|
CONTROL SYSTEMS, ROBOTICS, AND
AUTOMATION
Feedforward and Feedback Control
Feedforward or Open-Loop Control
Feedback or Closed-Loop Control
Some Simple Examples of Feedback
Control Systems
Elements of Feedback Control
Systems
Servomechanism, Regulator, and
Process Control
Continuous and Discontinuous
Operation of Automatic Control
Systems
Analysis and Design of Feedback
Control Systems
Describing the Dynamical
Behavior of Systems
Performance Objectives
Controller Design
Non-Standard Types of Control
Systems
Higher-Level Control Systems
Adaptive Control Systems
Large-Scale Systems
Control of Discrete-Event
Systems and Hybrid Systems
Supervisory Distributed Control
Systems
Fault Diagnosis and
Fault-Tolerant Control Systems
Applications
Control of Robot Manipulators
Other Technical Applications
Nontechnical Fields of
Application
Computational Tools for
Application of Control Systems
History
Outlook on Some Trends in Future
Research and Developments
ELEMENTS OF CONTROL SYSTEMS
System modeling
Mathematical models of dynamical
systems
Differential Equation Models for
Lumped Parameter Systems in
Continuous-time Domain
State Space Description of
Lumped Parameter Systems
Time-invariant Linear Systems
Discrete-time Systems or
Sampled-Data Systems
Block Diagram Representation and
Simplification
Distributed Parameter Systems
Deterministic and Stochastic
Systems
Non-linear Models and
Linearization
Causal and Non-causal Systems
Stable and Unstable Systems
Single-Input-Single-Output
(SISO) and
Multiple-Input-Multiple-Output
(MIMO) Systems
Systems control
Open-loop Control
Feedback Control
Closed-loop Behavior of Control
Systems
Control Strategies
BASIC ELEMENTS OF CONTROL
SYSTEMS
Dynamical Systems
Graphical Description of Systems
Open-loop Control and
Closed-loop Control
Principal Functions of Control
The Basic Structure of Control
Systems
Some Typical Examples of Control
Voltage Control of a D.C.
Generator
Course Control of a Ship
Liquid Level Control
Control of a Heat Exchanger
A Brief Overview of the History
of Control Systems
GENERAL MODELS OF DYNAMICAL
SYSTEMS
Mathematical Models
Dynamic and Static Behavior of
Systems
System Properties
Linear and Non-linear Systems
Lumped and Distributed Parameter
Systems
Time-varying and Time-invariant
Systems
Systems with Continuous or
Intermittent Action
Systems with Deterministic or
Stochastic Properties
Causal and Non-causal Systems
Stable and Unstable systems
SISO and MIMO Systems
DESCRIPTION OF CONTINUOUS LINEAR
TIME-INVARIANT SYSTEMS IN TIME
DOMAIN
Description by differential
equations
Electrical Systems
Mechanical Systems
Thermal systems
System description with
reference to special signals
Step and Impulse Response
Functions
The Convolution Integral
System description in state
space
State Space Description for SISO
Systems
State Space Description for MIMO
Systems
DESCRIPTION OF CONTINUOUS LINEAR
TIME-INVARIANT SYSTEMS IN
FREQUENCY DOMAIN
Laplace Transformation
Fourier Transformation
Transfer Function of a Dynamical
System
Definition
Poles and Zeros of G(s)
Transfer Functions of
Interconnected Systems
Relation between G(s)and the
State-Space Representation
The Complex G-Plane
Frequency-Response of a
Dynamical System
Definition
Polar Plot Representation
Bode-Diagram Representation
The Most Common Dynamical
Systems
Element with P-Action
(Proportional Action or Gain)
Element with I-Action
(Integration)
Element with D-Action
(Differentiation)
Element with PT1-Action
(First-Order Lag Element)
Element with PT2-action
(Second-Order Lag Element)
Bandwidth of a Dynamic System
Minimum and Non-minimum Phase
Systems
CLOSED-LOOP BEHAVIOR OF
CONTINUOUS LINEAR
TIME-INVARI-ANT SYSTEMS
Dynamic behavior of the
closed-loop system
Sensitivity of feedback control
systems to parameter variations
Stability
Steady-state error
PID controller and other
standard controller types
Behavior of Standard Controllers
in Closed-Loop Operation.
STABILITY CONCEPTS
The Definition of Stability
The Concept of Liapunov’s
Stability
The Second (Direct) Method of
Liapunov
Sylvester’s Criterion
Stability of Linear Systems
Simplest Types of Stable
Equilibrium States
Stability in the First
Approximation
Stability under Persistent
Disturbances
Further Liapunov-Related Types
of Stability
Stability Criteria for Linear
Time-Invariant Systems
The Routh-Hurwitz Stability
Criterion
The Hermite Stability Criterion
Kharitonov’s Criterion
Criterion of Leonhard-Mikhailov
The Nyquist Stability Criterion
CONTROLLER DESIGN IN TIME-DOMAIN
Problem formulation
Time-domain performance
specifications
Transient Performance
Integral Criteria
Calculation of the
ISE-Performance Index
Optimal controller settings
subject to the ISE-criterion
Example
Optimal Settings for
Combinations of PTn-Plants and
Standard Controllers of PID Type
Empirical procedures
Tuning Rules for Standard
Controllers
Ziegler-Nicols Tuning Rules
Some Other Useful Tuning Rules
Empirical Design by Computer
Simulation
Mixed time- and frequency-domain
design by standard polynomials
DESIGN IN THE FREQUENCY DOMAIN
Gain and Phase Margins
Gain Margin
Phase Margin
Examples
Relationship Between PM and
Damping Ratio
Types of Compensators
Design of PI and Lag
Compensators
Analysis of PI and Lag
Compensators
Design Rules for PI and Lag
Compensators
Example
Design of PD Compensators
(Realized by Rate Feedback)
Analysis of PD Compensations
Design Rules for PD (Rate
Feedback) Compensators
Example
Design of Lead Compensators
Analysis of Lead Compensators
Design Rules for Lead
Compensators
Example
Design of PID Compensators
Analysis of PID Compensators
Design Rules for PID
Compensators
Example
Design of Lead Compensators
Analysis of Lag-Lead
Compensators
Design Rules for Lag-Lead
Compensation
Example
PID CONTROL
Process Models
Performance Evaluation of PID
Control Systems
Action Modes of PID Controllers
Design of PID Control Systems
Selection of Action Mode
Identification of Process Model
Parameters
Tuning of PID Parameters
Advanced Topics
Windup of the Integral Element
and Anti-Windup Mechanism
Two-Degree-of-Freedom PID
Controllers
Sophisticated Models
Other Tuning Methods for PID
Parameters
INTERNAL MODEL CONTROL
The Internal Model Control
Structure
Closed-loop Transfer Functions
for IMC
Internal Stability
Asymptotic closed-loop behavior
(System Type)
Performance Measures
Internal Model Control Design
Procedure
Requirements for Physical
Realizability on q, the IMC
Controller
Limitations to Perfect Control:
the Need for an IMC Design
Procedure
Statement of the IMC Design
Procedure
Application of IMC design to
Simple Models
Example 1a: PI Tuning for A
First-Order System
Example 1b: PI Tuning for a
First-Order System with RHP Zero
Example 1c: PI with Filter
Tuning for a First-Order System
with LHP Zero
Example 2: PID Tuning for a
Second-Order System with RHP
Zero
Example 3: PID with Filter
Tuning for a second-Order Model
with RHP Zero
Example 4: Dead-time
Compensation for a First-Order
with Delay Plant.
