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Multivariable Feedback Control Systems


Development of Application Package and Educational Laboratory Equipment for Analysis and Design of Linear and Nonlinear Multivariable Feedback Control Systems

Tech Area / Field

  • MAN-COM/CAD and CAM/Manufacturing Technology
  • INF-SOF/Software/Information and Communications
  • MAN-MCH/Machinery and Tools/Manufacturing Technology
  • MAN-MPS/Manufacturing, Planning, Processing and Control/Manufacturing Technology
  • SAT-AER/Aeronautics/Space, Aircraft and Surface Transportation

3 Approved without Funding

Registration date

Leading Institute
National Polytechnical University of Armenia, Armenia, Yerevan

Supporting institutes

  • Closed Joint-Stock Company "Infokom-Alpha", Armenia, Yerevan


  • Universita Degli Studi di Siena, Italy, Siena\nUniversity of Thessaloniki / Department of Mathematics, Greece, Thessaloniki\nUniversity of Calgary, Canada, AB, Calgary\nLouisiana State University / Department of Mechanical Engineering, USA, LA, Baton Rouge\nUS Military Academy, USA, NY, West Point\nEADS Space Transportation (EADS ST GmbH), Germany, Bremen\nUniversity of Glasgow / Department of Electronics and Electrical Engineering, UK, Glasgow\nInstitute Superior Tecnico / Institute for Systems and Robotics, Portugal, Lisbon\nCleveland State University / Electrical and Computer Engineering, USA, OH, Cleveland\nNational Instruments / National Instruments Russia, Russia, Moscow\nKingston University / Faculty of Engineering, UK, Kingston\nMaritime University of Szczecin, Poland, Szczecin\nCaledonian University, UK, Glasgow

Project summary

Multivariable feedback control is an urgent and therefore a highly active research area in modern control theory and engineering. This is due to the fact that multivariable (called also multi-input multi-output [MIMO]) control systems are widespread in different branches of industry (e.g. power, textile, steel production, oil-refining, automotive, etc., industries) and in numerous technical applications such as aerospace and marine engineering, robotics, angular position control of radars and telescopes, active vibration isolation systems, adaptive optics, and many others.

One of the most efficient approaches to the MIMO systems analysis and design is based on the Characteristic Gain Loci (CGL) method proposed by renowned English theorist A.G.J. MacFarlane and his colleagues in 1970-80s. For a long time, the CGL method has been considered in the technical literature as a sophisticated method applicable mainly to the stability analysis of linear MIMO systems. Based on the ideas of the CGL method, scientific leader of the Project O.Gasparyan developed in his works an engineering theory of linear and nonlinear MIMO control systems as a straightforward extension of the classical control theory to the multidimensional case. The corresponding methods and techniques were successfully used for the design of a number of astronomical and special-purpose space telescopes. Being unknown before to the international scientific community, these methods and techniques have aroused recently keen interest in academia and industry. In particular, John Wiley & Sons (Chichester, UK) publishing house signed a contract with O.Gasparyan for writing a textbook “Linear and Nonlinear Multivariable Feedback Control: A Classical Approach”.

The introduction of any new theoretical approach into engineering practice and academy demands availability of special computer-aided means (preferably, in the form of interactive Graphical User Interfaces [GUIs]) that would allow engineers, researchers or students to implement the analysis and design of control systems. On the other hand, the effective study of new design principles in control engineering cannot be performed without adequate educational and training laboratory equipment.

Actually, two different branches of industry have been initiated by the mentioned necessity for the specialized application packages and educational laboratory equipment, and a great number of the corresponding products are available now in the commercial market.

Thus, the problem of Computer-Aided Control System Design (CACSD) is now one of the central problems in modern control engineering. As a result, many commercial firms are intensively engaged in that area. The recognized world leaders here are such corporations and firms as The MathWorks, Inc., National Instruments, The Wolfram Research, Inc., MCS Software (all - USA), and some others.

It should be noted that the application of the well-known GUIs in the CACSD domain is mainly restricted to linear single-input single-output (SISO) control systems (The SISO Design Tool [The MathWorks, Inc.], LabViewControl Design Assistant [National Instruments], The Control System Professional [The Wolfram Research, Inc.], Analysis & Simulation Toolkit [MCS.EASY5 Software], VisSim [Visual Solutions, Inc.], etc.). An evident progress in extending the CACSD tools to linear MIMO systems relates to the methods of robust control (the most indicative example is the Robust Control Toolbox in MATLAB). However, these methods virtually do not allow taking into account such extremely important structural features of MIMO control systems as uniformity, symmetry, anti-symmetry, etc., which narrows to a certain extent the application limits of the robust control methods and reduces the efficiency of synthesized with their help controllers.

