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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 space ILCalgorithms: Bounded Error Algorithm (BEAILC) and Constrained Output algorithm (COILC), as well as the comparison between these two algorithms through simulations. The obtained results have shown that COILC algorithm converges faster than BEAILC algorithm when compared with the same learning and feedback parameters, due to lower trajectory restrictions. Also, it has been shown that an increase in feedback gains can decrease the number of iteration terminations during the learning process, thus allowing for more of the trajectory error information to be learned from during the single iteration. Moreover, simulations have shown that the decrease in learning parameter values will increase the number of iterations required to obtain the desired tracking accuracy.

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 Grönwall inequality, a new sufficient condition for robust finite-time stability of such systems is established. Finally, a numerical example is given to show the effectiveness of the obtained result.

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 applied to cancel out the model nonlinearities. In the outer loop the advanced iterative learning control algorithm of sgnPDD2 type is applied as a feedforward controller and classical PD controller as a feedback controller. Uncertainties are added in order to examine the controller design robustness. Numerical simulation is carried out.

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. Also, for the first time, we proposed a proposed ILC PDα type for a given class of uncertain, fractional order, singular systems. 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.

This paper presents the most important information and describes the activities of the 6th Congress of the Serbian Society of Mechanics which was held on mountain Tara, on 19- 21 June, 2017. The Congress was organized by the Serbian Society of Mechanics. Brief summaries of the plenary lectures and some of 99 accepted papers, which admittedly attracted the most interest were shown as well.

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 frequently used manipulator tasks which could be easily implemented and used as ready-made application software. Important class of industrial robot applications involves end-effector trajectories in planar surfaces. Development of robot programming language procedure intended for determination of object plane normal with respect to frame of interest, as well as programming of end-effector orientation is presented in this paper. This procedure can be used as integral part of task oriented robot programing applications as well as a procedure for explicit programming languages, and it is illustrated in practical example with the robot Lola 15.

In this paper two different methods for determination of frictionless joint reaction forces and moments are presented. The considered multibody system has an open kinematic chain structure. The first method refers to the determination of resultant joint reaction forces and moments based on the Rodrigues approach suitable for computation in a symbolic form. The second method presented is the method based on the so-called vectors of the body mass moments and vector rotators coupled for a pole and oriented axes. Both approaches are presented and discussed on the three- like rigid multibody system.

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 study fractional order singular systems in the pseudo-state space. An closed-loop fractional order PDalpha type ILC of the fractional-order singular system is investigated. Also, open-closed loop of the fractional order P-PDa type ILC is considered. Sufficient conditions for the convergence in the time domain of the proposed ILC schemes are given by the corresponding theorems and proved. Finally, numerical simulations show the feasibility and effectiveness of the proposed approach.

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 fractional order derivatives and using the Euler-Bernoulli beam theory. The solution is proposed by using the method of separation of variables. Eigenvalues and mode shapes are determined for three typical boundary conditions. The fractional order differential equation in terms of a time function is solved by using the Laplace transform method. Time dependent behavior is examined by observing the time function for different values of fractional order parameter and different ratios of other parameters in the model. Validation study is performed by comparing the obtained results for a special case of our model with corresponding molecular dynamics simulation results found in the literature. [Projekat Ministarstva nauke Republike Srbije, br. OI 174001, br. OI 174011 i br. TR 35006]

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 example is presented to illustrate the validity of the obtained result.

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 resulted in reducing output oscillations (chattering-free) of the given robot. Finally, a simulation example shows the feasibility and effectiveness of the proposed approach.

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 shown that they determine an area in the phase space in which the state of the system should be in order that its dynamic balance is kept. It is also shown by appropriate simulations of motion of the system in the dynamic balance that these conditions are not sufficient for the system to keep its upright posture, but are in connection with its controllability. It is briefly discussed what are the necessary conditions for this system in dynamic balance to keep its upright posture.

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. ILC is suitable for controlling a wider class of mechatronic systems - it is especially suitable for motion control of robotic systems that attract and hold an important position in biomechatronical, technical systems involving the application, military industry, etc. The first part of the paper presents the results relating to the application of higher integer order PD type ILC with numerical simulation. Also, another integer order ILC scheme is proposed for a given robotic system with three degrees of freedom for task-space trajectory tracking where the effectiveness of the suggested control is demonstrated through a simulation procedure. In the second part, the results related to the application of the fractional order of ILC are presented where PDα type of ILC is proposed firstly, for a fractional order linear time invariant system. It is shown that under some sufficient conditions which include the learning operators, convergence of the learning system can be guaranteed. Also, PIβDα type of ILC is suggested for a fractional order linear time delay system. Finally, sufficient conditions for the convergence in the time domain of the proposed ILC were given by the corresponding theorem together with its proof.

