to improve disturbance rejection.
Smart Process Distillation Application Improves Recovery And Saves EnergyJim Cahill
The document summarizes a case study where a SmartProcess Distillation Optimizer was implemented on a large purification distillation column. The optimizer improved recovery and reduced energy usage. It immediately started reducing distillate rate and product losses by 22% while maintaining purity specifications. Steam usage was reduced by an average of 7%, resulting in estimated annual savings of over $700k. The project was completed in two weeks following a functional design study, demonstrating excellent payback.
This document summarizes a presentation on introducing algorithms and analyzing their performance. It defines an algorithm as a step-by-step procedure to solve a problem and transform inputs to outputs. There are two ways to analyze performance: space complexity and time complexity. Time complexity depends on the input size and running time of the algorithm. An example compares two algorithms for finding the maximum number in an array: one sorts the array in O(n^2) time while the other compares each element to the first in O(n) time. The conclusion states that analyzing an algorithm's resource usage is more important than just designing it.
This document discusses data structures and algorithms. It defines data structures as how data is organized in memory and algorithms as computational steps to solve problems. The first step to solve a problem is obtaining an abstract model by defining relevant entities and operations. Data structures model static data and algorithms model dynamic changes to data. Properties of good algorithms include being finite, definite, feasible, correct, and efficient. Analyzing algorithms involves determining their time and space complexity using theoretical and empirical methods. Complexity is classified based on how resource needs grow relative to problem size.
Synthesis of analytical methods data driven decision-makingAdam Doyle
This document summarizes Dr. Haitao Li's presentation on synthesizing analytical methods for data-driven decision making. It discusses the three pillars of analytics - descriptive, predictive, and prescriptive. Various data-driven decision support paradigms are presented, including using descriptive/predictive analytics to determine optimization model inputs, sensitivity analysis, integrated simulation-optimization, and stochastic programming. An application example of a project scheduling and resource allocation tool for complex construction projects is provided, with details on its optimization model and software architecture.
This document discusses fundamentals of algorithms including:
- What algorithms are and their evolution from Persian mathematicians.
- The process of designing algorithms including defining inputs, outputs, and order of instructions.
- The need for algorithms to be correct according to their specifications and methods for confirming correctness.
- Iterative design issues such as use of loops, efficiency considerations, and estimating execution time.
- Algorithmic strategies like divide and conquer, backtracking, dynamic programming, and heuristics.
This document provides an introduction to algorithms and their design and analysis. It discusses what algorithms are, their key characteristics, and the steps to develop an algorithm to solve a problem. These steps include defining the problem, developing a model, specifying and designing the algorithm, checking correctness, analyzing efficiency, implementing, testing, and documenting. Common algorithm design techniques like top-down design and recursion are explained. Factors that impact algorithm efficiency like use of loops, initial conditions, invariants, and termination conditions are covered. Finally, common control structures for algorithms like if/else, loops, and branching are defined.
The document discusses the topic of designing and analyzing algorithms. It states that algorithm design and analysis is an important topic that is frequently covered in exams. It defines an algorithm as a set of unambiguous instructions that takes inputs and produces outputs within a finite amount of time. The key aspects of designing an algorithm are understanding the problem, choosing a data structure and strategy, specifying and verifying the algorithm, analyzing its efficiency, and implementing it in a programming language. Algorithm analysis involves measuring the time and space complexity.
This document outlines the requirements for the capstone term project in ME 3012 Systems Analysis & Control. Students will work individually or in pairs to design a feedback controller to improve the performance of a real-world system. They must choose a system, perform open-loop modeling and analysis, design at least three feedback controllers, compare closed-loop performance, and present results. An interim status report is due on February 23rd and the final written report and oral presentation are due on April 14th. The project aims to provide hands-on experience with feedback controller design for real-world applications.
