Mihailo P. Lazarević

University of Belgrade · Department of Mechanics

This paper presents a method for the implementation of a robot forward kinematics algorithm that complies with the Denavit-Hartenberg (DH) convention in Robot Operating System (ROS). The integration of the algorithm in ROS is based on the representation of DH parameters in dual quaternion space. The main motivation for the presented research is to...

In this paper, the finite-time stability for nonlinear neutral multi-term fractional order systems with time-varying input and state delays is investigated. By use of the generalized Gronwall inequality and extended form of the generalized Gronwall inequality, new sufficient conditions for finite-time stability of such systems are obtained. Finally...

Wave attenuation, filtering and guiding is an ongoing topic of scientific research, as there are many opportunities for improvement of existing solutions in modern industry. One of the recent advancements has been made with the use of non-reciprocal metamaterials. Certain properties of metamaterials have made them suitable for use in various engine...

This paper presents a new optimization method for PID controller cascaded with a lead-lag compensator (PIDC). Parameters of PIDC controller are obtained by solving the constrained optimization problem. We propose two variants of optimality criterion. First one is defined through the max-min optimization problem wherein objective function is the amp...

Safe and efficient training using flight simulation training devices (FSTD) is one of the fundamental components of training in the commercial, military, and general aviation. When compared with the live training, the most significant benefits of ground trainers include improved safety and the reduced cost of a pilot training process. Flight simula...

In this paper, the trajectory tracking problem of a nonlinear robotic system with 3DOFs under the control signal obtained through nonlinearly constrained state spaceIterative Learning Control (ILC) methods is considered. The focus of this paper is the analysis of different control system parameters on the convergence rate of two constrained state s...

In this paper, a new open-loop PD2D? type a fractional order iterative learning control (ILC) is studied for joint space trajectory tracking control of a linearized uncertain robotic arm. The robust convergent analysis of the tracking errors has been done in time domain where it is theoretically proven that the boundednesses of the tracking error a...

Recently, calculus of general order [Formula: see text] has attracted attention in scientific literature, where fractional operators are often used for control issues and the modeling of the dynamics of complex systems. In this work, some attention will be devoted to the problem of viscous friction in robotic joints. The calculus of general order a...

This paper presents the new algorithms of fractional order PID control based on genetic algorithms in the position control of a 3 DOF`s robotic system driven by DC motors. The objective of this work is to find out the optimal settings for a fractional PI D   controller in order to fulfill the proposed design specifications for the closed-loop sys...

A development of a robot control system is a highly complex task due to nonlinear dynamic coupling between the robot links. Advanced robot control strategies often entail difficulties in implementation, and prospective benefits of their application need to be analyzed using simulation techniques. Computed torque control (CTC) is a feedforward contr...

Considering the fertilization process as an oscillatory phenomenon, based on mechanotransduction theory of sperm–oocyte interaction, influence of sperm velocity and their specific arrangement on outer surface of oocyte- Zona pellucida (ZP) relative to the oscillatory behavior of ZP was studied using discrete continuum oscillatory spherical net mode...

This article addresses the problem of finite-time stability for uncertain neutral nonhomogeneous fractional-order systems with time-varying delays where a stability test procedure is suggested. Based on the extended form of the generalized Gr?nwall inequality, a new sufficient condition for robust finite-time stability of such systems is establishe...

In this paper an advanced iterative learning control algorithm for rehabilitation exoskeletons is proposed. A simplified biomechanical model is used as the control object to verify control algorithm feasibility. The control design is proposed as two level controller consisting of inner and outer loop. In the inner loop the feedback linearization is...

Motion control of robotic manipulators is frequently realized by independent control of the DC motors actuating robot joints. Namely, nonlinearities, coupling between actuators and other complex dynamics are neglected if high gear ratios between the actuators and robot joints are considered. This paper proposes a fractional-order lag network or a f...

In this paper we present the solution of exact equations of motion for coupled axial and bending vibrations of a non-uniform axially functionally graded (AFG) cantilever beam with a body of which mass center is eccentrically displaced in axial and transverse direction with respect to the beam's end. The Euler-Bernoulli beam theory is implemented to...

In this paper the fractional order lag compensator is introduced for the control of robot manipulators. Mathematical model of the robotic system is derived using the Rodriquez approach which, due to a high gear ratio between the actuators and robot joints, reduces to a linear model. Then, fractional order compensator is designed according to the sy...

This paper presents an efficient method of designing complex compensators without integral action. Compensators with this structure have application in robotics and mechatronic systems. The desired performance and robustness indices are achieved by a suitable selection of single adjustable parameter lambda which makes the proposed method flexible a...

