Computer-aided multivariable control system design for processes with time delays

A report is presented on the results of the second benchmark control problem prepared by the Benchmark Working Group of the IEEE Control Systems Society Technical Committee on computer-aided control system design (CACSD). The problem deals with a continuous-time missile autopilot design. The purpose of this benchmark is to provide a useful measure of some of the capabilities of computer-aided control system design packages. The problem requires time simulations, eigenvalue calculations, and frequency-response plots of relatively high-order linear systems. The problem is described, and the results submitted to date are summarized. >

Features in the design of a graphical man-machine interface for pre-processing the inputs to computer-aided control system design software are described in this paper. The primary objective is to allow the control engineer to communicate with a modem graphics workstation in a natural, familiar and friendly way, by means of block diagrams, signal flow graphs and standard mathematical text. Graphical methods for the input and output of these are described. Transformations between different system descriptions are considered which allow all algebraic manipulations and reductions to be performed on signal flow graphs. For these manipulations, rule-based methods are shown to be effective. The possibility of using symbolic computation languages for algebraic operations is also considered.

A description is given of a computer-aided control system design package, NLCON, that supports analysis and design functions for single-input/single-output nonlinear control systems with a single nonlinearity. The single nonlinearity can be one of seven nonlinearities commonly encountered in mechanical systems, and its location within the system is not restricted. The controller design benefits from designer experience, but it is facilitated by the software package, since program operation is highly interactive and the interface is user friendly. The analysis functions supported include sinusoidal-input describing functions and limit-cycle analysis, frequency-response determination, and jump-resonance analysis. Design functions include procedures for compensator modification to modify limit-cycle and jump-resonance behavior. A design advisory is provided for some simple design situations. Examples to illustrate various facets of program operation are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A program for handling multiple phases of the design cycle in process control system design

Parameter Estimation of the Nonlinear Dynamics of a Thyristor Driven DC-Motor Experimental Set-Up Using HMF-Method

WAMS (Wide-Area Measurement Systems) involve all kinds of communicating channels. Different channels have different time delays and randomicity of time-delay. So closed-loop power systems ought to be modeled as nonlinear dynamic systems with multiple time delays and varying time delays. A method is proposed in this paper to design a controller that can adapt to feedback signals with multiple time delays and varying time delays. The method is based on the topological characteristics of stable time-delay regions, the LMIs (Linear Matrix Inequalities) method, GA (Genetic Algorithm) and the balanced truncation model-reduced algorithm. Numerical results form a tow-area four-machine power system demonstrate that the controller derived from the above method can damp low-frequency oscillations in the system for the feedback signals with multiple time delays and varying time delays.

BENCHMARK PROBLEMS FOR COMPUTER-AIDED CONTROL SYSTEM DESIGN

In this article, we study the controllability of finite-dimensional dynamical control systems modelled by semilinear impulsive ordinary differential equations with multiple constant time delays in the control function. Initially, we recall a necessary and sufficient condition for the controllability of the corresponding linear system without impulses, with multiple constant time delays in the control function in terms of a matrix rank condition. Then under some sufficient conditions, we show that the actual system is also controllable for certain classes of non-linearities and impulse functions. We employ Schauder fixed-point theorem and Banach contraction mapping principle to establish the results. Our obtained results are applicable for both autonomous and non-autonomous systems. An example is given to illustrate the theoretical results.

Stability analysis for LTI systems with multiple time delays using the bounds of its imaginary spectra

A description is given of the development of a novel interactive computer-aided control system design (CACSD) package for the design of linear multivariable control systems. The package incorporates the stable factorization design technique and other recent design methodologies, such as the systematic design approach. To provide a high level of interactive design environment for the user, knowledge-based expert system development tools are provided within the package. In addition, the user is provided with the facilities to write user-defined functions and procedures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

&lt;p style='text-indent:20px;'&gt;This research paper deals with the investigation of global robust stability results for Cohen-Grossberg neural networks involving the multiple constant time delays. The activation functions in this neural network model are supposed to be in the set of non-decreasing slope-bounded nonlinear functions and the uncertainties in the constant network parameters are considered to have bounded upper norms. By employing a proper positive definite Lyapunov-type functional and using homeomorphism mapping theory, we propose some novel sets of novel conditions that assure both existence, uniqueness and global robust asymptotic stability of equilibrium points of this nonlinear Cohen-Grossberg-type neural network model involving the multiple time delays. The derived robustly stable conditions mainly rely on examining some proper relationships that are imposed on constant valued interconnection matrices of this delayed neural network. These stability conditions can be certainly verified by employing various simple and useful properties of real interval matrices. Some comparisons are made to address the key advantages of these novel criteria over previously reported corresponding results. An instructive example is also examined to observe novelty of these proposed criteria.&lt;/p&gt;

The problem of the delay-dependent stability of linear systems with multiple time delays is discussed. A new method is first presented for a system with two time delays, in which free weighting matrices are used to express the relationships among the terms of the Leibniz-Newton formula. Next, this method is used to show the equivalence between a system with two identical time delays and a system with a single time delay. Then, a numerical example verifies that the criterion given is effective and is a significant improvement over the existing ones. Finally, the basic idea is extended to a system with multiple time delays.

Exponential stability criteria of uncertain systems with multiple time delays

It is well known that the modeling issues in Dynamical systems in chemical processes, networked control systems and automation systems are very complex and model may contain subsystems with different delays. Because of the mathematical complexity, the robust control of these types of multiple time delay system is a challenging one. The problem becomes more difficult and complex when the system is having time delays in both the denominator and the numerator. In this paper a new method is proposed for approximating general multiple time delay continuous-time transfer function system with multiple time delays in both the denominator and the numerator to a single input/output delay. Both Single Input Single Output(SISO) and Multi Input Multi Output(MIMO) cases have been considered. In this proposed methodology, the Approximated Generalized Time Moments (AGTM)/ Approximated Generalized Markov Parameter (AGMP) methods are used to transform the multiple time delay system into a single input/output delay system. A Linear Matrix Inequality (LMI) approach is developed for synthesizing robust H∞ control of the approximated time delay system. The efficacy of the proposed method is shown through illustrative examples. It is evident from the simulation results that the approximated system is stable with the proposed LMI H∞ controller.

The problem of assigning all poles of a closed-loop system in a specified disk by dynamic output feedback is considered for discrete systems with multiple non-commensurate time delays. This kind of pole assignment problem is called D-pole placement, and its relation to robustness properties is discussed. Thus, the robust D-pole placement is subsequently proposed and a robust criterion is derived to ensure D-stability of the discrete multiple time-delay systems subject to parametric uncertainties. Furthermore, with this robust criterion, the bounds can also be estimated for allowable parametric uncertainties that guarantee all the poles of the discrete uncertain multiple time-delay systems to remain inside the specified disk. Finally, an example is given to illustrate obtained results. >