IMC-PID Tuning Rules for Plants
with Integrator Dynamics
IMC-PID tuning Rules for
First-Order with Delay Plants
Additional IMC Design Topics
SMITH PREDICTOR AND ITS
MODIFICATIONS
Controller design
Performance comparison
Modification for high order
systems
Modification for rapid load
rejection
Modifications for open-loop
unstable systems
DIGITAL CONTROL SYSTEMS
The Basic Structure of Digital
Control Systems
Discrete-Time Systems
Analysis of Linear
Time-Invariant Discrete-Time
Systems
Sampled-Data Systems
Description and Analysis of
Sampled-Data Systems
Example 1
Example 2
Analysis of Sampled-Data Systems
Stability
Definitions and Basic Theorems
of Stability
Stability of Linear,
Time-Invariant, Discrete-Time
Systems
Bounded-Input, Bounded-Output
Stability
Stability Criteria
The Routh Criterion using the
Mobius Transformation
Example 3
The Jury Criterion
Example 4
Example 5
Example 6
Controllability
Example 7
Example 8
Observability
Example 9
Loss of Controllability and
Observability due to Sampling
Example 10
Kalman Decomposition
DISCRETE-TIME, SAMPLED-DATA,
DIGITAL CONTROL SYSTEMS, AND
QUANTIZATION EFFECTS
Discrete-Time Systems
Properties of Discrete-Time
Systems
Linearity
Time-Invariant System
Causality
Description of Linear,
Time-Invariant, Discrete-Time
Systems
Difference Equations
Transfer Function
Impulse Response or Weight
Function
State-Space Equations
Analysis of Linear,
Time-Invariant, Discrete-Time
Systems
Analysis Based on the Difference
Equation
Analysis Based on the Transfer
Function
Analysis Based on the Impulse
Response
Analysis Based on the State
Equations
Sampled-Data Systems
D/A and A/D Converters
Hold Circuits
Description and Analysis of
Sampled-Data Systems
Analysis Based on the State
Equations
Analysis Based on H(kT)
Analysis based on H(z)
Digital Control Systems
Comparison between Digital and
Continuous-Time Control Systems
Quantization Effects
Truncation and Rounding
DISCRETE-TIME EQUIVALENTS TO
CONTINUOUS-TIME SYSTEMS
Design of Discrete-Time Control
Systems for Continuous-Time
Plants
Sampling and A/D Conversion
Reconstruction and D/A
Conversion
Discrete-Time Equivalents of
Continuous-Time Plants
Discretizing Continuous-Time
Controllers
Numerical Approximation of
Differential Equations
Euler's Forward Method (One
Sample)
Euler's Backward Method (One
Sample)
Trapezoidal Method (Two Sample)
An Example
Mapping Between S and Z Planes
Using Euler's and
Tustin's Methods
Frequency Response
Approximations
Bilinear Transformation with
Frequency Prewarping
Discretization of
Continuous-Time State Variable
Models
Discrete-Time Models of
Continuous-Time Systems
Discrete-Time Approximations of
Continuous-Time Systems
DESIGN METHODS FOR DIGITAL
CONTROLLERS, SAMPLE-RATE
Design Methods for Digital
Controllers
Discrete-Time Controller Design
Using Indirect Techniques
Direct Digital Controller Design
via the Root-Locus Method
Direct Digital Controller Design
Based on the Frequency Response
Bode Diagrams
Example 1
Nyquist Diagrams
The PID Controller
State-Space Design Methods
Optimal Control
Sample Rate
Example 2
REAL-TIME IMPLEMENTATION
A Simple Real-Time System
Computational Delay and Jitter
Real-Time Integration of
Continuous-Time States
Implementation on Fixed-Point
Processors
Implementation on Floating-Point
Processors
Real-Time Operating Systems
Intertask Communication in
Multitasking Systems
Distributed Real-Time Systems
Time Triggered Systems for
Safety Critical Applications
Development Tools for Real-Time
Implementation
DESIGN OF STATE SPACE
CONTROLLERS (POLE PLACEMENT) FOR
SISO SYSTEMS
Design Objective
General Remarks on State Space
Design
System Class
Accompanying Example: Inverted
Pendulum on Cart
DESCRIPTION AND ANALYSIS OF
DYNAMIC SYSTEMS IN STATE SPACE
Extraction of the State Space
Representation from the Transfer
Function G(s)
Solution 1: Control Canonical
Form
Solution 2: Observer Canonical
Form
Solution 3: Modal Canonical Form
(Diagonal and
Jordan Canonical Form)
Transformation to Diagonal Form
Solution of the State Equations
Matrix Exponential
Solution of the State Equations
by State Transition Matrix
Solution of the homogeneous
state differential equation from
the modal canonical form
Stability
Controllability and
Observability
Definition of Controllability
Criteria of Controllability
Definition of Observability
Observability Criteria
Interpretation of
Controllability and
Observability
Controllability and
Observability of eigenvalues
Pole-Zero Cancellations
Minimal Realization
Discrete Time Systems
CONTROLLER DESIGN
Objectives and Structure of
State Feedback Control
Determination of the
pre-compensator g
Determination of the Controller
k
Determination by Matching of
Coefficients
Determination from Control
Canonical Form
Determination by Transform to
Control Canonical Form:
Ackermann’s Formula
Design Parameters
Example: Inverted Pendulum
Discrete-Time State Feedback and
Dead-Beat Behavior
OBSERVER DESIGN
Objectives and Structure of the
State Observer
Design of the Observer
Observer Design by Matching of
Coefficients
Observer Design by
State-Feedback Design Procedure
Design Parameters
Example: Inverted Pendulum
The Observer in Closed-Loop
Control- The Separation
Principle
Reduced Order Observer
Example
Discrete- Time Observers
EXTENDED CONTROL STRUCTURES
Steady State Behaviour under
realistic assumptions
External Disturbances
Model Uncertainty and Parameter
Variations
PI- State Feedback Control
Structure and Design
Properties and Further
Extensions
Model-based dynamic
pre-compensator
Structure and Design
Combination with
PI-state-feedback
BASIC NONLINEAR CONTROL SYSTEMS
Forms of nonlinearity
Structure and behaviour
Stability
Aspects of design
DESCRIBING FUNCTION METHOD
The Sinusoidal Describing
Function
The Evaluation of some DFs
Limit Cycles and Their Stability
DF Accuracy
Some Examples of DF Usage
Feedback
Loop
Containing a Relay with Dead
Zone
Autotuning in Process Control
Closed Loop Frequency Response
Compensator Design
Additional Aspects
SECOND ORDER SYSTEMS
Basic Principles
Analysis Using the Phase Plane
Example1
Example 2
Example 3
STABILITY THEORY
Linearization: Stability in the
First Approximation
The Direct Method of Lyapunov
Nonlinear Systems
Linear Systems
POPOV AND CIRCLE CRITERION
Kalman-Yakubovich-Lemma
Criteria for Absolute Stability
CONTROL BY COMPENSATION OF
NONLINEARITIES
Plants with Actuator
Nonlinearities
Parameterized Inverses
State Feedback Designs
Output Feedback Inverse Control
Output Feedback Designs
Designs for Unknown Linear
Dynamics
Designs for Multivariable
Systems
Designs for Nonlinear Dynamics
Neural Network based Adaptive
Inverse Compensation
An illustrative Example
ESTIMATION AND COMPENSATION OF
NONLINEAR PERTURBATIONS BY
DISTURBANCE OBSERVERS
Problem Statement
Theory
Estimation of Nonlinearities
Comments on (9)
Choice of fictitious model
PI-observer
Convergence and Estimation
Errors
High gain proof
Estimation errors
Lyapunov approach
Compensation of Nonlinearities
Closed-Loop
Control System
Applications
ANTI WINDUP AND OVERRIDE CONTROL
PI-Control with Input
Saturations
Problem Statement and Test Cases
The Reset Windup Effect
Anti Windup Structures
Transient Responses for the Test Cases
Stability Properties
Stability Analysis of the Test Cases
Summary
Plants of dominant Second Order
Problem Statement
The Plant Windup Effect
Stability Properties
Anti Plant Windup Structures
Extensions
Summary
Output Constrained Control
Basic Concepts
Stability Analysis
An Example
Summary
GAIN-SCHEDULING
Linearization Theory
Series expansion linearisation
about a single trajectory or
equilibrium point
Series expansion linearisation
families
Off-equilibrium linearisations
Divide and Conquer
Gain-Scheduling Design
Classical gain-scheduling design
Neural/fuzzy gain-scheduling
Gain-scheduling using
off-equilibrium linearisations
LPV Gain-Scheduling
LPV systems
Small-gain LFT approaches
Lyapunov-based LPV approaches
Quadratic Lyapunov function
approaches
Parameter-dependent Lyapunov
function approaches
Outlook
MODELING AND SIMULATION OF
DYNAMIC SYSTEMS
Systems, processes and models
Simulation
Classification of systems and
models
Properties of systems and models
Properties of models only
Some additional remarks on the properties 'static' and 'dynamic'
Modeling
Some general considerations
Modeling and modeler
Modeling and modeling goals
Model structure
Model complexity
Verification and validation
Numerical aspects
System structure and model structure
System descriptions and relations between models
A short history of simulation
Continuous-time simulation
Discrete-event simulation
SOME BASICS IN MODELING OF
MECHATRONIC SYSTEMS
System Variables and System
Elements
Energy Storage Elements
Generalized Kinetic Energy
Generalized Potential Energy
The General Case
Coupling Elements
Electromechanical Example
- Solenoid Valve
Hydromechanical Example - Hydraulic
Piston Actuator
Static Elements
Mechanical Example - The
Rayleigh Dissipation Function
Kirchhoff Networks
Kirchhoff’s Laws
Tellegen’s Theorem
Fundamental Matrices
Port-Hamiltonian Systems
Electromechanical Example -
Solenoid Valve.