The paper designs an appropriate iterative learning control (ILC) algorithm based on the trajectory characteristics of upper exosk el eton robotic system. The procedure of mathematical modelling of an exoskeleton system for rehabilitation is given and synthesis of a control law with two loops. First (inner) loop represents exact linearization of a...

In this communication, we propose a nonlocal fractional viscoelastic model of a nanobeam resting on the fractional viscoelastic foundation and under the influence of the longitudinal magnetic field and arbitrary number of attached nanoparticles. Size effects are taken into account using the differential form of the nonlocal constitutive relation to...

Three-dimensional (3-D) shape modelling from a flat sheet by lasers needs numerous irradiations along surface paths with different parameters of heating. In this study it was attempted to form a three-dimensional shaped surface by laser. The main aim of the study was to analyse the impact of various machining parameters like laser power, scan speed...

In this paper we will implement new hardware control for 7 DOFs (Degrees of freedom) advanced robotic arm research platform (NeuroArm) equipped with various sensors. New hardware platform consists of Nano Pi platform which is used as a PC platform for standard PLC (programmable logic controller's) unit and will replace old system that consists of 7...

This paper presents a dynamic model-based design of a control system and an approach toward a drive selection of a centrifuge motion simulator (CMS). The objective of the presented method is to achieve the desired performance while taking into account the complexity of the control system and the overall device cost. An estimation of a dynamic inter...

This paper presents simple, flexible and effective approximation method for fractional order lead-lag compensators. The proposed method relies on a Padé approximation of linear fractional order transfer functions, giving rational approximations of order N accurate enough for control applications as soon as N is greater than 2 or 3. An example of fe...

In this paper a closed-loop PDα - type iterative learning control (ILC) of fractional order linear singular time-delay system is considered. 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. Al...

Pilots of modern combat aircraft are exposed to the devastating effects of high acceleration forces and unusual orientation. The pilots’ ability to perform tasks under these extreme flight conditions must be examined. A centrifuge flight simulator (CFS) for pilot training is designed as a three-degree-of-freedom 3DoF manipulator with rotational axe...

This paper presents an effective design method of PID controller with series differential compensator ie. PIDC controller. The adjustable parameters of a PIDC controller are: proportional gain kp, integral gain ki, derivative gain kd, the second order derivative gain kh and filter time constant Tf. The proposed design procedure is based on pole pla...

This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this stud...

Design of user-friendly and at the same time powerful robot programming methods is the subject of significant efforts undertaken by the international robotics community. For the purpose of facilitating robot programming, with regard to the most common present-day applications in industry, it would be useful to develop programming procedures for fre...

Dominant pole placement is a useful technique designed to deal with the problem of controlling a high order or time-delay systems with low order controller such as the PID controller. This paper tries to solve this problem by using D-decomposition method. Straightforward analytic procedure makes this method extremely powerful and easy to apply. Thi...

This paper deals with the stability problem of two types of inverted pendulum controlled by a fractional order PD controller. Rotational inverted pendulum and cart inverted pendulum are under-actuated mechanical systems with two degrees of freedom and one control input. Detailed mathematical models of both pendulums are derived using the Rodriguez...

This paper presents a novel, simple, flexible and effective discretization method for linear non-rational systems including arbitrary linear fractional order systems (LFOS). The discretization algorithm relies on the direct integration in the complex domain and application of ARX (AutoRegressive eXogenous) model. Parameters of ARX-model are obtaine...

This paper will provide some an applications of memristors and mem-systems with a particular focus on electromechanical systems and analogies that holds great promise for advanced modeling and control of complex objects and processes. Also, we present the connection between fractional order differintegral operators and behavior of the mem-systems....

In this paper, we investigate the free damped vibration of a nanobeam resting on viscoelastic foundation. Nanobeam and viscoelastic foundation are modeled using nonlocal elasticity and fractional order viscoelasticity theories. Motion equation is derived using D’Alambert’s principle and involves two retardation times and fractional order derivative...

In this paper, the stability problem of Furuta pendulum controlled by the fractional order PD controller is presented. A mathematical model of rotational inverted pendulum is derived and the fractional order PD controller is introduced in order to stabilize the same. The problem of asymptotic stability of a closed loop system is solved using the D-...

This paper presents a new discretization method of PI/PID controller using the Padé approximation. It is shown that the direct application of Padé approximation to the transfer function of a continuous PI/PID controller simply leads to the appropriate discrete equivalent. The described method is compared with the most frequently applied discretizat...

In this paper, the finite-time stability criteria are extended to nonlinear nonhomogeneous perturbed fractional-order systems including multiple time-varying delays. The sufficient conditions of a stability for the fractional systems with multiple time delays are obtained by using the generalized and classical Gronwall’s approach. A numerical examp...

