Design Of Linear Control Systems Research Articles

Linear Control System Analysis and Design

Linear Control System Analysis and Design

Linear systems analysis program

The computer program LSAP (Linear Systems Analysis Program) is an interactive program with graphics capability that can be used for the analysis and design of linear control systems. Nearly all classical design tools are available, including manipulation of transfer functions and generation of root locus, time response, and frequency response plots. The program is capable of working with both continuous time systems and sampled data systems. For continuous time systems, the Laplace transform is used, and for sampled data systems, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</tex> -transform is used. The capability of converting from a Laplace transform to a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</tex> -transform is provided.

Matrix factorization and Chandrasekhar equations techniques in the design of linear quadratic optimal control systems

A unified presentation of matrix factorization and Chandrasekhar equations techniques for solving linear quadratic optimal control problems is given in cases of continuous-and discrete-time invariant systems. These techniques are used for designing optimal systems via an augmentation of the system by disturbances and reference models.

Minimal response time design for linear multivariable sampled-data control systems

The method of minimum, finite settling time design used for single-loop systems is extended to cover multivariable systems. Sensitivity analysis is applied and results of considerable generality are derived which indicate the effects of gain changes and pole or zero movement in the plant transfer functions. A design policy is developed which satisfies the need for low sensitivity in implementation. Further development evolves a design technique in which speed of response can be systematically traded for sensitivity. At the same time the technique satisfies the need to achieve a digital control algorithm of minimal complexity. The method of design has been shown to be particularly relevant to systems with lightly damped open-loop modes and an example of this type of system is analysed in detail.

Multivariable controller design for linear systems having multiple time delays

AbstractA multivariable, multidelay compensator, capable of handling general, linear time delay problems is derived in a form applicable both in continuous and discrete time. The controller developed is shown to have the same structure as the linear‐quadratic optimal feedback controller for input delays and reduces to the Smith predictor (and the analytical predictor) for the special case of a single time delay. Some examples representative of engineering practice are used to demonstrate the effectiveness of the controller.

Program Package for Computer Aided Design of Linear Control Systems

A program package for computer aided design of linear control systems (LS) is described which allows the following problems to be solved: (i) synthesis with quadratic cost, (ii) pole and zero assignment, (iii) synthesis with any attainable linearly equivalent form, (iv) synthesis of reduced order observers with any attainable dynamics, (v) synthesis of dynamic compensators and (vi) synthesis of output regulators. Subroutines developed for (iii) - (vi) are based on original results of the authors. The package written in FORTRAN IV uses the standard IBM S/360, S/370 computers software.

Computer Aided Design of Linear Systems via L-A-S Language

The paper describes a hign level interactive conversational language L-A-S (Linear Algebra and Systems) used in analysis and design of linear control systems. The L-A-S language is written in FORTRAN-IV (DEC-10) but its use does not require the knowledge of standard programming languages. Modular structure of the language permits easy modification, updating and extensions. The syntax and semantics are simple, staraitforward so that familiarity with the language may be easily attained. For more than one year the L-A-S language has been used in automatic control education and research at the University of Campinas, Brasil and University of Illinois, USA.

Programme Suite for CAD of Multivariable Control Systems by Poles Assignment Technique

A programe suite for Computer - Aided Design (CAD) of multivariable linear control systems by means of poles assignment technique is described. The suite provides two main parts analysis and syntesis. The part syntesis includes the majority of well known and novel computational procedures devoted to the mentioned problem. The control can be formed by unity or full rank feedback matrices. Special emphasis has been paid on the procedures for poles assignment and simultaneous satisfaction of additional design reguirements.

L-A-S (Linear Algebra and System) language and its use in control system education and research

The paper describes a high level interactive conversational language L-A-S (Linear Algebra and Systems) used in analysis and design of linear control systems. The L-A-S language is written in FOR-TRAN-IV (DEC-PDP 10) but its use does not require the knowledge of standard programming languages. Modular structure of the language permits easy modification updating and extensions. The syntax and semantics are simple and straightforward so that familiarity with the language may be easily attained.

Sequential design of linear multivariable systems

The paper describes and critically assesses, in the light of recent advances, the sequential return difference method for the computer-aided design of linear multivariable control systems. In this method, a sequence of single-loop designs, using classical procedures, yields a multivariable design satisfying various criteria such as stability, disturbance attenuation, low interaction and integrity.

Design-performance-measure statistics for stochastic linear control systems

Formulas for statistics of the standard integral quadratic performance measure used in stochastic linear control system design are derived. The formulas are expressed in terms of dynamical variables under the usual assumptions on noise, plant, and admissibility of control. All of these dynamical variables are expressed as linear transformations of plant state estimates. The practicality of this work, which is directed toward the establishment of new, statistically based design procedures for stochastic linear systems, is demonstrated by example.