The document discusses randomized algorithms. Randomized algorithms employ randomness as part of their logic, using random bits to guide their behavior. This allows them to achieve good average performance over many trials. The output or running time of a randomized algorithm is a random variable. Advantages include simplicity, efficiency through testing many possibilities, and better complexity bounds than deterministic algorithms. Disadvantages include potential for hardware failures from long runtimes, high memory usage for repeated processes, and longer runtimes as operations split into many parts.
Fpga implementation of optimal step size nlms algorithm and its performance a...eSAT Publishing House
This document discusses the implementation of an optimal step size normalized least mean square (NLMS) adaptive filtering algorithm on an FPGA. It begins with background on LMS and NLMS algorithms. It then derives the optimal step size NLMS algorithm and discusses its theoretical performance advantages over fixed step size LMS. The paper presents the FPGA implementation of the optimal step size NLMS algorithm for audio noise cancellation. Simulation results show the proposed algorithm has faster convergence, lower error rates, and superior noise cancellation performance compared to LMS and variable step size LMS algorithms. Area utilization and maximum operating frequency are also compared for the different implementations on an Altera Cyclone III FPGA.
Fpga implementation of optimal step size nlms algorithm and its performance a...eSAT Journals
Abstract The Normalized Least Mean Square error (NLMS) algorithm is most popular due to its simplicity. The conflicts of fast convergence and low excess mean square error associated with a fixed step size NLMS are solved by using an optimal step size NLMS algorithm. The main objective of this paper is to derive a new nonparametric algorithm to control the step size and also the theoretical performance analysis of the steady state behavior is presented in the paper. The simulation experiments are performed in Matlab. The simulation results show that the proposed algorithm as superior performance in Fast convergence rate, low error rate, and has superior performance in noise cancellation. Index Terms: Least Mean square algorithm (LMS), Normalized least mean square algorithm (NLMS)
On the Performance of the Pareto Set Pursuing (PSP) Method for Mixed-Variable...Amir Ziai
This document describes a study on modifying the Pareto Set Pursuing (PSP) method to solve multi-objective optimization problems with mixed continuous and discrete variables. The PSP method was originally developed for problems with only continuous variables. The modifications allow it to handle mixed variable problems. The performance of the modified PSP method is compared to other multi-objective algorithms based on metrics like efficiency, robustness, and closeness to the true Pareto front with a limited number of function evaluations. Preliminary results on benchmark problems and two engineering design examples show that the modified PSP is competitive when the number of function evaluations is limited, but its performance decreases as the number of design variables increases.
This document discusses algorithm design and provides information on various algorithm design techniques. It begins with definitions of an algorithm and algorithm design. It then discusses the importance of algorithm design and some common algorithm design techniques including dynamic programming, graph algorithms, divide and conquer, backtracking, greedy algorithms, and using flowcharts. It also provides brief descriptions and examples of each technique. The document concludes by listing some advantages of designing algorithms such as ease of use, performance, scalability, and stability.
This document provides an overview of the randomized algorithms course. It defines randomized algorithms as algorithms whose output or running time depends on both the input and random bits chosen. Two types are described: Las Vegas algorithms always produce the correct output but have random running time, and Monte Carlo algorithms may produce incorrect output with some probability but have deterministic running time. Randomized algorithms are often simpler and more efficient than deterministic ones. Examples of problems solved more easily with randomized algorithms include sorting, finding the smallest enclosing circle, computing minimum cuts, and primality testing. The course will cover programming assignments, midterm and final exams, with passing criteria outlined. Office hours and contact details are provided.
This document discusses different types of randomized algorithms. It begins by defining randomized algorithms as algorithms that can access random bits during execution. It then discusses reasons for using randomized algorithms, including simplicity and speed advantages over deterministic algorithms. It describes Las Vegas algorithms as randomized algorithms that always produce the correct output or indicate failure. As an example, it summarizes the randomized quicksort algorithm and how it makes random choices during partitioning. It also briefly discusses Monte Carlo algorithms that can produce incorrect outputs with bounded error probabilities for decision problems. Finally, it provides an overview of the min-cut algorithm for finding the minimum cut in a graph by randomly contracting edges.