Iterative learning control (ILC) is one of the recent topics in control theories and it is a powerful control concept that iteratively improves the behavior of processes repetitive in their nature. ILC is suitable for controlling a wider class of mechatronic systems - it is especially suitable for the motion control of robotic systems that attract and hold an important position in technical systems involving control applications, military industry, etc. This paper addresses the problem of iterative learning control (ILC) for fractional nonlinear time delay systems. Particularly, we study fractional order time delay systems in the state space form with unknown bounded constant time delay as well as time-varying delay. Sufficient conditions for the convergence of a proposed PDα type of a learning control algorithm for a class of fractional state space time delay systems are presented in the time domain. Also, a feedback-feed forward PDα type robust iterative learning control (ILC) of the given fractional order uncertain time delay system is considered. We consider fractional order time delay systems in the state space form with uncertain bounded constant time delay in particular. Sufficient conditions for the convergence in the time domain of the proposed PDα ILC are given by the corresponding theorem together with its proof. Finally, a simulation example shows the feasibility and effectiveness of the proposed approach.

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, with specified initial and terminal positions, at unchanged value of mechanical energy during motion. Differential equations of motion, where the reactions of nonholonomic constraints and control forces figure, are obtained on the basis of general theorems of mechanics. Here, this is more convenient to use than some other methods of analytical mechanics applied to nonholonomic mechanical systems, where a subsequent physical interpretation of the multipliers of constraints is required. The formulated brachistochrone problem, with adequately chosen quantities of state, is solved as simple a task of optimal control as possible in this case by applying the Pontryagin maximum principle. The corresponding two-point boundary value problem of the system of ordinary nonlinear differential equations is obtained, which has to be numerically solved. Numerical procedure for solving the two-point boundary value problem is performed by the method of shooting. On the basis of thus obtained brachistochronic motion, the active control forces, along with the reactions of nonholonomic constraints, are defined. Using the Coulomb friction laws, a minimum required value of the coefficient of sliding friction is defined, so that the considered system is moving in accordance with nonholonomic bilateral constraints.

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, since it introduces a new parameters k and σ in single-dispersion Cole impedance equation. These parameters characterize the width of interval around fractional index α and they are important for more accurate describing bioimpedance properties of human skin. The impedance spectrum was measured in a finite frequency range up to 100 kHz. Our proposed modified Cole model fits much better to experimental curve in a given frequency range compared to existing Cole models. The fitting is done using the Levenberg-Marquardt nonlinear least squares.

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 rotational matrices, a need for unambiguous, compact, singularity free, computationally efficient method for representing rotational information is imposed. As a solution, unit quaternions are proposed and kinematic modeling in dual quaternion space arose. In this paper, an overview of spatial descriptions and transformations that can be applied together within these spaces in order to solve kinematic problems is presented. Special emphasis is on a different mathematical formalisms used to represent attitude of a rigid body such as rotation matrix, Euler angles, axis-angle representation, unit quaternions, and their mutual relation. Benefits of kinematic modeling in quaternion space are presented. New direct kinematics algorithm in dual quaternion space pertaining to a particular manipulator is given. These constructs and algorithms are demonstrated on the human centrifuge as 3 DoF robot manipulator.

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, for the input temperature and flow of air to the expansion turbine, it is necessary to determine the appropriate differential equations of the cryogenic process of mixing of two gaseous airflows at different temperatures before entrance to the expansion turbine. Thereafter, the model is linearized and decoupled and consequently classical PID and fractional order controllers are taken to assess the quality of the proposed technique. A set of optimal parameters of these controllers are achieved through the genetic algorithm optimization procedure by minimizing a cost function. Our design method focuses on minimizing performance criterion which involves IAE, overshoot, as well as settling time. A time-domain simulation was used to identify the performance of controller with respect to a traditional optimized PID controller. [Projekat Ministarstva nauke Republike Srbije, br. 35006]

This paper presents some of the capabilities of Webots-a robotics simulation software. Using Webots as the development environment one can obtain model, program as well as simulate robots. First, key features and components of Webots are described and then it is presented how to construct a model of robotic system in it. Then, a control system is designed based on mathematical model of robot system in order to solve the problem of positioning of the end-effector. Results obtained in Webots environments are compared with those from Matlab/Simulink, so one can confirm the control system design procedure and accuracy of physics simulation. An example of more complex task that the robot manipulator needs to execute is given in the remainder of this paper. It is a so called Tower of Hanoi problem, where is particularly solved the inverse kinematics problem in detail. A part of C programming code which has been used for controlling the robot in Webots is explained at the end.

