Milan Cajić

Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field

Nanocomposites and magnetic field effects on nanostructures have received great attention in recent years. A large amount of research work was focused on developing the proper theoretical framework for describing many physical effects appearing in structures on nanoscale level. Great step in this direction was successful application of nonlocal continuum field theory of Eringen. In the present paper, the free transverse vibration analysis is carried out for the system composed of multiple single walled carbon nanotubes (MSWCNT) embedded in a polymer matrix and under the influence of an axial magnetic field. Equivalent nonlocal model of MSWCNT is adopted as viscoelastically coupled multi-nanobeam system (MNBS) under the influence of longitudinal magnetic field. Governing equations of motion are derived using the Newton second low and nonlocal Rayleigh beam theory, which take into account small-scale effects, the effect of nanobeam angular acceleration, internal damping and Maxwell relation. Explicit expres...

Robotic system with viscoelastic element modeled via fractional Zener model

In this communication, we propose a four-parameter fractional derivative Zener model for modeling of a viscoelastic element connected into a robotic system. We used force-displacement relation in order to obtain generalized forces of the element connected to two different bodies in the system. Generalized forces of the element are derived using the principle of virtual work. In order to obtain numerical results, we suggested a robotic system with three degrees of freedom. Behavior of generalized forces is examined for changes of fractional order parameter and relaxation time.

Multi-mode active vibration control of a nanobeam using a non-square MIMO PID controller

In this paper, we suggest a robust non-square MIMO (4×8) PID controller for the multi-mode active vibration damping of a nanobeam. Nanobeam is modeled by using the nonlocal continuum theory of Eringen to consider the small-scale effects and Euler-Bernoulli beam theory. The problem is analyzed for the free vibration case with Heaviside type disturbance of a nanobeam with and without the controller. The proposed system has four inputs and eight outputs, where by using the static decoupling method, decoupled system of four transfer functions is obtained. The controller parameters dependig on one tuning parmeter are designed to suppress the step disturbance on the input without overshooting. All theoretical results are verified with several numerical examples.

Stabilization of double inverted pendulum system by using a fractional differential compensator

In this paper stability problem of double inverted pendulum controlled by a fractional differential compensator is investigated. Pendubot is an underactuated mechanical system, i.e. it has only one control input and two degrees of freedom. Detailed mathematical model of Pendubot is derived using the Rodriguez method and then fractional order lead compensator is introduced in order to stabilize it around unstable upright position. D-decomposition method is used to solve the problem of asymptotic stability of closed loop system. Stability regions in control parameters space are calculated using this technique, which allows tuning of the fractional differential compensator to be carried out.

PD α -type iterative learning control for fractional-order singular time-delay system

In this paper a closed-loop PDα — type iterative learning control (ILC) of fractional order singular time-delay system is considered. In particular, we discuss fractional order linear singular timed-delay systems in state space form. The sufficient conditions for the convergence in time domain of the proposed PD-alpha type ILC for a class of fractional order singular system are given by the corresponding theorem together with its proof. Finally, the validity of the proposed PDα ILC scheme for a class of fractional order singular time-delay system is verified by a numerical example.