MiL Testing of Highly Configurable Continuous ControllersLionel Briand
This document describes research on model-in-the-loop (MiL) testing of highly configurable continuous controllers. The researchers developed an approach using dimensionality reduction, surrogate modeling, and search-based techniques to efficiently test controllers across large configuration spaces. They applied their approach to an industrial conveyor belt controller case study. Evaluation results showed that their technique could find stability, smoothness, and responsiveness violations that previous approaches had missed. It provided a scalable way to thoroughly test continuous controller models over varied parameter configurations.
This document discusses the process of algorithm design and analysis. It outlines 9 key techniques for solving problems algorithmically: 1) Understanding the problem, 2) Ascertaining computational capabilities, 3) Determining exact or approximate solutions, 4) Choosing appropriate data structures, 5) Using algorithm design techniques, 6) Specifying the algorithm, 7) Proving correctness, 8) Analyzing efficiency, and 9) Coding the algorithm. These techniques provide a systematic approach to developing procedural solutions to problems through specific instructions to obtain answers.
The document discusses clock-driven scheduling for real-time systems. It covers key concepts like static schedules, cyclic executives, frame size constraints, job slicing, and algorithms for constructing static schedules. Notations are introduced to represent periodic tasks, and assumptions made for clock-driven scheduling are explained. Methods to improve the average response time of aperiodic jobs through slack stealing are also summarized.
This document introduces algorithms and their characteristics. It discusses the two phases of programming as problem solving and implementation. It covers understanding the problem, designing the algorithm, proving correctness, analyzing complexity, and coding the algorithm. Common algorithm design techniques like divide-and-conquer, greedy methods, and dynamic programming are presented. The document also discusses representing algorithms in pseudocode and natural language, and analyzing worst-case, average-case, and best-case complexity.
This presentation discusses code optimization and performance tuning. It covers identifying time and space complexity of algorithms, examining programming constructs like loops and functions, and using performance libraries. Some key points include defining time complexity as the time taken by algorithm steps, optimizing loops by techniques like unrolling and reducing work inside loops, and the advantages of using pre-existing performance libraries like reducing errors and development time.
The document presents a methodology for modeling and compensating for friction in motion control systems using support vector regression (SVR). It discusses how friction is a nonlinear phenomenon that affects precision in motion control. It then describes developing an SVR model to identify and compensate for friction without requiring an explicit parametric friction model. The SVR model was able to significantly reduce position error in point-to-point and tracking motion control tests compared to not having compensation.
4 modeling and control of distillation column in a petroleum processnazir1988
This document describes the modeling and simulation of a condensate distillation column in a petroleum process. It presents a calculation procedure to model the column based on an energy balance structure using reflux rate and boilup rate as inputs to control distillate purity and bottom product impurity. A nonlinear dynamic model of the column is developed and simulated in MATLAB. The simulation shows the column can maintain product quality under normal operations but quality decreases with disturbances like changes in feed rate. A reduced-order linear model is then developed for use in model-reference adaptive control to improve disturbance rejection.
Smart Process Distillation Application Improves Recovery And Saves EnergyJim Cahill
The document summarizes a case study where a SmartProcess Distillation Optimizer was implemented on a large purification distillation column. The optimizer improved recovery and reduced energy usage. It immediately started reducing distillate rate and product losses by 22% while maintaining purity specifications. Steam usage was reduced by an average of 7%, resulting in estimated annual savings of over $700k. The project was completed in two weeks following a functional design study, demonstrating excellent payback.
Study of model predictive control using ni lab viewiaemedu
This document discusses the implementation of model predictive control (MPC) using National Instruments LabVIEW software. It begins with introductions to MPC and LabVIEW. It then covers constructing state space and transfer function models in LabVIEW. Simulation results are presented for MPC applied to first order systems with and without time delay. MPC performance is compared to PID control, showing MPC can handle constraints and optimize process operation while PID cannot. The document concludes MPC simulation using LabVIEW is successful and simulation results are useful for control system design.
