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Optimal and robust synthesis of controllers for motion control system of partially paralyzed man


V.I. Kapalin – Dr. Sc. (Eng.), Professor, Moscow State University of Information Technologies, Radio Engineering and Electronics (MIREA). E-mail: L.A. Klyuev – Engineer, Employee of Yandex. E-mail: N.E. Vedyashkina – Post-graduate Student, Mathematic Engineer, MIEM HSE (Moscow). E-mail:

Modern methods for the synthesis of regulators with feedback systems use method of optimal control and method of robust control. Application of modal control makes it possible to construct regulators according to the desired poles layout of the feedback system. Another way of the design in this approach consists in use of the optimum control theory. Both ways of the design can be performed with MATLAB by means of Control System Toolbox. The analysis of transient responses can be carried out with Simulink. An alternative to this approach is a robust control. It gives an opportunity to analyze the influence of the possible inaccuracies in the mathematical model of the controlled object. The according regulators design can be carried out also with MATLAB by means of Robust Control Toolbox. The purpose of the present paper is to build optimum and robust regulators for the important case of the control of movements of the partly paralyzed person. The model of the neuromuscular system was given by the transfer function of the second order. The design was performed as for the nominal values of the parameters for its variations due to the personal featured of the patients and their fatigue. The first regulator was built by use of the Riccati equation for single input - single output system with Control System Toolbox. After that the set of the transient responses was constructed with Robust Control Toolbox for the investigation of the influences of the parameters variations of the model. To build controller two Riccati equations were applied using robust control theory, and built a suboptimal control. This process was performed with Robust Control Toolbox. The Bode diagrams were applied to compare two obtained regulators. Its analysis clearly shows that from the point of view of stability margins the best result is given by the robust regulator. The linear suboptimal regulator also gives a good performance and has the advantage in simplicity of its realization.


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