Hydromechanical Example
- Hydraulic Piston Actuator
MODELING AND SIMULATION OF
DISTRIBUTED PARAMETER SYSTEMS
Modeling of distributed
parameter systems
Model Derivation - basic
principles
More PDEs-classifications
PDE order
Linearity, quasilinearity and
nonlinearity
Elliptic, parabolic and
hyperbolic PDEs
Convection - diffusion
(dispersion)-reaction PDEs
Boundary conditions
Parameter estimation
Model simplification and
reduction
Simulation of distributed
parameter systems
Analytical solution procedures
Spectral methods and weighted
residual approximations
Spatial discretization
Time integration
Early versus Late Lumping
MODELING LANGUAGES FOR
CONTINUOUS AND DISCRETE SYSTEMS
Aims of Modeling Languages
Historical background
A Modeling Approach
Physical background
The Multi-Port Approach
Modeling Languages
VHDL-AMS
Modelica
A comparison of VHDL-AMS and
Modelica
MODELING AND SIMULATION OF
LARGE-SCALE HYBRID SYSTEMS
General Concepts
System Representations and
Software Tools
Representations of Discrete Event and Continuous Systems
Representations for Hybrid Systems
Object-oriented Modeling of
Physical Systems
Hybrid Elements
Hybrid Systems Arising from Physical Abstractions
Equation-Based Modeling of Discrete Event Systems
Integration of Complex Discrete
Event and Object-Oriented Models
Modeling Aspects
Numerical Aspects
Ongoing Research and Future
Challenges
MODELING AND SIMULATION OF
DYNAMIC SYSTEMS USING BOND
GRAPHS
Early history
Modeling and simulation of
dynamic behavior of physical
systems
Key aspects of the port-based
approach
Bond Graph Notation
Node types
Constitutive relations
Relation to other representations
Systematic conversion of a simple electromechanical system model
into a bond graph representation
Causality
Notation
Causal port properties
Causality assignment
Conversion of a causal bond graph into a block diagram
Causal paths
Generation of a set of mixed algebraic and differential equations
Linear analysis
Impedance analysis using bond graphs
Hierarchical modeling
Word bond graphs
Multibonds
Multiport generalizations
Sources
Multiport storage elements
Multiport resistors
Multiport transducers
Multiport components
Arrays
Port-based modeling and
simulation of dynamic behavior
of physical systems in terms of
bond graphs: a simple example
Future trends
RAPID PROTOTYPING FOR MODEL AND
CONTROLLER IMPLEMENTATION
Definition of Rapid Prototyping
Goals
General solution
Implementation in Software
Implementation in Hardware
Real-time simulation,
Hardware-in-the-loop (HIL)
Simulation acceleration
SIMULATION SOFTWARE -
DEVELOPMENT AND TRENDS
Continuous Roots of Simulation
CSSL Structure in Continuous
Simulation
Structure of the Model Frame
Requirements for the Experimental Frame
Numerical Algorithms in
Simulation Systems
Simulation Software and CACSD
Tools
Analysis Methods in Simulation
Systems
Implicit Models – Algebraic
Loops – Differential-Algebraic
Equations
Discrete Elements in Continuous
Modelling and Simulation
Hybrid modelling and simulation
– Combined Modelling and
Simulation
Simulation in Specific Domains
Developments beyond CSSL
Discrete Event Simulation
Statistic Roots and Events
Modelling Concepts in Discrete Simulation
Random Number Generators
Object-oriented Approaches to
Modelling and Simulation
Choice and Comparison of
Simulation Software
Hints for Simulator Choice
Comparison of Simulation Tools
FREQUENCY DOMAIN SYSTEM
IDENTIFICATION
A brief introduction to
identification
Basic Steps in the Identification Process
Collect Information about the System
Select a Model Structure to represent the System
Match the selected Model to the Measurements
Validate the selected Model
Description of the Stochastic Behavior of Estimators: What can be
expected from a good Estimator?
Location Properties: Unbiased and Consistent Estimates
Dispersion Properties: Efficient Estimators
A Statistical Approach to the Estimation Problem
Least Squares Estimation
Weighted Least Squares Estimation
The Maximum Likelihood Estimator
System Identification: problem
statement
Experiment Setup
Choice of the Setup: ZOH><BL
Choice of the Excitation Signals
Choice of a model structure
Plant Model
Noise Models
Match the Model to the Data
The Errors-in-variables Formulation
Differences and Similarities with the ‘Classical’ Time Domain
Identification Framework
Model Selection and Validation
Time and frequency domain
identification
Time and Frequency Domain Identification: Equivalencies
Initial Conditions: Transient versus Leakage Errors
Windowing in the Frequency Domain, (non causal) Filtering in Time
Domain
Time and Frequency Domain Identification: Differences
Choice of the Model
Unstable Plants
Noise Models: Parametric or Non-parametric Noise Models
Extended Frequency Range: Combination of Different Experiments
The Errors-in-variables Problem
Selection of an identification
scheme
Questions
Application?
Domain?
Excitation?
Noise?
Advices
MEASUREMENTS OF FREQUENCY
RESPONSE FUNCTIONS
An introduction to the discrete
Fourier transform
The Sampling Process
The Discrete Fourier Transform
(DFT-FFT)
Discretization in Time
Windowing
Discretization in Frequency
The DFT-expressions
DFT-properties of Periodic
Signals,
Integer Number of Periods
Measured
No Integer Number of Periods
Measured.
