Ebook: Multivariable Computer-controlled Systems: A Transfer Function Approach

The transfer function approach is widely used in classical control theory for its easy handling and physical meaning. Although the use of transfer functions is well-established for linear time-invariant systems, it is not suitable for non-stationary systems among which are sampled-data systems and processes with periodically varying coefficients. Computer-controlled continuous-time processes are a very important subset of periodic sampled-data systems which are not treatable using ordinary transfer functions.

Having established the ability of the parametric transfer function to solve this problem for single-input, single-output systems in previous work, the authors extend these methods, which incorporate time-dependence, to the idea of the parametric transfer matrix in a complete exposition of analysis and design methods for multiple-input, multiple-output (MIMO) sampled-data systems.

Multivariable Computer-controlled Systems is divided into three parts:

• Preliminary algebraic material describing the established fundamentals of polynomial and rational matrices necessary for the understanding of later chapters.

• Control problems, important in their own right but which also have a substantial bearing on what follows (eigenvalue assignment and the use of z- and zeta-transforms in discrete systems).

• Frequency methods for the investigation of MIMO sampled-data systems (parametric discrete-time models; stability; stochastic methods; H₂ optimization and L₂ design).

Appendices covering basic mathematical formulae and the description of two MATLAB^® toolboxes round out this self-contained guide to multivariable control systems.

Of special interest to researchers in automatic control and to development engineers working with advanced control technology, Multivariable Computer-controlled Systems will also interest mathematical control theorists and graduate students studying advanced methods of computer-based control.

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The transfer function approach is widely used in classical control theory for its easy handling and physical meaning. Although the use of transfer functions is well-established for linear time-invariant systems, it is not suitable for non-stationary systems among which are sampled-data systems and processes with periodically varying coefficients. Computer-controlled continuous-time processes are a very important subset of periodic sampled-data systems which are not treatable using ordinary transfer functions.

Having established the ability of the parametric transfer function to solve this problem for single-input, single-output systems in previous work, the authors extend these methods, which incorporate time-dependence, to the idea of the parametric transfer matrix in a complete exposition of analysis and design methods for multiple-input, multiple-output (MIMO) sampled-data systems.

Multivariable Computer-controlled Systems is divided into three parts:

• Preliminary algebraic material describing the established fundamentals of polynomial and rational matrices necessary for the understanding of later chapters.

• Control problems, important in their own right but which also have a substantial bearing on what follows (eigenvalue assignment and the use of z- and zeta-transforms in discrete systems).

• Frequency methods for the investigation of MIMO sampled-data systems (parametric discrete-time models; stability; stochastic methods; H₂ optimization and L₂ design).

Appendices covering basic mathematical formulae and the description of two MATLAB^® toolboxes round out this self-contained guide to multivariable control systems.

Of special interest to researchers in automatic control and to development engineers working with advanced control technology, Multivariable Computer-controlled Systems will also interest mathematical control theorists and graduate students studying advanced methods of computer-based control.

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The transfer function approach is widely used in classical control theory for its easy handling and physical meaning. Although the use of transfer functions is well-established for linear time-invariant systems, it is not suitable for non-stationary systems among which are sampled-data systems and processes with periodically varying coefficients. Computer-controlled continuous-time processes are a very important subset of periodic sampled-data systems which are not treatable using ordinary transfer functions.

Having established the ability of the parametric transfer function to solve this problem for single-input, single-output systems in previous work, the authors extend these methods, which incorporate time-dependence, to the idea of the parametric transfer matrix in a complete exposition of analysis and design methods for multiple-input, multiple-output (MIMO) sampled-data systems.

Multivariable Computer-controlled Systems is divided into three parts:

• Preliminary algebraic material describing the established fundamentals of polynomial and rational matrices necessary for the understanding of later chapters.

• Control problems, important in their own right but which also have a substantial bearing on what follows (eigenvalue assignment and the use of z- and zeta-transforms in discrete systems).

• Frequency methods for the investigation of MIMO sampled-data systems (parametric discrete-time models; stability; stochastic methods; H₂ optimization and L₂ design).

Appendices covering basic mathematical formulae and the description of two MATLAB^® toolboxes round out this self-contained guide to multivariable control systems.

Of special interest to researchers in automatic control and to development engineers working with advanced control technology, Multivariable Computer-controlled Systems will also interest mathematical control theorists and graduate students studying advanced methods of computer-based control.

Content:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Polynomial Matrices....Pages 3-51
Fractional Rational Matrices....Pages 53-104
Normal Rational Matrices....Pages 105-145
Front Matter....Pages 147-147
Assignment of Eigenvalues and Eigenstructures by Polynomial Methods....Pages 149-181
Fundamentals for Control of Causal Discrete-time LTI Processes....Pages 183-238
Front Matter....Pages 239-239
Parametric Discrete-time Models of Continuous-time Multivariable Processes....Pages 241-277
Mathematical Description, Stability and Stabilisation of the Standard Sampled-data System in Continuous Time....Pages 279-306
Analysis and Synthesis of SD Systems Under Stochastic Excitation....Pages 307-346
H2 Optimisation of a Single-loop Multivariable SD System....Pages 347-380
$ mathcal{L}_2 $ -Design of SD Systems for 0 < t < ?....Pages 381-428
Back Matter....Pages 429-478

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The transfer function approach is widely used in classical control theory for its easy handling and physical meaning. Although the use of transfer functions is well-established for linear time-invariant systems, it is not suitable for non-stationary systems among which are sampled-data systems and processes with periodically varying coefficients. Computer-controlled continuous-time processes are a very important subset of periodic sampled-data systems which are not treatable using ordinary transfer functions.

Having established the ability of the parametric transfer function to solve this problem for single-input, single-output systems in previous work, the authors extend these methods, which incorporate time-dependence, to the idea of the parametric transfer matrix in a complete exposition of analysis and design methods for multiple-input, multiple-output (MIMO) sampled-data systems.

Multivariable Computer-controlled Systems is divided into three parts:

• Preliminary algebraic material describing the established fundamentals of polynomial and rational matrices necessary for the understanding of later chapters.

• Control problems, important in their own right but which also have a substantial bearing on what follows (eigenvalue assignment and the use of z- and zeta-transforms in discrete systems).

• Frequency methods for the investigation of MIMO sampled-data systems (parametric discrete-time models; stability; stochastic methods; H₂ optimization and L₂ design).

Appendices covering basic mathematical formulae and the description of two MATLAB^® toolboxes round out this self-contained guide to multivariable control systems.

Of special interest to researchers in automatic control and to development engineers working with advanced control technology, Multivariable Computer-controlled Systems will also interest mathematical control theorists and graduate students studying advanced methods of computer-based control.

Content:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Polynomial Matrices....Pages 3-51
Fractional Rational Matrices....Pages 53-104
Normal Rational Matrices....Pages 105-145
Front Matter....Pages 147-147
Assignment of Eigenvalues and Eigenstructures by Polynomial Methods....Pages 149-181
Fundamentals for Control of Causal Discrete-time LTI Processes....Pages 183-238
Front Matter....Pages 239-239
Parametric Discrete-time Models of Continuous-time Multivariable Processes....Pages 241-277
Mathematical Description, Stability and Stabilisation of the Standard Sampled-data System in Continuous Time....Pages 279-306
Analysis and Synthesis of SD Systems Under Stochastic Excitation....Pages 307-346
H2 Optimisation of a Single-loop Multivariable SD System....Pages 347-380
$ mathcal{L}_2 $ -Design of SD Systems for 0 < t < ?....Pages 381-428
Back Matter....Pages 429-478
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