During the 1960's, with the introduction of digital computers, we have witnessed an intensive activity in discrete-data control systems [1]-[9]. With the recent invention of the “ubiquitous” microprocessors, there is a renewed interest in digital control systems [10]-[15]. The present book by Phillips and Nagle is one of such recent books.

Digital control system analysis and design

This paper presents an overview of singular perturbations and time scales (SPaTS) in control theory and applications during the period 1984-2001 (the last such overviews were provided by [231, 371]). Due to the limitations on space, this is in way intended to be an exhaustive survey on the topic.

Singular perturbations and time scales in control theory and applications: An overview

Analytical model of displacement amplification and stiffness optimization for a class of flexure-based compliant mechanisms

Singular Perturbations and Time Scales in Guidance and Control of Aerospace Systems: A Survey

For purpose of simulation of vehicle dynamics, a physical model of an automotive shock absorber has been developed and implemented in several software packages for multibody simulations. In the present paper, the damper model structure is shortly elaborated together with some measurement and estimation techniques to retrieve the model parameters, possibly from dynamometer measurements only. These techniques are illustrated on a shock absorber normally used on the front suspension of a BMW series 7.

Simulation tools, modelling and identification, for an automotive shock absorber in the context of vehicle dynamics

1 Discrete Models in Systems Engineering.- 1.1 Introduction.- 1.2 Some Illustrative Examples.- 1.2.1 Direct Digital Control of a Thermal Process.- 1.2.2 An Inventory Holding Problem.- 1.2.3 Measurement and Control of Liquid Level.- 1.2.4 An Aggregate National Econometric Model.- 1.3 Objectives and Outline of the Book.- 1.4 References.- 2 Representation of Discrete Control Systems.- 2.1 Introduction.- 2.2 Transfer Functions.- 2.2.1 Review of Z-Transforms.- 2.2.2 Effect of Pole Locations.- 2.2.3 Stability Analysis.- 2.2.4 Simplification by Continued-Fraction Expansions.- 2.2.5 Examples.- 2.3 Difference Equations.- 2.3.1 The Nature of Solutions.- 2.3.2 The Free Response.- 2.3.3 The Forced Response.- 2.3.4 Examples.- 2.3.5 Relationship to Transfer Functions.- 2.4. Discrete State Equations.- 2.4.1 Introduction.- 2.4.2 Obtaining the State Equations.- A. From Difference Equations.- B. From Transfer Functions.- 2.4.3 Solution Procedure.- 2.4.4 Examples.- 2.5 Modal Decomposition.- 2.5.1 Eigen-Structure.- 2.5.2 System Modes.- 2.5.3 Some Important Properties.- 2.5.4 Examples.- 2.6 Concluding Remarks.- 2.7 Problems.- 2.8 References.- 3 Structural Properties.- 3.1 Introduction.- 3.2 Controllability.- 3.2.1 Basic Definitions.- 3.2.2 Mode-Controllability Structure.- 3.2.3 Modal Analysis of State-Reachability.- 3.2.4 Some Geometrical Aspects.- 3.2.5 Examples.- 3.3 Observability.- 3.3.1 Basic Definitions.- 3.3.2 Principle of Duality.- 3.3.3 Mode-Observability Structure.- 3.3.4 Concept of Detectability.- 3.3.5 Examples.- 3.4. Stability.- 3.4.1 Introduction.- 3.4.2 Definitions of Stability.- 3.4.3 Linear System Stability.- 3.4.4 Lyapunov Analysis.- 3.4.5 Solution and Properties of the Lyapunov Equation.- 3.4.6 Examples.- 3.5 Remarks.- 3.6 Problems.- 3.7 References.- 4 Design of Feedback Systems.- 4.1 Introduction.- 4.2 The Concept of Linear Feedback.- 4.2.1 State Feedback.- 4.2.2 Output Feedback.- 4.2.3 Computational Algorithms.- 4.2.4 Eigen-Structure Assignment.- 4.2.5 Remarks.- 4.2.6 Example.- 4.3 Deadbeat Controllers.- 4.3.1 Preliminaries.- 4.3.2 The Multi-Input Deadbeat Controller.- 4.3.3 Basic Properties.- 4.3.4 Other Approaches.- 4.3.5 Examples.- 4.4 Development of Reduced-Order Models.- 4.4.1 Analysis.- 4.4.2 Two Simplification Schemes.- 4.4.3 Output Modelling Approach.- 4.4.4 Control Design.- 4.4.5 Examples.- 4.5 Control Systems with Slow and Fast Modes.- 4.5.1 Time-Separation Property.- 4.5.2 Fast and Slow Subsystems.- 4.5.3 A Frequency Domain Interpretation.- 4.5.4 Two-Stage Control Design.- 4.5.5 Examples.- 4.6 Concluding Remarks.- 4.7 Problems.- 4.8 References.- 5 Control of Systems with Inaccessible States.- 5.1 Introduction.- 5.2 State Reconstruction Schemes.- 5.2.1 Full-Order State Reconstructors.- 5.2.2 Reduced-Order State Reconstructors.- 5.2.3 Discussion.- 5.2.4 Deadbeat State Reconstructors.