DFT of Burst Signals
Spectral representation of
periodic signals
Analysis of FRF measurements
using periodic excitations
Measurement Setup
Error Analysis
Bias Error on the FRF
Variance Analysis of the FRF
Reducing FRF measurement errors
for periodic excitations
Basic Principles
Processing Repeated Measurements
Improved Averaging Methods for
Non-synchronized Measurements
Coherence
FRF measurements using random
excitations
Basic Principles
Reducing the Noise Influence
Systematic Errors
Variance
Leakage Errors
FRF measurements of multiple
input multiple output systems
Guidelines for FRF measurements
Advice 1: Use periodic
excitations
Advice 2: Select the best FRF
estimator
Periodic Excitations
Random Excitations
Advice 3: Pretreatment of data
ESTIMATION WITH KNOWN NOISE
MODEL
Estimation algorithms - general
General Form of Cost Functions
Minimization of Cost Functions
Quick Tools to Analyze
Estimators
Asymptotic Properties
Estimation algorithms - specific
Linear Least Squares
Nonlinear Least Squares
Total Least Squares Algorithms
Total Least Squares
Generalized Total Least Squares
Maximum Likelihood
Approximate Maximum Likelihood
Iterative Quadratic Maximum
Likelihood
Bootstrapped Total Least Squares
Subspace Algorithms
Illustration and overview of the
properties
Real Measurement Example
Overview of the Properties
Extensions
Systems with Time Delay
Identification in Feedback
High Order Systems
Model selection - Model
Validation
Detection of Undermodeling
Detection of Overmodeling
Whiteness Test on Residuals
Model Validation
FREQUENCY DOMAIN SUBSPACE
ALGORITHMS
Model equations
Plant Model
Noise Model
Subspace algorithms
Algorithm for Discrete-time
Systems
Algorithm for Continuous-time
Systems
Asymptotic Properties
Practical remarks
Simulation examples
Continuous-time System
Discrete-time System
Real measurement example
ESTIMATION WITH UNKNOWN NOISE
MODEL
Estimation algorithms
Maximum Likelihood
Generalized Total Least Squares
Bootstrapped Total Least Squares
Subspace Algorithms
Instrumental Variables
Illustration and overview of the
properties
Overview of the Properties
Simulation Example
Real Measurement Example
Identification of parametric
noise models
Identification in feedback
Model selection
MODAL ANALYSIS
The “Modal” Model
Single Degree of Freedom
Multiple Degree of Freedom
Mode Shapes and Operating
Deflection Shapes
Observability and
Controllability of Modes
Frequency-Domain Identification
of Modes
Least Squares Estimation
Common-Denominator Model
Linearity in the Parameters
Reduced
Normal
Equations
Fast Implementation of the
Reduced
Normal Equations
Solving the Reduced
Normal
Equations
Stabilization chart
Maximum Likelihood Estimation
Gauss-Newton Optimization
Confidence Intervals
Application
IDENTIFICATION OF LINEAR SYSTEMS
IN TIME DOMAIN
What Is System Identification?
The Need of Mathematical Models
Classification of Models
Mathematical Modeling
Applying System Identification
The Setup
Some Basic Concepts
Identifiability
Identification Methods
Least Squares Method
Instrumental Variable Methods
The Basic Case
Extended IV Methods
Consistency Analysis
Asymptotic Distribution
Prediction Error Methods
Description
Properties
Subspace Identification Methods
Recursive Identification
Algorithms
Real-Time Algorithms
Identification for Control
Continuous-Time Identification
LEAST SQUARES AND INSTRUMENTAL
VARIABLE METHODS
Models as predictors
Linearly Parameterized
Predictors
Estimating the model parameters
Solving the Least Squares
Problem
Stochastic analysis
Preliminaries
Deterministic Regressors
Stochastic Regressors
Instrumental variable method
Computing the estimate
Multivariable systems
Optimal weighted LS estimator
PREDICTION ERROR METHODS
Description
General Linear Dynamic Models
ARMAX Models
State Space Models
Optimal Prediction
Interpretations
Implementation Aspects
Optimization
Evaluation of Gradients
Extensions
Prefiltering of Data
Modified Criterion Function
Using Multistep Prediction
Errors
Properties
Identifiability
Convergence and Consistency
Asymptotic Accuracy and
Distribution
Model Approximation
SUBSPACE IDENTIFICATION METHODS
Notation
Block Hankel Matrices and State Sequences
Model Matrices
Geometric Tools
Orthogonal Projections
Oblique Projections
Deterministic subspace
identification
Calculation of a State Sequence
Computing the System Matrices
Stochastic subspace
identification
Calculation of a State Sequence
Computing the System Matrices
Combined
deterministic-stochastic
subspace identification
algorithm
Calculation of a State Sequence
Computing the System Matrices
Variants
Comments and perspectives
Software
RECURSIVE ALGORITHMS
Recursive Algorithm for Constant
Coefficients
Least Squares (LS)
Extended Least Squares (ELS)
RLS with Forgetting Factors
Instrumental Variables Estimate
Stochastic Approximation Estimate
Stochastic Gradient Algorithm
Recursive Algorithms Derived From Off-Line Identification
Convergence of Estimates
Time-Varying Systems
IDENTIFICATION FOR CONTROL
Identification of approximate
models
Prediction error identification
Closed-loop process-model
mismatch
Identification of
control-relevant approximate
models
Identification from closed-loop
data
Iterative Identification and
Control
Extensions
CONTINUOUS -TIME IDENTIFICATION
A model transformation
Parameter Transformations
Noise Modeling
Parameter Estimation
Numerical Iterative Optimization
Statistical Consistency and
Convergence
Orthogonalization and Numerical
Aspects
IDENTIFIABILITY OF LINEAR
CLOSED-LOOP SYSTEMS
Identifiability Concepts
Deterministic Identifiability
Stochastic Identifiability
Structural Identifiability
System Identifiability
Strong System Identifiability
Parameter Identifiability
Identifiability Conditions for
Closed-Loop Systems -A Short
Overview
SISO Systems
MIMO systems
Complete and Partial
I/O-Identifiability of
Multivariable Closed-Loop
Systems
Motivation
Definition of complete and
partial I/O-identifiability
Results
RELATIONS BETWEEN TIME DOMAIN
AND FREQUENCY DOMAIN PREDICTION
ERROR METHODS
Prediction error methods
Time Domain
Frequency Domain
Asymptotic Properties
A Comparison
Closed Loop
Frequency Domain ARX Case
ARX Example
Discussion
Numerical example
IDENTIFICATION OF TIME VARYING
SYSTEMS
Simple Limited Memory Algorithms
Modeling the Parameter
Variations: The Dynamic Transfer
Function (DTF) Model
Optimization of the
Hyperparameters
Illustrative Examples
A Simulation Example
A Real Data Example
IDENTIFICATION OF NONLINEAR
SYSTEMS
Parametric Models
Regression Models
Kolmogorov-Gabor (KG-)
Polynomial Model
Basis Function Network Models
The Basic Idea
Nonlinear Network Model
Structures
Input-Output Models Based on
Nonlinear Differential Equations
Nonlinear State-Space Models
State-Space Modeling by
Filtering
Sliding Mode System Reference
Adaptive Model (SRAM)
Subspace Models
Nonparametric Models
The Volterra Series Model
The Wiener Kernel Model
Generalized Frequency Response
Models
Other Types of Nonparametric
Models
Step Response Model
Phase Plane Model
Non-parametric State Dependent
Parameter Model
Semi-Parametric Models
Fuzzy Models
Mamdani-Model
Takagi-Sugeno-Model
Neuro-Fuzzy (NF-) Models
Specific Nonlinear Models
Block-oriented Models
Hammerstein Model
Wiener Model
Other Block-oriented Models
The Bilinear Model
Signal Dependent Parameter
Models
Identification Methods
Estimation of Model Parameters
Parameter Estimation for
LIP-Type Models
Parameter Estimation for
Non-LIP-Type Models
Prediction Error Methods