Charles H. Cope is a law school graduate seeking admission to the Pennsylvania bar. He has experience working as a judicial fellow for the Superior Court of Pennsylvania and as a summer clerk and associate for federal courts and law firms. Cope earned his J.D. from the University of Virginia School of Law and has a B.A. in English Literature from Washington and Lee University.
Model Predictive Control For Integrating ProcessesEmerson Exchange
The document discusses controlling integrating processes like liquid levels using model predictive control (MPC). It explains that integrating processes require control since they have no natural equilibrium. The key points covered are:
- MPC can effectively control integrating processes by considering feedback, model correction, rotation factors, and tuning parameters.
- Tuning time to steady state, penalty on move, and model correction factor impact control performance for setpoint changes and load disturbances.
- With proper tuning, MPC provides improved control of integrating processes compared to conventional PI control.
Robust model predictive control for discrete-time fractional-order systemsPantelis Sopasakis
In this paper we propose a tube-based robust model predictive control scheme for fractional-order discrete-
time systems of the Grunwald-Letnikov type with state and input constraints. We first approximate the infinite-dimensional fractional-order system by a finite-dimensional linear system and we show that the actual dynamics can be approximated arbitrarily tight. We use the approximate dynamics to design a tube-based model predictive controller which endows to the controlled closed-loop system robust stability properties
The document provides an overview of model predictive control (MPC), including its advantages, concept, terminology, applications, prediction models, state space models, optimization windows, closed-loop control systems, constraints, and numerical solutions. MPC has advantages like intuitive concepts, easy tuning, handling multivariable processes, and treating constraints simply. It requires a process model and derivation of the control law is more complex than PID. MPC uses prediction models within an optimization window to minimize a cost function while satisfying constraints. Numerical solutions involve techniques like quadratic programming.
M. Tech. Thesis: Control System Design for an Energy Efficient Operation of P...Pallavi Kumari
This document describes the design and optimization of a ternary Petlyuk column for separating a benzene-toluene-xylene mixture. The column is divided into six tray sections with specified numbers of trays in each section. Base case operating conditions are determined that minimize reboiler duty. These include specifications for product purities and a vapor side draw ratio. Temperature and composition profiles at the optimized conditions are presented, achieving a minimum reboiler duty of 1619 kW.
A View of MPC Control from Operations to DesignJim Cahill
The document provides an overview of the various display, navigation, and configuration options available in a DeltaV system. It describes how users can access alarms, loop details, MPC variables, trends, and engineering environments with the appropriate privileges. Composite blocks and drilling down/backing out of block configurations are also summarized.
Physiologically Based Modelling and Predictive ControlPantelis Sopasakis
This document describes a physiologically based pharmacokinetic (PBPK) modeling and model predictive control (MPC) approach for optimal drug administration. It involves 4 main steps:
1) Developing PBPK models using mass balance equations to describe drug distribution in compartments like plasma, red blood cells, and kidneys.
2) Discretizing the PBPK models and designing an observer to estimate unmeasured states using the measured plasma concentration.
3) Formulating an MPC problem to determine optimal drug administration inputs over a prediction horizon while satisfying constraints like toxicity limits.
4) Solving the MPC problem online to determine the optimal control action and adjust the drug dosage based on the
1) The document describes a synchronous reference frame (DQ) based current control scheme for a four-leg voltage source inverter active power filter to compensate for current harmonics and unbalances from nonlinear loads.
2) The four-leg inverter topology allows compensation of single-phase nonlinear loads that cause unbalanced currents.
3) Simulation results demonstrate the compensation performance of the proposed active power filter and control scheme under steady-state and transient conditions.
Model Predictive Control based on Reduced-Order ModelsPantelis Sopasakis
This document presents a method for model predictive control (MPC) using reduced-order models. Many physical systems are modeled using partial differential equations with thousands of states, making MPC computationally challenging. The method reduces the model order by treating some states as disturbances and estimating their bounds. An invariance result shows the error remains bounded. The MPC optimization problem is formulated subject to the reduced constraints. Simulation results show the reduced-order MPC matches full-order MPC performance while being significantly faster to compute.
how_rockwell_automation_optimized_its_product_costing_processJohn Jordan
Rockwell Automation transitioned its product costing process from many legacy systems to a single SAP instance. The summary is:
1) Rockwell optimized SAP costing with minimal manual data maintenance by leveraging out-of-the-box functionality and custom programs to automatically update cost-relevant master data.