In this paper, the applications of biologically inspired modeling and control of (bio)mechanical (non)redundant mechanisms are presented, as well as newly obtained results of author in mechanics which are based on using fractional calculus. First, it is proposed to use biological analog-synergy due to existence of invariant features in the execution of functional motion. Second, the model of (bio)mechanical system may be obtained using another biological concept called distributed positioning (DP), which is based on the inertial properties and actuation of joints of considered mechanical system. In addition, it is proposed to use other biological principles such as: principle of minimum interaction, which takes a main role in hierarchical structure of control and self-adjusting principle (introduce local positive/negative feedback on control with great amplifying), which allows efficiently realization of control based on iterative natural learning. Also, new, recently obtained results of the author in the fields of stability, electroviscoelasticity, and control theory are presented which are based on using fractional calculus (FC). [Projekat Ministarstva nauke Republike Srbije, br. 35006]

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 characterized by a high level of interdisciplinarity and complexity in the technical system and the relevant development processes. The main challenge in this respect is how to deal with the high complexity of and a variety of interdependencies in such products. We are therefore presenting a framework for integrated mechatronic product and process modelling - extended M-FBFP framework. This framework provides different independent perspectives of the overall product to improve their architecture. As a result of the proposed framework, risk analysis through subsystems in the components domain and through processes in the technical processes domain is enabled and it is now possible to provide feedback on product architecture. To obtain optimally robust product architectures from available alternative solutions, an evaluation analysis was performed across all stages, including the initialization and subsequent refinements with several evaluation criteria: complexity, interdependency and process duration. To test the validity of the proposed framework, we are presenting a case study involving a climate chamber with heat regeneration.

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 given system, and the second (outer) loop is synthesis of a iterative learning control law which consists of two loops, open and closed loop. In open loop ILC sgnPDD2 is applied, while in feedback classical PD control law is used. Finally, a simulation example is presented to illustrate the feasibility and effectiveness of the proposed advanced open-closed iterative learning control scheme.

This paper proposes an M-FBFP framework with the objective to help designers tackle the problem of risk emerging from product architecture and the effects of uncertain operating conditions. The proposed framework combines matrix approaches (QFD and MDM) and the FBFP method. The QFD is an integrated set of tools for recording user requirements, engineering characteristics that satisfy these requirements, and any tradeoffs that might be necessary between the engineering characteristics, while the MDM is applied to model structural arrangements and dependencies between the domains and within themselves. The FBFP method, on the other hand, is applied at the functional level, provides potential failure information based on product functions during conceptual design in product subsystems. As a result of the proposed framework, risk analysis of subsystems becomes possible and feedback on product architecture could be provided. To test validity of the proposed approach, here is presented a case study with climate chamber with heat regeneration.

This paper suggests a quaternion approach for the modeling kinematics and dynamics of rigid multi-body systems. Instead of the regular 'Newton-Euler' and Lagrange method used in the traditional way, Lagrange's equations of second kind in the covariant form are used by applying Rodriguez approach and quaternion algebra. A model of multi-body system of n rigid bodies in terms of quaternions is obtained, which is useful for studying kinematics, dynamics as well as for research of control system designs.

This paper presents a new optimisation method for PID controller cascaded with a lead-lag compensator (PIDC). Parameters of the controller are obtained by solving the constrained optimisation problem. We propose two variants of the optimality criterion. The first one is defined through the max–min optimisation problem wherein objective function is the amplitude frequency response of the PIDC controller. The second one is based on an effective approximation of the minimum value of the amplitude frequency response of the PIDC controller. Consequently, we obtain a computationally less expensive problem. Both variants of optimality criterion result in efficient load disturbance and noise rejection, while robustness is ensured by constraining the value of the maximum sensitivity Ms. Good reference shaping is supported with proper constraints based on the Amplitude Optimum (AO) principle. Numerous batches of processes typically encountered in the industry are used to demonstrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]