A design technique for linear multivariable feedback systems

A systematic approach is developed for the design of linear multivariable feedback control systems based on a manipulation of the set of frequency-conscious eigenvalues and eigenvectors of an open-loop transfer-function matrix. The key idea behind the approach used is that of an approximately-commutative controller. An algorithm for approximation of a frame of complex vectors by a frame of real vectors is developed and plays a basic role in the systematic design approach. An example, based on industrial plant data, is given showing how the design method is used.

Linear Control System Analysis and Design

Linear Control System Analysis and Design

Book Review: Linear Control System Analysis and Design: Conventional and Modern

Book Review: Linear Control System Analysis and Design: Conventional and Modern

Interactive Computer Aided Design of Control Systems

The paper describes operation and use of an interactive software LINSYS used in analysis and design of linear control systems. LINSYS is written in FORTRAN-IV but its use does not require the knowledge of computer programming. Modular structure of the software permits easy modification and extention. LINSYS routines may be also used either independently, or combined, for solving a specific control problem not covered by the software.LINSYS consists of a main program and three oackages RIC, PPL, and ANAL. RIC solves the algebraic Riccati equation, while PPL is used for pole placement and observer design. Within ANAL the user can solve several control problems such as controllability and observability tests, calculation of the state transition matrix, transformation into the Jordan form, etc. Using LINSYS plotting routines it is possible to plot eigenvalue locations and time domain responses to initial conditions and polynomial input signal. Undesired options may be easily avoided by trying an appropriate reply to a computer generated message. All inputs specifying the system to be analysed are format-free. LINSYS is written for DEC-10 digital computer but with slight modifications may be executed on any digital computer having interactive CRT or paper tape terminals.

Compensator design for linear multivariable systems

A configuration and an orderly procedure for the design of linear multivariable control systems are presented. This procedure employs transfer function matrices to specify the system response to set point changes and disturbances. Neither a state-variable formulation nor solution of the matrix Riccati equation are required. The design procedure is illustrated by a simple example involving an unstable system.

Dominant Mode Design of Third-Order Linear Control Systems: Part 2 Open Loop Poles and System Design

This completes the design method begun in the part published in the previous issue by providing loci of the corrected open loop poles required for the selected systems. Two examples are given to illustrate the new approach to performance limitations and correction methods. Pole relocation by cancellation is advocated and the consequences of inexact cancellation are discussed. The mathematics used in the program for the loci is given in two Appendices.

New Design of Linear Control Systems Based on the Principle of State and Output Feed-Back

In this paper, it is shown that the design of a linear control system with following properties: (1) having no steady state error can be guaranteed for all inputs (applied to the control system) and disturbances (applied to the controlled object) described by p-th order polynomials, (2) any set of arbitrarily designated eigenvalues can be always realized, (3) the property (1) of the steady state error can be held unchanged in spite of the change or the ambiguity of system parameters in controlled objects, can be established by the use in combination of state and output (controlled variable) feed-back. Throughout this paper, it is assumed that controlled objects are all controllable observable time-invariant linear systems with m inputs, m outputs and n state variables, and always satisfy a certain condition concerning a steady state solution of the systems. The structure and design formula of the control system for each of the following four cases are given: (1) continuous type of controlled objects (a) with directly measurable states only or (b) with directly unmeasurable states and (2) discrete type of controlled objects (c) with directly measurable states only or (d) with directly unmeasurable states. The practical design procedure and some discussion are also given.

New Interpretations and Justifications for Worst Case Min-Max Design of Linear Control Systems

A method of designing a feedback controller for a linear dynamic system disturbed by additive white noise treats the noise as a maximizing (vindictive) opponent and minimaximizes a quadratic performance criterion which is the difference between the original criterion, for the system performance, and a quadratic function of the maximizing player (noise). This procedure, though well known, is viewed with some suspicion as it appears to be a very pessimistic design method in that it assumes that the noise will “conspire” to oppose the controller in the most perverse way. We show, however, in this paper that the controller obtained in this manner is the same as that obtained by minimizing the expected value of an exponential function of the given quadratic performance criterion. When looked at from this viewpoint the “worst case design” does not appear to be too pessimistic since the exponential criterion is rather appealing. Of theoretical interest is the fact that existence of a solution to the zero sum differential game (which arises in the worst case formulation) implies and is implied by existence of the expected value of the exponential performance criterion.

Low-sensitivity design of optimal linear control systems with transportation lag

The design of low-sensitivity optimal linear control systems with transportation lag, which are relatively insensitive to parameter variations, is presented. The optimal control is with respect to a quadratic performance criterion which includes the state variable, control variable, state sensitivity function and control sensitivity functions as its arguments. A detailed example shows that the low-sensitivity design is superior to the conventional optimal design with respect to sensitivity.