MECHANICS OF MACHINES AND MECHANISMS - MODELS AND MATHEMATICAL METHODS
Plan rada Seminara Mehanika mašina i mehanizama - modeli i matematičke metode za NOVEMBAR 2018.
UTORAK, 20.11.2018. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36
Milan Cajić, Mathematical Institute of SASA, Belgrade, Serbia
VIBRATION OF NONLOCAL ELASTIC AND FRACTIONAL VISCOELASTIC BEAMS WITH ATTACHED MASSES USING TWO DIFFERENT METHODS
In this presentation we will observe the free vibration models of beams with attached masses using two different methods. In the introduction, a history of beam-mass models will be reviewed and compared with respect to modern approaches. Exact method based on compatibility conditions will be presented for the nonlocal fractional viscoelastic nanobeam with a single attached mass. This example will serve to validate more general nanobeam model with attached arbitrary number of masses and influenced by the external magnetic field that is solved via approximate method and analyze in complex and time domain via integral transform methods. Advantages and deficiencies of both models will be emphasized in the conclusion.
UTORAK, 27.11.2018. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36
Mihailo P. Lazarević, Faculty of Mechanical Engineering in Belgrade, Serbia
APPLICATIONS OF (NON)-INTEGER ORDER CALCULUS ON ADVANCED MODELING AND CONTROL OF (BIO) MECHANICAL SYSTEMS: NEW RESULTS
In recent years, there have been extensive research activities related to applications of fractional calculus i.e. calculus of non-integer order in nonlinear dynamics, mechatronics, bioengineering as well as control theory. On the other hand, in many systems in nature are inherently under-actuated, with fewer actuators than degrees of freedom. Double inverted and cart inverted pendulum present well-known models of corresponding biomechanical systems and they are highly nonlinear mechanical systems with one control input and two degrees of freedom. Stability problem of two previous types of inverted pendulum controlled by a non-integer order PD controller in combination with partial feedback linearization technique is studied. Determining its stability regions in parameters space of a fractional order PD controller is studied and presented. Also, it is presented the procedure of mathematical modeling of an exoskeleton systems for rehabilitation with three DOFs and 4 DOFs using the Rodriguez method and synthesis of a iterative control law with two closed loops. Particularly, a new open-closed-loop PIDD2 /PID type iterative learning control (ILC) is studied for joint space trajectory tracking control of time-varying NeuroArm robot robotic manipulator. We propose control system which consists of a computed torque controller for linearizing robot dynamics. Then open-closed ILC is applied to the linearized system to further enhance tracking performance for repetitive tasks and deal with the model uncertainties. It is theoretically proven that the boundednesses of the tracking error are guaranteed in the presence of model uncertainty. Further, we investigate and suggest an open-closed-loop of fractional order P/P Dalpha type iterative learning control (ILC) for fractional order singular complex system. Sufficient conditions for the convergence in time domain of the proposed fractional order ILC for a class of fractional order singular system are obtained. Finally, numerical examples are presented to illustrate the effectiveness of the proposed open-closed ILC scheme of non-integer order for a class of non-integer order singular complex system.
Seminar Mehanika mašina i mehanizama - modeli i matematičke metode započeo je sa radom u junu 2018.god. Seminar se održava do dva puta mesečno, utorkom u periodu od 17.00 - 19.00 u Matematičkom institutu SANU.