2) A daily costing process was established to cost new materials based on changes to their status, with failed costings flagged for review.
3) Challenges included complexities from changes in procurement sources and a lack of communication between global master data owners and cost accounting.
simulation and control in chemical enginneringThành Lý Phạm
This document describes the Group of Chemical Process Modeling, Control and Simulation at the University "Babeş-Bolyai" in Cluj-Napoca, Romania. It outlines the research areas and projects, laboratory equipment, mathematical models developed, and international meetings attended by the research group from 1999-2003. The group's work involves modeling, simulation, optimization, and advanced control of various chemical processes.
This document discusses distillation of binary mixtures. It begins by defining distillation as a process that separates a feed mixture into multiple products, often an overhead distillate and a bottoms product, using the differences in volatility between components. The key design factors for distillation include feed composition, desired separation, operating pressure, reflux ratio, number of stages, condenser/reboiler type, and column internals. Vapor-liquid equilibrium concepts like relative volatility and Raoult's law determine the feasibility of separation. Single-stage processes like flash distillation, simple batch distillation, and steam distillation are also introduced.
The document discusses harmonics, their sources, effects and mitigation techniques. Some key points:
1) Harmonics are generated by non-linear loads and can cause overheating, equipment failures and power quality issues. Common sources are power electronic equipment, arc furnaces and electronic ballasts.
2) Harmonics can have instantaneous effects like resonance, noise and interference or longer term impacts like increased losses and equipment degradation. Proper mitigation is needed to control costs.
3) Passive and active filters are commonly used to mitigate harmonics. Passive filters include tuned and detuned filters while active filters can dynamically cancel harmonics. Case studies show filters reducing currents and distortion while improving power factor.
Trajectory Control With MPC For A Robot Manipülatör Using ANN ModelIJMER
In this study, in a computer the dynamic motion modelling of manipulator and control of
trajectory with an algorithm this has been tested. First after dynamic motion simulation of manipulator
has been made MPC Control. The result in this study we can observe that computed torque method gives
better results than MPC methods. So in trajectory control it is approved of using computed torque
method. In last part of this study the results are estimated forward development are exemined and
suggested. The model predictive control (MPC) technique for an articulated robot with n joints is
introduced in this paper. The proposed MPC control action is conceptually different with the trajectory
robot control methods in that the control action is determined by optimising a performance index over
the time horizon. A neural network (NN) is used in this paper as the predictive model.
The document discusses using model predictive control and artificial neural networks to control an unstable maglev system. Model predictive control is presented as an advanced control method that can model and control highly nonlinear systems like maglev better than PID controllers. It relies on dynamic models and optimization to calculate future control inputs while honoring constraints. Artificial neural networks are also discussed as they can inherently model nonlinear systems and help optimize control parameters after system identification. The document proposes using MPC and ANNs together to control the position of a levitated maglev ball by manipulating control current inputs.
This document provides an overview of various operations research (OR) models, including: linear programming, network flow programming, integer programming, nonlinear programming, dynamic programming, stochastic programming, combinatorial optimization, stochastic processes, discrete time Markov chains, continuous time Markov chains, queuing, and simulation. It describes the basic components and applications of each model type at a high level.
A simplified predictive control algorithm for disturbance rejectionISA Interchange
This document presents a simplified predictive control algorithm for improved disturbance rejection in chemical processes. The standard model predictive control (MPC) assumes disturbances remain constant over the prediction horizon, which can result in poor disturbance suppression. The authors propose a simple disturbance predictor (SDP) that uses curve fitting of past data to predict unmeasured deterministic disturbances for a single step ahead. This is combined with a simplified MPC to reduce computational burden. Simulation results on examples show the SDP approach achieves improved regulatory performance and zero steady-state offset under various disturbance conditions compared to standard disturbance prediction methods.