- 5.2.5 Examples.- 5.3 Observer-Based Controllers.- 5.3.1 Structure of Closed-Loop Systems.- 5.3.2 The Separation Principle.- 5.3.3 Deadbeat Type Controllers.- 5.3.4 Example.- 5.4 Two-Level Observation Structures.- 5.4.1 Full-Order Local State Reconstructors.- 5.4.2 Modifications to Ensure Overall Asymptotic Reconstruction.- 5.4.3 Examples.- 5.5 Discrete Two-Time-Scale Systems.- 5.5.1 Introduction.- 5.5.2 Two-Stage Observer Design.- 5.5.3 Dynamic State Feedback Control.- 5.5.4 Example.- 5.6 Concluding Remarks.- 5.7 Problems.- 5.8 References.- 6 State and Parameter Estimation.- 6.1 Introduction.- 6.2 Random Variables and Gauss-Markov Processes.- 6.2.1 Basic Concepts of Probability Theory.- 6.2.2 Mathematical Properties of Random Variables.- A. Distribution Functions.- B. Mathematical Expectation.- C. Two Random Variables.- 6.2.3 Stochastic Processes.- A. Definitions and Properties.- B. Gauss and Markov Processes.- 6.3 Linear Discrete Models with Random Inputs.- 6.3.1 Model Description.- 6.3.2 Some Useful Properties.- 6.3.3 Propagation of Means and Covariances.- 6.3.4 Examples.- 6.4 The Kalman Filter.- 6.4.1 The Estimation Problem.- A. The Filtering Problem.- B. The Smoothing Problem.- C. The Prediction Problem.- 6.4.2 Principal Methods of Obtaining Estimates.- A. Minimum Variance Estimate.- B. Maximum Likelihood Estimate.- C. Maximum A Posteriori Estimate.- 6.4.3 Development of the Kalman Filter Equations.- A. The Optimal Filtering Problem.- B. Solution Procedure.- C. Some Important Properties.- 6.4.4 Examples.- 6.5 Decentralised Computation of the Kalman Fikter.- 6.5.1 Linear Interconnected Dynamical Systems.- 6.5.2 The Basis of the Decentralised Filter Structure.- 6.5.3 The Recursive Equations of the Filter.- 6.5.4 A Computation Comparison.- 6.5.5 Example.- 6.6 Parameter Estimation.- 6.6.1 Least Squares Estimation.- A. Linear Static Models.- B. Standard Least Squares Method and Properties.- C. Application to Parameter Estimation of Dynamic Models.- D. Recursive Least Squares.- E. The Generalised Least Squares Method.- 6.6.2 Two-Level Computational Algorithms.- A. Linear Static Models.- B. A Two-Level Multiple Projection Algorithm.- C. The Recursive Version.- D. Linear Dynamical Models.- E. The Maximum A Posteriori Approach.- F. A Two-Level Structure.- 6.6.3 Examples.- 6.7 Problems.- 6.8 References.- 7 Adaptive Control Systems.- 7.1 Introduction.- 7.2 Basic Concepts of Model Reference Adaptive Systems.- 7.2.1 The Reference Model.- 7.2.2 The Adaptation Mechanism.- 7.2.3 Notations and Some Definitions.- 7.2.4 Design Considerations.- 7.3 Design Techniques.- 7.3.1 Techniques Based on Lyapunov Analysis.- 7.3.2 Techniques Based on Hyperstability and Positivity Concepts.- A. Popov Inequality and Related Results.- B. Systematic Procedure.- C. Parametric Adaptation Schemes.- D. Adaptive Model-Following Schemes.- 7.3.3 Examples.- 7.4 Self-Tuning Regulators.- 7.4.1 Introduction.- 7.4.2 Description of the System.- 7.4.3 Parameter Estimators.- A. The Least Squares Method.- B. The Extended Least Squares Method.- 7.4.4 Control Strategies.- A. Controllers Based on Linear Quadratic Theory.- B. Controllers Based on Minimum Variance Criteria.- 7.4.5 Other Approaches.- A. Pole/Zero Placement Approach.- B. Implicit Identification Approach.- C. State Space Approach.- D. Multivariable Approach.- 7.4.6 Discussion.- 7.4.7 Examples.- 7.5 Concluding Remarks.- 7.6 Problems.- 7.7 References.- 8 Dynamic Optimisation.- 8.1 Introduction.- 8.2 The Dynamic Optimisation Problem.- 8.2.1 Formulation of the Problem.- 8.2.2 Conditions of Optimality.- 8.2.3 The Optimal Return Function.- 8.3 Linear-Quadratic Discrete Regulators.- 8.3.1 Derivation of the Optimal Sequences.- 8.3.2 Steady-State Solution.- 8.3.3 Asymptotic Properties of Optimal Control.- 8.4 Numerical Algorithms for the Discrete Riccati Equation.- 8.4.1 Successive Approximation Methods.- 8.4.2 Hamiltonian Methods.- 8.4.3 Discussion.- 8.4.4 Examples.- 8.5 Hierarchical Optimization Methodology.- 8.5.1 Problem Decomposition.- 8.5.2 Open-Loop Computation Structures.- A. The Goal Coordination Method.- B. The Method of Tamura.- C. The Interaction Prediction Method.- 8.5.3 Closed-Loop Control Structures.- 8.5.4 Examples.- 8.6 Decomposition-Decentralisation Approach.- 8.6.1 Statement of the Problem.- 8.6.2 The Decoupled Subsystems.- 8.6.3 Multi-Controller Structure.- 8.6.4 Examples.- 8.7 Concluding Remarks.- 8.8 Problems.- 8.9 References.