In this paper two different methods for determination of frictionless jointreaction forces and moments are presented. The considered multibodysystem has an open kinematic chain structure. The first method refers to thedetermination of resultant joint reaction forces and moments based on the Rodrigues approach suitable for computation in a symbolic...

Iterative learning control (ILC) is one of the recent topics in control theories and it is suitable for controlling a wider class of mechatronic systems - it is especially suitable for the motion control of robotic systems. This paper addresses the problem of application of fractional order ILC for fractional order singular system. Particularly, we...

In the present paper we investigate the fractal boundary value problems for the Fredholm\Volterra integral equations, heat conduction and wave equations by using the local fractional decomposition method. The operator is described by the local fractional operators. The four illustrative examples are given to elaborate the accuracy and reliability o...

The theory and applications of fractional calculus had a considerable progress in recent decades. Fractional calculus attracts much attention since it plays an important role in many fields of science and engineering. Dynamical systems and control are one of the most active areas in applications of fractional calculus. Especially, the study of stab...

In this paper a novel design method of PID controller for the assigned closed-loop system performance is given by applying pole spectrum and D-decomposition. Given procedure enables to determine a set of admissible PID controller parameters for which the considered system is relatively stable, i.e. meets requirements specified on the closed-loop sy...

According to the available literature, penetrating sperm creates an oblique path trough Zona pellucida (ZP) – the most outer surface of oocytes. Considering fertilization process as an oscillatory phenomenon, the influence of sperm impact angle relative to the oscillatory behavior of mouse ZP is described by using the discrete continuum mechanical...

The model of a rigid body and heavy foot joined by the revolute joint in the constant gravitational field is described. The rigid body moves in the vertical plane, whereas the heavy foot lies on the flat, very rough horizontal support. Conditions for the dynamic balance of this system are mathematically expressed by using the ZMP method. It is show...

We propose a novel mathematical framework to examine the free damped transverse vibration of a nanobeam by using the nonlocal theory of Eringen and fractional derivative viscoelasticity. The motion equation of a nanobeam with arbitrary attached nanoparticle is derived by considering the nonlocal viscoelastic constitutive equation involving fraction...

This paper proposes a sliding mode control of a 3-DOF robotic system driven by DC motors. Primarily, a conventional sliding mode controller based on a pd sliding surface is designed. Numerical simulations have been carried out to show the proposed control system's robustness properties as well as the significance of the proposed control which resul...

This paper presents a robust second-order feedback [Formula: see text] type iterative learning control (ILC) for a class of uncertain fractional-order singular systems. Sufficient conditions for the robust convergence of the proposed [Formula: see text] type of learning control algorithm, with respect to the bounded external disturbance and uncerta...

A feedback-feedforward PDalpha type iterative learning control (ILC) of fractional order uncertain time delay system is considered. Particularly, we discuss fractional order time delay systems in state space form with uncertain bounded constant time delay. Sufficient conditions for the convergence of a proposed PDalpha type of learning control algo...

A new frequency-domain algorithm for optimization of PID regulators having a fractional differential compensator connected in series (PIDCα) has been developed. The adjustable parameters of the regulator are: proportional gain k, integral gain ki, relative attenuation factor of PID zeros ζ, zero of the fractional differential compensator-1/τ and fr...

The modern dynamical systems of various physical natures, such as natural, social, economic, and technical ones, are complexes of various subsystems. They are connected by processes of intensive dynamic interaction and exchange of energy, matter, and information and incorporate nonlinear dynamics, memory, complicated transients, bifurcation and cha...

Radio Frequency Identification (RFID) is a revolution in industrial control, because it has the potential to simplify and make more robust tracking of parts or part carriers through manufacture, storage, distribution, and at the end of the supply chain. We try to present intelligent mobile robot navigation technique using radio frequency identifica...

This paper deals with the design of a new algorithm of PID control based on fractional calculus (FC) in production of technical gases, i.e. in a cryogenic air separation process. Production of low pressure liquid air was first introduced by P. L. Kapica and involved expansion in a gas turbine. For application in the synthesis of the control law, fo...

Fractional order models of a spring/spring-pot and spring/spring-pot/actuator element connected into a multibody system are proposed in order to represent smart materials and components in adaptronic systems by introducing new tuning parameter. The models are introduced into dynamic equations via generalized forces and using the Lagrange's equation...

In recent years, nonlocal elasticity theory applied for the prediction of the vibration behavior of nanostructures has attracted considerable attention of the scientific community. When internal damping of nanostructures needs to be taken into account, in most of the available works classical viscoelastic models are used. This work reports the free...

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...