Numerical Search Methods
Estimation of Model Structure
Model Validation
Critical Valuation of the Most
Important Nonlinear Models
NONPARAMETRIC SYSTEM
IDENTIFICATION
Representation of Nonlinear
Systems
Identification of Wiener Kernels
Wiener’s Orthogonal Expansion
Method
Lee-Schetzen’s Method
Identification of Volterra
Kernels
Hooper-Gyftopoulos Method
Watanabe-Stark’s Method
Kashiwagi-Sun’s Method
Frequency Domain Approach
IDENTIFICATION OF NARMAX AND
RELATED MODELS
System Identification
Nonlinear Models vs. Linear
Models
The NARMAX model
Practical Implementations of the
NARMAX model
Polynomials and Rational Implementations
Neural Network Representations
Multilayer Perceptron Networks
Radial Basis Function Networks
Wavelet Implementations
The Wavelet Network
Wavelet Multiresolution Models
The NARMAX Method
Structure Determination and Parameter Estimation
Nonlinear in the Parameter Models
Linear in the Parameters Models
Model Validation
Mapping the NARMAX Model in the
Frequency Domain
A Practical Example
SYSTEM IDENTIFICATION USING
NEURAL NETWORKS
Artificial
Neural Networks
Static
Neural Networks
Multi-Layer Perceptron Networks
Radial-Basis Function Networks
Local
Model Networks
Dynamic Neural Networks
Dynamic Multi-Layer Perceptron
Networks
Recurrent Networks
System
Identification using Artificial
Neural Networks
Identification of Discrete-Time
Systems
Identification of
Continuous-Time Systems
Miscellaneous Issues
SYSTEM IDENTIFICATION USING
FUZZY MODELS
Nonlinear Dynamic Models for
System Identification
Fuzzy Models
Mamdani Model
Takagi-Sugeno model
Fuzzy Logic Operators
Dynamic Fuzzy Models
Identification of Fuzzy Models
Structure and Parameters
Estimation of Consequent
Parameters
Construction of Antecedent
Membership Functions
Model Validation
Illustrative Example
SYSTEM IDENTIFICATION USING
WAVELETS
Wavelets A Brief Overview
The Continuous Wavelet Transform
Wavelet Series
Dyadic Wavelets
Wavelet Multiresolution
Approximations
System Identification
System Identification using
Wavelets
System Identification Using
Wavelet Networks
The Wavelet Network Model
Structure Selection and
Parameter Estimation for Wavelet
Network Models
Wavelet Multiresolution Models
The B-spline Wavelet
Multiresolution Model Structure
Model Sequencing and Structure
Selection
PARAMETER ESTIMATION FOR
DIFFERENTIAL EQUATIONS
The Hartley Transformation
The Continuous Hartley Transform
(CHT)
Properties of CHT
Scaling of Variable
Convolution in Time-domain
Multiplication in the
Time-Domain
Differentiation
The Discrete Hartley Transform
(DHT)
The Hartley Modulating Functions
Definition
Properties of HMF
Spectra for Derivatives of
Signals
Spectra for the Product of a
Measured Signal and the
Derivative of Another
Formulation of the parameter
estimation equation
Linear Systems
Integrable Nonlinear Systems
Modulatible Nonlinear Systems
Computational Issues
Computation of CHT using DHT
Computation of HMF Spectra
Computing the Estimates
Frequency-weighted Estimation
Illustrative Examples
Application to an Inverted
Pendulum Model
Derivation of System Equations
Data Generation
Formulating the Parameter
Estimation Equations
PARAMETER ESTIMATION FOR
NONLINEAR CONTINUOUS-TIME
STATE-SPACE MODELS FROM SAMPLED
DATA
Mathematical Preliminaries
The Prediction-Error Approach to
Parameter Estimation
State-Space Models and State
Estimation
Parameter Estimation for
State-Space Models
State Augmentation
Prediction-Error Approach
Remarks
IDENTIFICATION IN THE FREQUENCY
DOMAIN
Linear System Identification
SI/SO Linear Models
MI/SO Linear Models
Nonlinear System Identification
Volterra Nonlinear Models
Hammerstein and Wiener Nonlinear
Models
SI/SO Nonlinear Models
Models With Nonlinear Feedback
PARAMETRIC IDENTIFICATION USING
SLIDING MODES
State Identification
Parameter Identification
State and parameter
identification
Simulations results
Noiseless Context
Robustness Study
BOUND-BASED IDENTIFICATION
Bounded-error estimation
Characterization of the feasible
set for the parameters
The Error is Affine in the
Parameters
The Error is not Affine in the
Parameters
LINEAR-MODEL CASE
Bounding a linear model: the
simplest case
Computation of the exact
feasible set
Approximate parameter bounding
Limited-complexity polytopes
Ellipsoidal bounding
Box bounding
Parallelotope bounding
Hybrid algorithms
Parameter bounding with unknown
output-error bound
Parameter bounding with
uncertain explanatory-variables
vector
Clashes and outliers
Parameter bounds for
time-varying linear systems
Heuristic recursive bounding of
time-varying parameters using
ellipsoids
Bounding of time-varying
parameters treated as state
variables
NONLINEAR-MODEL CASE
Definitions and notation
Classification of non-linear
parameter bounding algorithms
Intersection
Encapsulation
Discrete approximation
Projection
Special model classes
Example
PRACTICAL ISSUES OF SYSTEM
IDENTIFICATION
The Framework
Starting Point
Some Typical Model Structures
Estimating the Parameters
The User and the System
Identification Problem
The Tool: Interactive Software
Choice of Input Signals
Common Input Signals
Preprocessing Data
Drifts and Detrending
Prefiltering
Selecting Model Structures
Some Applications
CONTROL OF LINEAR MULTIVARIABLE
SYSTEMS
Linear Multivariable Systems
Emergence of State Space Approach
Discrete-time Control
Riccati Equation and Stabilization for Continuous-time Systems
Design Procedure
Static Output Feedback and Dynamic Compensation
Servo Control and Internal Model Principle
Design and Analysis based on Frequency Response
Control System Example
Control System Example
Parameters of the system
DESCRIPTION AND CLASSIFICATION
IN MIMO DESIGN
Models
Dynamical systems and
Laplace
transform
State-space equations
Transfer-function Matrices
Polynomial matrix models
Differential-delay models
A parallel development for
discrete-time systems
Model Reduction and
Approximation
Control Systems Design
SISO feedback systems
Nyquist stability test for SISO
systems
Control design specifications
Root-Locus
Phase and Gain Margin
Guidance from special cases
Some Comments on State Space
Methods
Translating SISO concepts into
MIMO world
Some Basic Relationships
Interaction and Robustness in
MIMO systems
Frequency domain methods
Background
Design and Interaction
Design and Eigenstructure of
Q(s)
The Development of Frequency
Domain Optimisation Methods
Multivariable Root-loci
Simple MIMO Models in Design
The Future?
Time domain techniques
Eigenstructure and Pole
Allocation
Measurement Issues and Observers
Optimal Control
Interaction and Decoupling
Disturbance Rejection
Direct Computational Search
Methods
The Future?
Non-standard MIMO problems
CANONICAL FORMS FOR STATE SPACE
DESCRIPTIONS
State Space Representations,
Matrix Pencils and State Space
Transformations
Matrix Pencils and Kronecker
Form
Background
Matrix Pencils and Strict
Equivalence
Smith Forms, Invariants and
Duality
Regular Pencils, Elementary
Divisors and Weierstrass Form
Singular Pencils, Minimal Bases
and Kronecker Form:
Canonical Form under Similarity:
Autonomous Descriptions with no
outputs
Kronecker Form under the Full
State Space Transformation Group
Brunovsky Canonical forms under
Coordinate and Feedback
Transformations
The System S(A,B) and its
Kronecker form
The system S(A,C) and its
duality with S(A,B)
Canonical Forms under Coordinate
Transformations
Echelon Form of Polynomial
Matrices
Canonical Form for (A,B), (C,A)
pairs under similarity
Transformations.