Application of a merit function based interior point method to linear model p...Zac Darcy
This paper presents robust linear model predictive control (MPC) technique for small scale linear MPC
problems. The quadratic programming (QP) problem arising in linear MPC is solved using primal dual
interior point method. We present a merit function based on a path following strategy to calculate the step
length α, which forces the convergence of feasible iterates. The algorithm globally converges to the optimal
solution of the QP problem while strictly following the inequality constraints. The linear system in the QP
problem is solved using LDLT
factorization based linear solver which reduces the computational cost of
linear system to a certain extent. We implement this method for a linear MPC problem of undamped
oscillator. With the help of a Kalman filter observer, we show that the MPC design is robust to the external
disturbances and integrated white noise.
This document provides an overview of iterative and recursive algorithms. It begins with defining iterative algorithms as executing steps in iterations to find successive approximations of a solution. Key aspects of iterative algorithms discussed include loop invariants, typical errors, and different types of iterative methods. Recursion is then introduced as algorithms that call themselves with smaller inputs and solve larger cases based on smaller cases. Examples of recursive algorithms are provided for computing even numbers, powers of 2, sequential search, and testing natural numbers. In summary, the document covers the basic concepts and structures of iterative and recursive algorithms through definitions, examples, and comparisons between the two approaches.
IRJET- Design and Implementation of Closed Loop Boost Converter with IMC ...IRJET Journal
1. The document describes the design, simulation, and implementation of a closed-loop boost converter using an Internal Model Control (IMC) controller to improve voltage regulation performance.
2. An IMC controller is applied to a boost converter circuit in MATLAB Simulink to achieve better output voltage regulation compared to a conventional PID controller. This includes improved characteristics like settling time and overshoot.
3. The IMC controller structure provides benefits over traditional feedback control, including the ability to explicitly account for plant-model mismatch and disturbances not measured by the controller. This results in more robust performance and easier tuning compared to PID control.
PERFORMANCE COMPARISON OF TWO CONTROLLERS ON A NONLINEAR SYSTEMijccmsjournal
Various systems and instrumentation use auto tuning techniques in their operations. For example, audio
processors, designed to control pitch in vocal and instrumental operations. The main aim of auto tuning is
to conceal off-key errors, and allowing artists to perform genuinely despite slight deviation off-key. In this
paper two Auto tuning control strategies are proposed. These are Proportional, Integral and Derivative
(PID) control and Model Predictive Control (MPC). The PID and MPC controller’s algorithms
amalgamate the auto tuning method. These control strategies ascertains stability, effective and efficient
performance on a nonlinear system. The paper test and compare the efficacy of each control strategy. This
paper generously provides systematic tuning techniques for the PID controller than the MPC controller.
Therefore in essence the PID has to give effective and efficient performance compared to the MPC. The
PID depends mainly on three terms, the P ( ) gain, I ( ) gain and lastly D ( ) gain for control each
playing unique role while the MPC has more information used to predict and control a system.
PERFORMANCE COMPARISON OF TWO CONTROLLERS ON A NONLINEAR SYSTEMijccmsjournal
Various systems and instrumentation use auto tuning techniques in their operations. For example, audio processors, designed to control pitch in vocal and instrumental operations. The main aim of auto tuning is to conceal off-key errors, and allowing artists to perform genuinely despite slight deviation off-key. In this paper two Auto tuning control strategies are proposed. These are Proportional, Integral and Derivative (PID) control and Model Predictive Control (MPC). The PID and MPC controller’s algorithms amalgamate the auto tuning method. These control strategies ascertains stability, effective and efficient performance on a nonlinear system. The paper test and compare the efficacy of each control strategy. This paper generously provides systematic tuning techniques for the PID controller than the MPC controller. Therefore in essence the PID has to give effective and efficient performance compared to the MPC. The PID depends mainly on three terms, the P () gain, I ( ) gain and lastly D () gain for control each playing unique role while the MPC has more information used to predict and control a system.