This paper deals with stability problem of inverted pendulum controlled by a fractional order PD controller. D-decomposition method for determining stability region in controller parameters space is hereby presented. The D-decomposition problem for linear systems is extended for linear fractional systems and for the case of nonlinear parameters dep...

This paper proposes advanced control strategy for a rotary inverted pendulum (RIP). RIP is an underactuated mechanical system because it has only one control input and two degrees of freedom. Because of its complex nonlinear dynamics, RIP is usually used to test performance of different control algorithms. First, laboratory electromechanical system...

This paper provides an overview of the recently presented and published results relating to the use of iterative learning control (ILC) based on and integer and fractional order. ILC is one of the recent topics in control theories and it is a powerful control concept that iteratively improves the behavior of processes that are repetitive in nature....

Rapid development of biological science and technologies will further improve the active applications of control engineering by advanced biomimetic and biologically inspired research. First of all, it has promoted a biologically inspired control synergy approach that allows the resolution of redundancy of a given robotized system. In particular, th...

Rapid development of biological science and technologies will further improve the active applications of control engineering by advanced biomimetic and biologically inspired research. First of all, it has promoted a biologically inspired control synergy approach that allows the resolution of redundancy of a given robotized system. In particular, th...

Electrical impedance measurement data and fractional calculus have been utilized for modeling bioimpedance properties of human skin. We introduced and proposed revisited Cole model using modified distributed order operator based on the Caputo-Weyl fractional derivatives. Our proposed model presents essentially modified single-dispersion Cole model,...

Formulation of proper and efficient algorithms for robot kinematics is essential for the analysis and design of serial manipulators. Kinematic modeling of manipulators is most often performed in Cartesian space. However, due to disadvantages of most widely used mathematical constructs for description of orientation such as Euler angles and rotation...

In this monograph several aspects of fractional calculus will be presented ranging from its brief history over control applications and stability problems for time delay systems to applications in bio-engineering fields with illustrative examples. The advantages of fractional calculus have been described and pointed out in the last few decades by m...

This paper analyzes the problem of brachistochronic planar motion of a mechanical system with nonlinear nonholonomic constraint. The nonholonomic system is represented by two Chaplygin blades of negligible dimensions, which impose nonlinear constraint in the form of perpendicularity of velocities. The brachistrochronic planar motion is considered,...

In this paper the problem of stability of linear discrete-time fractional order systems is addressed. It was shown that some stability criteria for discrete time-delay systems could be applied with small changes to discrete fractional order state-space systems. Accordingly, simple conditions for the stability and robust stability of a particular cl...

Many phenomena are naturally described in terms of dynamical systems of infinite order. Such phenomena cannot be adequately described by an interconnection of a finite number of accumulating elements, i.e., by means of differential or difference equations of finite order. Among the well-known examples are distributed parameter systems, which are us...

The Fractional Calculus (FC) is a generalization of classical calculus concerned with operations of integration and differentiation of non-integer (fractional) order. The concept of fractional operators has been introduced almost simultaneously with the development of the classical ones. The first known reference can be found in the correspondence...

The current paper proposes a model for describing mechanical phenomena that occur during the process of mammal fertilization when spermatozoa impact the surface of Zona Pellucida. Zona pellucida (ZP) is a dynamical 3D matrix that surrounds the mammalian oocyte. In the process of fertilization, sperm cell has to penetrate this structure. To describe...

In this communication, the Rodriguez method is proposed for modeling dynamics of the robotic system, where Lagrange's equations of second kind of rigid bodies system in covariant form are used. Discrete hybrid elements with so called piezo-modified Kelvin-Voight (PKV) and magnetorheological (MRD) type of viscoelastic models with fractional order de...

To achieve predefined Gz load profile in high G training in human centrifuge, it is necessary to determine angular velocity and acceleration of a planetary axis (centrifuge arm). Initial value problem that can not be solved in closed form was obtained. Several discretization methods for calculating angular velocity of centrifuge arm driven by DC se...

In this paper it is suggested using a biologically inspired control synergy approach that allows the resolution actuator redundancy robotic control problem.Also, it is presented the advanced control algorithms of integer and fractional order PID control based on genetic algorithms in the position control of a 3DOs robotic system driven by DC motors...

The control of the contemporary mechatronic product is very demanding task due the nonlinearity of multibody system,plethora of working profile and rapid response in shortest possible time. Application of adaptronic devices in the whitegood products (e.g. washing machine and MR Dampers LORD RD-1005-3) a long time quite known and already economicall...

The complexity of mechatronic products, such as climate chamber subsystems, results in enormous difficulties in understanding where the main design process inefficiencies are. It is therefore extremely difficult to determine which improvements will have the most significant impact on a company or on a specific project. Mechatronic products are char...