Relationships to MFDs and
realization
MULTIVARIABLE POLES AND ZEROS
System Representations and
Classification
Background on Polynomial
matrices and Matrix Pencils
Finite Poles and Zeros of State
Space Models: Dynamics and their
Geometry
Eigenvalues, Eigenvectors and
Free Rectilinear Motions.
Forced Rectilinear Motions and
Frequency Transmission
Frequency Transmission Blocking
and State Space Zeros
Zero Structure and System
Transformations
The Zero Pencil of Strictly
Proper System
Decoupling Zeros
Finite Poles and Zeros of
Transfer Function Models
Dynamic Characterization of
Transfer Function Poles and
Zeros
Smith McMillan form
characterization of Poles and
Zeros
Matrix Fraction Description of
Poles and Zeros
Infinite Poles and Zeros
Smith McMillan form at infinity:
Infinite Poles and Zeros
McMillan Indices at a Point
Impulsive Dynamics and Infinite
Poles and Zeros
Proper Compensation and the
Smith-McMillan form at infinity.
Relationships Between the
Different Types of Zeros, Poles.
Algebraic Function
Characterization of Poles and
Zeros
Characteristic Gain Frequency
Functions.
Poles and Zeros of the System
Algebraic Functions.
Zero Structure Formation in
Systems Design
FREQUENCY DOMAIN REPRESENTATION
AND SINGULAR VALUE
DE-COMPOSITION
Preliminaries
The Laplace Transform and the
Z
-transform
Some Properties of the Laplace
Transform
Some Properties of the
Z
-transform
Norms of Vectors, Matrices and
the SVD
Norms of Finite-dimensional
Vectors and Matrices
The Singular Value Decomposition
Norms of Functions of Time
Induced Operator Norms
Norms of functions of complex
frequency
Connection Between time and
Frequency Domain Spaces
External and
internal representations of
linear systems
External Representation
External Description in the
Frequency Domain
The Bode and Nyquist Diagrams
Internal Representation
Solution in the Time Domain
Solution in the Frequency Domain
The
Concepts of Reachability and
Observability
The Finite Gramians
The Realization Problem
The Solution of the Realization
Problem
Realization of Proper Rational
Matrix Functions
Time and
frequency domain interpretation
of various norms
The Convolution Operator and the
Hankel Operator
Computation of the Singular
Values of
S
Computation of the Singular
Values of
H
Computation of Various Norms
The
H2
norm
The
H∞
norm
The Hilbert-Schmidt Norm
Summary of Norms
The Use of Norms in Control
System Design and Model
Reduction
Model Reduction
POLYNOMIAL AND MATRIX FRACTION
DESCRIPTION
Scalar Systems
Rational Transfer Function
From Transfer Function To
State-Space
Controllable Canonical Form
Observable Canonical Form
From State-Space To Transfer
Function
Minimality
Multivariable Systems
Matrix Fraction Description
Minimality
Properness
Non-Canonical Realizations
Controllable Form
Observable Form
Canonical Realizations
Hermite Form
Popov Form
From Right MFD To Left MFD
From State-Space To MFD
SYSTEM CHARACTERISTICS:
STABILITY, CONTROLLABILITY,
OBSERVABILITY
Mathematical model
Stability
Controllability
Fundamental results
Stabilizability
Output controllability
Controllability with Constrained
Controls
Controllability after the
introducing of sampling
Perturbations of controllable
dynamical systems
Minimum energy control
Observability
MODEL REDUCTION
What is Model Reduction?
Single Component Model Reduction
Multi-Component Model Reduction
The Quality of the Reduced Order Model
Characterization of the Single-Component Model Reduction Error
Linear System Properties
Input-Output Transfer Function
Controllability and Observability
Frequency Moments and Markov Parameters
Output Correlation and Power Moments
Norms
The Conjugate System, Inner, Outer and All-pass Transfer Functions
Model Reduction by Truncation
Minimal Transfer Equivalent Realizations
Component Cost Analysis
Matching Frequency and Power Moments
Balanced Realization and Truncation
Singular Perturbation Truncation
Model Reduction by Optimization
Norm Model Reduction
Norm Model Reduction
The Numerical Solution of Optimal Model Reduction Problems
A Glimpse on the Multi-Component
Model Reduction Problem
Frequency Weighted Balanced Truncation
Tutorial Examples
Example 1
Example 2
FULL-ORDER STATE OBSERVERS
Linear Observers
Continuous-Time Systems
Optimization
Pole-Placement
Discrete-Time Systems
The Separation Principle
Nonlinear Observers
Using Zero-Crossing or Quantized
Observations
Extended Separation Principle
Extended Kalman Filter
REDUCED-ORDER STATE OBSERVERS
Linear, Reduced-Order Observers
Nonlinear Reduced-Order
Observers
KALMAN FILTERS
White Noise
Linear Estimation
The Linear Optimal Estimator in
Discrete Time (Kalman Filter)
Summary of Equations for the
Discrete-Time Kalman Estimator
The Continuous-Time Optimal
Estimator (Kalman-Bucy Filter)
Nonlinear Estimation
Linearization about a Nominal
Trajectory
Linearization about the
Estimated Trajectory
Linearized and Extended Kalman
Filters
Implementation Methods
Modified Cholesky (UD)
Decomposition Algorithms.