Optimization of Fuzzy Logic controller for Luo Converter using Genetic Algor...IRJET Journal
This document summarizes research on optimizing a fuzzy logic controller for a Luo converter using a genetic algorithm. A fuzzy logic controller was designed for the Luo converter but its parameters were determined through trial and error. The document proposes using a genetic algorithm to optimize the fuzzy logic controller's rules, membership functions, and scaling gains in order to improve the controller's performance for the Luo converter. Simulation results showed that the genetic algorithm-optimized fuzzy logic controller provided faster response, better transient performance, and more robustness to variations compared to the original fuzzy logic controller.
UNIT-2 Quantitaitive Anlaysis for Mgt Decisions.pptxMinilikDerseh1
This document provides an overview of linear programming problems (LPP). It discusses the key components of linear programming models including objectives, decision variables, constraints, and parameters. It also covers formulation of LPP, graphical and simplex solution methods, duality, and post-optimality analysis. Various applications of linear programming in areas like production, marketing, finance, and personnel management are also highlighted. An example problem on determining optimal product mix given resource constraints is presented to illustrate linear programming formulation.
Presented in this short document is a description of what is well-known as Advanced Process Control (APC) applied to a small linear three (3) manipulated variable (MV) by two (2) controlled variable (CV) problem. These problems are also known as Model Predictive Control (MPC) (Grimm et. al., 1989) and Moving Horizon Control (MHC). Figure 1 shows the 3 x 2 APC problem configured in our unit-operation-port-state superstructure (UOPSS) (Kelly, 2004, 2005; Zyngier and Kelly, 2012) as an Advanced Planning and Scheduling (APS) problem as opposed to a traditional APC problem.
Although there is a tremendous amount of stability, performance and robustness theory associated with APC which can be directly assumed to APS problems (Mastragostino et. al., 2014), our approach is to show that APC can equally be set into an APS framework except that APS has far less sensitivity technology due to its inherent discrete and nonlinear modeling complexities i.e., especially non-convexities. In order to eliminate the steady-state offset between the actual value and its target, it is well-known to apply bias-updating though other forms of “parameter-feedback” is possible. Typically, APS applications only employ “variable-feedback” i.e., opening or initial inventories, properties, etc. but this alone will not alleviate the steady-state offset as demonstrated by Kelly and Zyngier (2008).
Data Evaluation and Modeling for Product Definition Engineering - ISE 677Justin Davies
This document discusses process planning and control for drafting activities at a product design engineering department of a gas turbine energy company. It summarizes the steps taken to analyze the current state of operations, identify inefficiencies, and develop metrics to measure performance and enable planning. Initial analysis using network flow diagrams revealed instances of rework loops and delays. Data from time logs was analyzed but found to have skewed distributions, making it difficult to establish baselines or track trends. Further analysis highlighted issues with the time logging tool and subjective estimates. A normalization method using confidence intervals was developed to establish a measurement baseline and enable improved planning and workload management.
Evolutionary Design of Backstepping Artificial Sliding Mode Based Position Al...CSCJournals
This paper expands a fuzzy sliding mode based position controller whose sliding function is on-line tuned by backstepping methodology. The main goal is to guarantee acceptable position trajectories tracking between the robot manipulator end-effector and the input desired position. The fuzzy controller in proposed fuzzy sliding mode controller is based on Mamdani’s fuzzy inference system (FIS) and it has one input and one output. The input represents the function between sliding function, error and the rate of error. The second input is the angle formed by the straight line defined with the orientation of the robot, and the straight line that connects the robot with the reference cart. The outputs represent angular position, velocity and acceleration commands, respectively. The backstepping methodology is on-line tune the sliding function based on self tuning methodology. The performance of the backstepping on-line tune fuzzy sliding mode controller (TBsFSMC) is validated through comparison with previously developed robot manipulator position controller based on adaptive fuzzy sliding mode control theory (AFSMC). Simulation results signify good performance of position tracking in presence of uncertainty and external disturbance.