As for the analytical investigation of nonlinear MIMO systems, the related tasks are not practically touched upon in the advanced packages on CACSD, though the problems of computer modelling of nonlinear MIMO systems are substantially solved in such packages as SIMULINK (MATLAB), Analysis & Simulation Toolkit (MCS.EASY5 Software) and others.

The development and manufacture of educational and training laboratory equipment for the study of feedback control systems is another extensive branch of industry worldwide. Among the producers of the control laboratory equipment are National Instruments, Educational Control Products, US Didactic, BOALEECO (all-USA), TQ Education and Training Ltd, Feedback Instruments Ltd, E&L Instruments Ltd, Bytronic International Ltd (all-UK), Quanser (Canada), The Lucas-Nülle Group of Companies (Germany) and others. These firms provide to universities, research institutions, and industrial sites a wide range of laboratory systems and experiments, actually covering all the fundamental principles of control engineering, from the introductory SISO control to advanced robust, optimal, adaptive control, etc. At the same time, here also there exists a definite lack of laboratory equipment for the study of multivariable feedback control, especially nonlinear MIMO control.

In the Project, it is planned the development of an interactive GUI (called The MIMO System Design Tool) working in the MATLAB environment and destined for the analysis and design, on the basis of the classical control methods, of linear and nonlinear MIMO feedback systems of the principal structural classes described in the technical literature. That GUI will realize the main theoretical approaches and results presented in the above-mentioned textbook by O.Gasparyan. The design of a MIMO system with any number of channels will be rigorously, that is without any approximation or model order reduction, accomplished in the GUI as the design of a certain fictitious SISO system with generally complex parameters. Here it is necessary to emphasize the following expected results, having important scientific and practical significance, which are actually not available in the CACSD packages of the world leading firms:

  1. Computational methods and techniques for the analysis of one-frequency limit cycle in nonlinear MIMO systems (on the basis of the describing function method).
  2. Computational methods and procedures for the absolute stability analysis of nonlinear MIMO systems (on the basis of V.M.Popov criterion, circular criteria, etc.).
  3. Program routines for the construction of multidimensional root loci for linear MIMO systems of the main structural types (uniform, symmetrical, anti-symmetrical, circulant, etc.).
  4. Interactive procedures and techniques for choosing the correction in linear and nonlinear MIMO systems on the basis of the central frequency-domain and root methods known from classical control theory (Bode, Nyquist, Nichols, Evans, etc.).

A distinctive and important feature of the planned GUI is that all the analysis and design procedures will be, regardless of the MIMO system order and the strength of cross-couplings, quite analogous to the traditional procedures used in the SISO control engineering. GUI The MIMO System Design Tool may find a wide application at the institutions and firms, engaged in the development and manufacture of complex MIMO control systems in various branches of industry and engineering. Besides, it may be used at universities, technical colleges, etc., as a visual and flexible tool presenting the fundamentals of classical and, within the scope of frequency-domain and root methods, modern control theory.

Another major task of the Project consists in the development and manufacture of a demonstration prototype for a set of complementary laboratory devices intended for the study of MIMO feedback control principles. The core device of that set will be a two-axis optical tracking system with a laser pointer supplied by additional instrumental facilities for introducing cross-couplings between separate channels of the system. By assigning appropriate values to the cross-connections in the two-axis system, the structure of the latter can be reduced to any desired type (uniform, symmetric, anti-symmetric, etc.) thereby allowing the study of salient features of the main structural classes of MIMO systems. By means of the developed laboratory equipment, the engineer, researcher or student may investigate dynamics and performance characteristics of the MIMO systems designed with the help of GUI The MIMO System Design Tool. Like that GUI, the planned laboratory equipment may be used at educational institutions and industry, for practical exercises, innovative control experiments, and for teaching and training at all levels – from introducing control principles to advanced MIMO control applications.

In future, it is planned to organize the production of both the GUI and the laboratory equipment, and thereby to make them both commercially available for educational and research institutions, as well as for the industry.

It is planned the participation in the Project of one Doctor of Engineering Sciences, five Candidates of Sciences (PhD), and six highly-qualified specialists having more than 15 years experience in the related fields. Five of the Project participants were involved in the development, manufacture, and flight tests of precise guidance systems for orbital astronomical telescopes “Orion-2” (launched in 1973), ”Astron” (1983), ”Glazar-1” (1987), “Glazar-2” (1990), as well as in the design and dynamical modelling of some other special-purpose pointing systems. The Project participants have published more than 160 scientific papers on the related topics.

The role of foreign collaborators will consist in exchange of information during project implementation, joint investigations, mutual review of technical reports, joint seminars, meetings, consultations, etc.

The proposed Project completely responds to the primary ISTC objective – to provide to weapons scientists and engineers the opportunity for peaceful scientific and research activity, promoting integration of scientists of CIS states into the international scientific community, reinforcing the transition to market-based economies responsive to civil needs, possibility of familiarizing foreign organizations with unique science research implemented in CIS.