Discrete systems, analysis, control, and optimization

This work demonstrates that the Karnopp-Margolis method for treating derivative causality in the bond graph produces a formulation that is equivalent to the classical Lagrange λ multipliers method for the modeling of planar mechanisms. It is then demonstrated that this formulation can be used to eliminate derivative causality in general. Furthermore, the method can be used as the basis for an algorithm which automates the derivation of the dynamic equations for nonlinear systems. It is also shown that the method can be used to treat the modeling of joint nonlinearities such as joint clearances and joint compliances.

Bond Graph Modeling of Planar Mechanisms With Realistic Joint Effects

Some bond graph structural properties: eigen spectra and stability

SUMMARY This paper describes a multiport approach to computer-aided modeling of vehicle dynamics. The modeling approach produces models that are suitable for the interactive design and evaluation of complex control strategies. The vehicle model which can be used for ride and handling analysis, is built from modular components. The components are programmed using the syntax of the computer aided control system design (CACSD) program EASYS. Seven modeling components are used to create a three-dimensional vehicle dvnamics model. The model is flexible enoug-h to simulate any suspension design with revolute joints. Each component of the model consists of a FORTRAN subroutine and a main calling module called a macro. To simplify the process of model building, the modeling components in the car model are designed to represent physical elements, such as the spring, damper, link or tire. To create a model, the components, which are represented by blocks, are interconnected through points, located on the blocks, ca...

Ashraf Zeid

Papers

Discrete systems, analysis, control, and optimization

Bond Graph Modeling of Planar Mechanisms With Realistic Joint Effects

Some bond graph structural properties: eigen spectra and stability

Some bond graph structural properties: eigen spectra and stability

A Modular Computer Model for the Design of Vehicle Dynamics Control Systems1