MES-2025 Keynote # 1

Application of the Characteristic Transfer Functions Method to the Design of Multivariable Control Systems in Robotics and Mechatronics

Prof. Oleg Gasparyan

Aerial Robotics Center and Control Systems Chair
National Engineering University of Armenia

Many feedback control systems in mechatronics and robotics, including aerial robotics, belong to the class of multivariable control systems, that is multi-input multi-output (MIMO) systems with cross-coupled dynamics of separate channels.

At present, many (if not the most) methods of multivariable feedback control described in the scientific and technical literature are based on the state-space representations of the MIMO control systems. One can mention here optimal control, model predictive control, sliding mode control, adaptive and robust control, etc. At the same time, being quite effective and formalized from the computational point of view, the state-space methods often lack in physical clarity that is inherent in the classical frequency-domain control methods of single-input single-output (SISO) feedback systems. The point is that the state-space methods are not suited well to describe important structural features of the multivariable systems, which is very crucial in designing appropriate MIMO controllers. Moreover, the state-space methods in many cases even do not assume any difference between SISO and MIMO control systems.

The lecture is devoted to the method of Characteristic Transfer Functions (CTF) also called the Gain Loci method. The method of CTFs rests on the transfer matrix representations of MIMO control systems and allows associating with an N-dimensional square, that is having the same number N of inputs and outputs, cross-connected MIMO system a set of N fictitious independent SISO systems. This creates a necessary basis for extending to multivariable case all the main frequency-domain and root-domain methods of classical feedback control concerning stability and performance analysis, design of controllers, etc. In fact, the method of CTFs, allows reducing the design of an N-dimensional multivariable feedback system to a design of a certain SISO system based on the common methods of classical feedback control, or, in other words, it reduces an N-dimensional task to a one-dimensional task. It is important to note that the developed analysis and design procedures and methods account for the main structural features of MIMO control systems known in practice, such as symmetry, skew-symmetry, uniformness, normality, etc.    

For the first time, it will be presented a graphical user interface (GUI) MIMOControlSysCAD, which has been developed at the Aerial Robotics Centre. The GUI works in the MATLAB environment and can be considered as a N-dimensional analogue of the well-known GUI Control System Designer in the Control System Toolbox in MATLAB.