The aim of this paper is to prove that fuzzy logic algorithm is a suitable control technique for fast processes such as electrical machines. This theory has been experimented on different kinds of electrical machines such as stepping motors, dc motors and induction machines (with 6 phases) and the experimental results show that the proposed fuzzy logic algorithm is the most suitable control technique for electrical machines since this algorithm is not time consuming and it is also robust between plant parameters variations.
Improvement in Quality of Power by PI Controller Hybrid PSO using STATCOMIRJET Journal
The document discusses using a hybrid particle swarm optimization (PSO) technique with a PI controller and STATCOM device to improve power quality and reduce costs. Voltage sags are a key power quality issue that are mitigated. The system is modeled in MATLAB Simulink. Simulation results show that using PSO to optimize the PI controller parameters and STATCOM operation leads to better voltage regulation and an improved inertia weight, demonstrating enhanced power quality and reduced costs.
This document discusses optimization problems in engineering applications. It begins by defining optimization and describing how it can be applied to engineering problems to minimize costs or maximize benefits. Some examples of engineering applications that can be optimized are described, such as designing structures for minimum cost or maximum efficiency. The document then discusses procedures for solving optimization problems, including recognizing and defining the problem, constructing a model, and implementing solutions. It also describes different types of optimization problems and methods for solving linear programming problems, including the graphical and simplex methods.
Operations research (OR) is an interdisciplinary approach for decision-making that uses mathematical modeling and analytical methods to arrive at optimal or near-optimal solutions to complex decision problems. OR was first applied during World War II to solve logistics and operations problems. It involves breaking problems down into components, representing them mathematically, and using analytical methods like linear programming to solve problems. The goal of OR is to determine the best solution to a problem by quantifying variables and using mathematical techniques and computer modeling.
Position Control of Robot Manipulator: Design a Novel SISO Adaptive Sliding M...Waqas Tariq
The document describes a novel adaptive sliding mode fuzzy PD fuzzy sliding mode control algorithm for position control of robot manipulators. The algorithm uses a single-input single-output fuzzy system to compensate for model uncertainties and eliminate chattering using a linear boundary layer method. It also online tunes the sliding function parameter using adaptation laws. The stability of the closed-loop system is proved mathematically using Lyapunov stability theory. The algorithm is analyzed and evaluated on a 2 degree of freedom robotic manipulator to achieve improved tracking performance compared to conventional sliding mode control approaches.
The document discusses different types of mathematical models, including deterministic and probabilistic models. It provides examples of each. It also discusses building, verifying, and refining mathematical models. Additionally, it covers optimization models, their components including objective functions and constraints. Finally, it discusses specific types of optimization models like linear programming, network flow programming, and integer programming.
Building a Raspberry Pi Robot with Dot NET 8, Blazor and SignalR - Slides Onl...Peter Gallagher
In this session delivered at Leeds IoT, I talk about how you can control a 3D printed Robot Arm with a Raspberry Pi, .NET 8, Blazor and SignalR.
I also show how you can use a Unity app on an Meta Quest 3 to control the arm VR too.
You can find the GitHub repo and workshop instructions here;
https://bit.ly/dotnetrobotgithub
Google Calendar is a versatile tool that allows users to manage their schedules and events effectively. With Google Calendar, you can create and organize calendars, set reminders for important events, and share your calendars with others. It also provides features like creating events, inviting attendees, and accessing your calendar from mobile devices. Additionally, Google Calendar allows you to embed calendars in websites or platforms like SlideShare, making it easier for others to view and interact with your schedules.
87. Dual mode paradigm (or closed-loop prediction) Terminal region in which the control law u=-Kx satisfies constraints. Initial state trajectory nc moves maximum Terminal State In at most nc samples, predicted state moves into the terminal region while satisfying constraints.
88. Open and closed-loop prediction Model Future inputs Future outputs OPEN LOOP PREDICTION Model M K Future outputs r Decision variables CLOSED LOOP PREDICTION