Bierman-Thornton UD Filtering
Bierman UD Observational Update
Thornton
UD Temporal Update
Present and Future Applications
of the Kalman Filter
POLE PLACEMENT CONTROL
Separation of state observation
and state feedback
The single-input case
Ackermann’s formula
Numerically stable calculation
via Hessenberg form
The multi-input case
Non-uniqueness
Feedback invariants
Deadbeat control
Reviving the Brunovski structure
Polynomial notation
Calculation without canonical
form
Numerically stable calculation
via HN form
EIGENSTRUCTURE ASSIGNMENT FOR
CONTROL
Definition of Eigenstructure
Assignment
Role of the System
Eigenstructure
Freedom for Eigenstructure
Assignment
Allowable Eigenvector Subspaces
Calculation of Controller
Matrices
Assignment of Desired
Eigenvectors
Compromise between Eigenvalues
and Eigenvectors
Parametric Eigenstructure
Assignment
Multiobjective Robust
Eigenstructure Assignment
Various Eigenstructure
Assignment Techniques
Basic Eigenstructure Assignment
Recursive Eigenstructure Assignment
Low Sensitive Eigenstructure Assignment
Robust Eigenstructure Assignment
Eigenstructure Assignment for Descriptor Systems
Eigenstructure Assignment for Dynamical Compensators
OPTIMAL LINEAR QUADRATIC CONTROL
The LQ regulator in continuous
time
The steady-state LQ regulator in
continuous time
The algebraic Riccati equation
Analytic solution of the Riccati
equation
Properties of the steady-state
LQ regulator in continuous time
Optimal pole locations and the
Chang-Letov design method
Relative stability margins
The inverse optimal control
problem
The LQ regulator in discrete
time
Time-varying plants
Steady-state output regulation
Optimal pole locations
Cheap control
Numerical methods
PONTRYAGIN’S MAXIMUM PRINCIPLE
An Example
The problem of Optimal Control
A More Rigorous Formulation of
the Problem
The Maximum Principle
A Discussion
The Time-Optimal Control Problem
Time-Optimal Control for Linear
Systems
Other Performance Indices
Interpretations and
generalizations of the Maximum
Principle
DECOUPLING CONTROL
Control of a Heat Exchanger
Model
Static Decoupling
Dynamic Decoupling
Process Control Decoupling
Concluding Remarks for the Heat
Exchanger
Dynamic Decoupling
Linear State Feedback with Input
Dynamics
Linear State Feedback
Square Systems
Output Feedback Decoupling
Block Decoupling
Triangular Decoupling
Cost of Decoupling
Static decoupling
Process Control Decoupling
Design
Ideal Decoupling
Simplified Decoupling
Inverted Decoupling
Other Topics
CONTROLLER DESIGN USING
POLYNOMIAL MATRIX DESCRIPTION
Polynomial Approach To Three
Classical Control Problems
Dynamics Assignment
Deadbeat Regulation
H2 Optimal Control
Numerical Methods for Polynomial
Matrices
Diophantine Equation
Spectral Factorization Equation
DESIGN TECHNIQUES IN THE
FREQUENCY DOMAIN
Frequency Responses and
Stability
Single loop stability
Multivariable stability using
Characteristic loci
Multivariable stability using
Gershgorin bands on Nyquist
arrays
Diagonal Dominance
Basic Design
Multivariable Design Methods
Integrating the multivariable
design methods
A Design Example for an Unstable
Chemical Reactor
Description of the chemical
reactor
Uncompensated squared down
reactor
Scaling
High and low frequency
compensation
Closed loop analysis
DESIGN TECHNIQUES FOR
TIME-VARYING SYSTEMS
Model Descriptions
State-Space Models
Input-Output Models
Impulse Response
Polynomial Fraction Descriptions
Converting from One Description
to Another
Frequency Domain Techniques
Stabilization Techniques
Stability
Lyapunov Stability
State Feedback Stabilization
Controllability,
Stabilizability, Observability,
and Detectability
Cheng’s Method
Optimal State-Feedback Regulator
Output Feedback
Pole Placement
Causal information controllers
Frozen time approach
Linear parameter varying systems
SERVO CONTROL DESIGN
Classical Servo Control Design
Integrator Based Control
Design Example: Industrial
Regulator
Phase Lag Control
Design Example: Phase Lag
Compensation
Phase Lead Control
Design Example: Phase Lead
Compensation
Modern Servo Control Design
Feedforward Control: Input
Shaping
Mathematical Analysis of the
Input Shaping Scheme
Design Example: Input Shaping
for Unit Step Command
Feedback Control
Controller Parameterization
Time Domain Parameter
Optimization
Design Example: Parameter
Optimization Method
Frequency Domain Parameter
Optimization
Design Example: Frequency Domain
Parameter Optimization
ROBUST CONTROL
Feedback and Robustness
Robustness and Integral Control
A Short History of Control
Theory and Robust Control
The Classical Period
Modern Control Theory
The Servomechanism Problem
Post-modern Control Theory
The Parametric Theory
Robustness of Control Systems
Performance Issues and Tradeoffs
Zero Steady State Errors
Feedback Stabilization of Linear
Systems
Stabilization by Observer Based
State Feedback
Pole Placement Compensators
YJBK Parameterization
Nyquist Criterion
Optimal Control: Linear
Quadratic Regulator (LQR)
Uncertainty Models and
Robustness
Gain and Phase Margin
Parametric Uncertainty
Nonparametric and Mixed
Uncertainty
H∞ Optimal Control
State Space Theory of H∞ Optimal
Control
Linear Matrix Inequalities
Frequency Domain Aspects of H∞
Optimal Control
µ Theory
Quantitative Feedback Theory
UNCERTAINTY MODELS FOR
ROBUSTNESS ANALYSIS
Notation and definitions
Uncertainty representation and
robustness problems
Unstructured uncertainty models
Structured uncertainty models
Highly structured (parametric)
uncertainty models
State space uncertainty models
Unstructured State Space Uncertainty
Parametric State Space Uncertainty
ROBUSTNESS UNDER REAL PARAMETER
UNCERTAINTY
Notations and Preliminaries
Parametric Uncertainty
Boundary Crossing and Zero
Exclusion
Real Parameter Stability Margin
l2 Real Parametric Stability
Margin
l2 Stability Margin for
Time-delay Systems
Extremal Results in Parametric
Robust Control Theory
Kharitonov’s Theorem
The Edge Theorem
The Generalized Kharitonov
Theorem
Frequency Domain Analysis of
Uncertain Systems
Frequency Domain Properties
Closed
Loop
Transfer Functions
Robust Classical Controller
Design
∞ OPTIMAL CONTROL
The Minimum Sensitivity Problem
Robustness and the Sensitivity
Functions
The Mixed Sensitivity Problem
The Standard Problem and its
Solutions
The Standard Problem
Early Solutions
Solution Based on Spectral
Factorization
State Space Solution
Other Solutions
Optimal Solutions
Extensions to Nonlinear and
Infinite-Dimensional Systems
Application to Robust Control
System Design
l1
ROBUST CONTROL
The l1 Norm
Robustness To Signal
Uncertainty: The l1 Norm
Minimization Problem
A Duality Result
The Scaled-Q Method for Solving
the l1
Optimization Problem
An Auxiliary Problem
Relating the Auxiliary Problem
to the l1
Problem
Example
Robustness to Unmodeled Dynamics
Conditions for Robustness
MU-SYNTHESIS
Control Design via D - K
Iteration
Linear Fractional
Transformations, LFTs
Robust Control Problem
Formulation
D - K Iteration for Complex
Uncertainty
Two-Step Procedure for
Scalar entries
d
of
D
Two-Step Procedure for Full D
(D, G) - K Iteration for Real
and Complex Uncertainty
Control Design Using Fixed-Order
Scalings
CONTROLLER DESIGN USING LINEAR
MATRIX INEQUALITIES
Design Specifications and Linear
Matrix Inequalities
Pole Region Assignment
H2 Performance
H¥ Performance
Controller Design Using Linear
Matrix Inequalities
Linearizing Change of Variables - State Feedback
Linearizing Change of Variables - Output Feedback
LMI Approach to Multiobjective Design
Existence of Solutions and Conservatism of Design
Illustrative Design Example:
Robust Control of a Power System
Stabilizer
Problem Description
Design Specifications in Terms of a Generalized Plant
Modeling the Parameter Uncertainty
LMI-Based Design
ROBUST CONTROL OF NONLINEAR
SYSTEMS: A CONTROL LYAPUNOV
FUNCTION APPROACH
Robust Control Lyapunov Function
(RCLF)
Disturbance attenuation
Construction of RCLFs by
Backstepping
Cost-to-Come Function for Output
Feedback
FUNDAMENTALS OF THE QUANTITATIVE
FEEDBACK THEORY TECHNIQUE
The MISO Analog Control Systems
MISO System
Synthesize Tracking Models
Disturbance Model
J LTI Plant Models
Nominal Plant
U-Contour (Stability bound)
Optimal Bounds Bo(jw) on Lo(jw)
Tracking Bounds
Disturbance Bounds
Synthesizing (or
Loop
Shaping) and Lo(s) and
F(s)
Prefilter Design
Simulation
QFT CAD Packages
The MISO Discrete Control System
s- To z-Plane Transformation:
Tustin Transformation
The MISO Sampled-data Control
System
QFT Technique Applied To The
Pseudo-Continuous-Time (PCT)
System
Introduction To PCT System DIG
Technique
The PCT System Of Figure 17
PCT Design Summary
Controller Implementation
Analysis of the Characteristic
Equation Qj(z)
Simulation and CAD Packages
MIMO Systems
Derivation of m2 MISO System
Equivalents
Tracking and Cross-coupling
Effect Specifications
Tracking Specifications
Disturbance Specification
(Cross-coupling Effect)
Determination of Tracking,
Cross-coupling, and Optimal
Bounds
Tracking Bounds
Cross-coupling Bounds
Optimal Bounds
QFT Methods of Designing MIMO
Systems
Method 1
Method 2
Synthesizing the
Loop
Transmission and Prefilter
Functions
Overview of the MIMO/QFT CAD
Package [12]
MIMO QFT With External (Input)
Disturbance(s)
QFT Application
ADAPTIVE CONTROL
Basic Concepts and Definitions
Historical Background
Gradient Based Adaptive Methods:
The MIT Rule and Park’s Proof of
Instability:
Stable Adaptive Systems
Lyapunov Theory Based Design
Identification and Adaptive
Control of Higher Order Systems
Identification
Control
Adaptive Observers
Non-minimal Representation
Minimal Representation
Error Models:
The Adaptive Control Problem
(Relative Degree n*=1)
The Adaptive Control Problem
(Relative Degree n* ≥2)
Persistent Excitation
Robust Adaptive Control
Time-Varying Systems
Unmodeled Plant Dynamics
Hybrid Adaptive Control
Relaxation of Assumptions
Multivariable Adaptive Control
Nonlinear Adaptive Control
Recent Contributions
Decentralized Adaptive Control
Adaptive Control Using Multiple
Models
RELAY AUTOTUNING OF PID
CONTROLLERS
Relay Autotuning
Analysis of Relay Autotuning
using the DF method
Controller Design Based on the
Critical Point
Further Considerations
SELF-TUNING CONTROL
Categorization of Self-Tuning
Controllers
Explicit or implicit
Continuous-time or discrete-time
Choice of controller design method
Choice of identification method
Implicit generalized minimum
variance control
Practical issues
Choice of design parameters
Integral action
Initial conditions
Examples
Example 1: Implicit Model-Reference Control
Example 2: Explicit Model-Reference Control
Example 3: Explicit Pole-placement Control of non-minimum phase
system
Examples 4 and 5 : Under-modeled systems
Future prospects
MODEL REFERENCE ADAPTIVE CONTROL
Dynamic Models
Identification Model
Reference Model
Explicit and Implicit Model
Following
Reference Model with Inputs
Model Reference Adaptive Control
Parameter Identification
ADAPTIVE PREDICITIVE CONTROL
System models and long-range
prediction
General long-range prediction models
Dynamic matrix control prediction model
Generalized predictive control prediction model
The GPC control law
Robustness analysis
Self-tuning aspects
STOCHASTIC ADAPTIVE CONTROL
Adaptive Control of Markov
Chains
Adaptive Control of ARMAX models
Adaptive Control of Continuous
Time Linear Stochastic Systems
Some Generalizations of Adaptive
Control
ADAPTIVE DUAL CONTROL
Stochastic Adaptive Control
Optimal Dual Controllers
Suboptimal Dual Controllers
Perturbation Signals
Constrained One-Step-Ahead
Minimization
Approximations of the Loss
Function
Modifications of the Loss
Function
Finite Parameter Sets
When To Use Dual Control?
ADAPTIVE NONLINEAR CONTROL
Backstepping
Tuning Functions Design:
Examples
General Recursive Design:
Procedure
Modular Design
Controller design
Identifier Design
CONTROL OF INTERMITTENT
PROCESSES
Definitions, physical and
mathematical models
Classes of Cyclic Processes
System Models
Transfer Function Models
Finite Horizon Operator Models
Repetitive and iterative
learning control schemes
Designing ILC for real world
applications
ILC as an Inverse Problem
Delays and Degree of Difference
Derivation of the Design Equation of ILC
Optimizing ILC
Design Aspects
Signal Conditioning
Robustness issues and focus of
research
Robustness Against Model Inaccuracies
Robustness Against Measurement Noise
Robustness Against Initial State Variations
Focus of Research
Industrial application examples
Iterative Learning Control of the Aluminium Extrusion Process
Controlling Multiple Input/Multiple Output Systems using ILC
Repetitive Control of a Scanner
Mirror
MODEL-BASED PREDICTIVE CONTROL
The Constrained Open-Loop
Optimal Control (COLOC) Problem
Zero Terminal-State MBPC
Set-Membership Terminal
Constraint
Time-Varying Ellipsoidal
Terminal Constraint
Models, Disturbances and
Robustness
Predictive Command Governors
NONLINEAR MODEL PREDICTIVE
CONTROL
Theoretical Aspects of NMPC
Stability
Infinite Horizon NMPC
Finite Horizon NMPC Schemes with Guaranteed Stability
Performance of Finite Horizon NMPC Formulations
Robust Stability
Inherent Robustness of NMPC
Robust NMPC Schemes
Output Feedback NMPC
Stability of Output-Feedback NMPC
Computational Aspects of NMPC
Solution Methods for the Open-Loop Optimal Control Problem
Solution of the NMPC Problem Using Direct Methods
Efficient Solution of the Open-Loop Optimal Control Problem
Efficient NMPC Formulations
MODEL BASED PREDICTIVE CONTROL
FOR LINEAR SYSTEMS
The MBPC Principle
SISO MBPC
The Process Model
The EPSAC Approach to MBPC
The Multistep Predictor
The Predictive Controller
Extensions
Stability and Robustness
Numerical Stability: Singular
Value Decomposition and
Principal Components Analysis
Nonlinear EPSAC (NEPSAC)
MIMO MBPC
The Method
The Control Objective
CONTROLS OF LARGE-SCALE SYSTEMS
Historical Background
Modeling and Model Reduction
Aggregation
Balanced Aggregation
Perturbation
Weakly Coupled Models
Strongly Coupled Models
Hierarchical Control
Goal Coordination:
Interaction Balance
Interaction Prediction
Decentralized Control
Stabilization Problem
Fixed Modes and Polynomials
Stabilization via Dynamic
Compensation
CONTROL OF STOCHASTIC SYSTEMS
Models of Stochastic Systems
Optimal Stochastic Control
Stability of Stochastic Systems
Estimation of Stochastic Systems
Identification and Parameter
Estimation of Stochastic Systems
Control of Partially Observed
Systems
Adaptive Control
MODELS OF STOCHASTIC SYSTEMS
Random variables
Probability Density Function
Expectation Operator
The Mean Value
The Covariance Matrix
The Gaussian Probability Density
Function
Conditional Probability
Conditional Expectation Operator
Independent Random Vectors
Characteristic Function
Characteristic Function for
Gaussian Probability Density
Characteristic Function for
Independent Random Vectors
Description of stochastic
process
Correlation and Crosscorrelation
White Noise
Wiener Process, or Brownian
Motion
Stationary Processes
Ergodicity
Continuous and Discrete Time
Random Processes
Finite dimensional
approximations
Markov Process
The Chapman-Kolmogorov Equation
Hidden Markov Processes
Homogeneous Markov Process
The Fokker-Planck Equation
Spectra of Continuous-time
Random Processes
Power Density Spectra and
Colored Noise
Spectra of Discrete Time Random
Processes
Polynomial Approximation
MA Model
AR Model
ARMA Model
Mixed stochastic-deterministic
systems
CARMA/CARIMA and Box-Jenkins
Models
State-space Approximation
Stochastic differential
equations
Definition of a Stochastic
Differential Equation
Relation between Differential
Equations in the sense of Ito
and Stratonovich Wong-Zakai
Correction
STOCHASTIC STABILITY
Stability and Liapunov Functions
The Stochastic Problem:
Definitions and Preliminaries
Stochastic Liapunov Functions
Examples and the Perturbed
Liapunov Function
MINIMUM VARIANCE CONTROL
Prediction
Discrete-Time Model
Initial conditions
Stochastic Interpretation
| 
|
Login
