Mihailo P. Lazarević

Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach

In this paper, a stability test procedure is proposed for linear nonhomogeneous fractional order systems with a pure time delay. Some basic results from the area of finite time and practical stability are extended to linear, continuous, fractional order time-delay systems given in state-space form. Sufficient conditions of this kind of stability are derived for particular class of fractional time-delay systems. A numerical example is given to illustrate the validity of the proposed procedure.

Redundancy problem in writing: from human to anthropomorphic robot arm

This paper presents the analysis of motion of a redundant anthropomorphic arm during the writing. The modeling is based on the separation of the prescribed movement into two motions: smooth global, and fast local motion, called distributed positioning (DP). The distribution of these motions to arm joints is discussed. It is based on the inertial properties and actuation capabilities of joints. The approach suggested allows unique solution of the inverse kinematics of redundant mechanisms such as human arm and anthropomorphic robot arm. Distributed positioning is an inherent property of biological systems. Humans, when writing, as shown in literature and in our earlier work control their proximal joints, while the movement of distal joints follow them (synergy). To enhance capabilities of robots, new control schema are necessary. We show that robot control can be improved if it is biological analog. The major aim of this study is to promote such a hypothesis by using anthropomorphic robot arm in writing as an example.

Neural network Reinforcement Learning for visual control of robot manipulators

It is known that most of the key problems in visual servo control of robots are related to the performance analysis of the system considering measurement and modeling errors. In this paper, the development and performance evaluation of a novel intelligent visual servo controller for a robot manipulator using neural network Reinforcement Learning is presented. By implementing machine learning techniques into the vision based control scheme, the robot is enabled to improve its performance online and to adapt to the changing conditions in the environment. Two different temporal difference algorithms (Q-learning and SARSA) coupled with neural networks are developed and tested through different visual control scenarios. A database of representative learning samples is employed so as to speed up the convergence of the neural network and real-time learning of robot behavior. Moreover, the visual servoing task is divided into two steps in order to ensure the visibility of the features: in the first step centering behavior of the robot is conducted using neural network Reinforcement Learning controller, while the second step involves switching control between the traditional Image Based Visual Servoing and the neural network Reinforcement Learning for enabling approaching behavior of the manipulator. The correction in robot motion is achieved with the definition of the areas of interest for the image features independently in both control steps. Various simulations are developed in order to present the robustness of the developed system regarding calibration error, modeling error, and image noise. In addition, a comparison with the traditional Image Based Visual Servoing is presented. Real world experiments on a robot manipulator with the low cost vision system demonstrate the effectiveness of the proposed approach.

Further results on the stability of linear nonautonomous systems with delayed state defined over finite time interval

This paper extends some basic results from the area of finite time and practical stability to linear, continuous, time invariant nonautonomous time-delay systems. Sufficient conditions of this kind of stability, for particular class of time-delay systems, are derived.

Robust second-order PDα type iterative learning control for a class of uncertain fractional order singular systems:

This paper presents a robust second-order feedback PD α type iterative learning control (ILC) for a class of uncertain fractional-order singular systems. Sufficient conditions for the robust convergence of the proposed PD α type of learning control algorithm, with respect to the bounded external disturbance and uncertainity, have been established and specified for time domain. Finally, simulation examples are presented to illustrate the performance of the proposed fractional order ILC.

Dominant pole placement with fractional order PID controllers: D-decomposition approach

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. This technique is applicable to a wide range of transfer functions: with or without time-delay, rational and non-rational ones, and those describing distributed parameter systems. In order to control as many different processes as possible, a fractional order PID controller is introduced, as a generalization of classical PID controller. As a consequence, it provides additional parameters for better adjusting system performances. The design method presented in this paper tunes the parameters of PID and fractional PID controller in order to obtain good load disturbance response with a constraint on the maximum sensitivity and sensitivity to noise measurement. Good set point response is also one of the design goals of this technique. Numerous examples taken from the process industry are given, and D-decomposition approach is compared with other PID optimization methods to show its effectiveness.

Discrete time delayed system stability theory in the sense of Lyapunov: new results

Our aim is to improve the existing results concerning asymptotic stability of a particular class of linear discrete time delay systems. This work extends one of the basic results in the area of Lyapunov (asymptotic) to linear, discrete, time invariant time-delay systems. This result is given in the form of only sufficient conditions and represent further improvement of the existing results concerning the asymptotic stability of systems described by vector state representation of the form x(k +1) = A/sub 0/x(k) + A/sub 1/x(k-1). This result is less conservative than those in existing literature. To the best knowledge of the authors, such results have not yet been reported.

Fractional order PD control of Furuta pendulum: D-decomposition approach

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 dependence. Some comparisons of fractional and integer order PID controllers are given based on simulation results.

Fractional PID Controller Tuned by Genetic Algorithms for a Three DOF's Robot System Driven by DC motors

Abstract This paper presents the new algorithms of fractional order PID control based on genetic algorithms in the position control of a 3 DOFs robotic system driven by DC motors. The objective of this work is to find out the optimal settings for a fractional PI α D β controller in order to fulfill the proposed design specifications for the closed-loop system. The effectiveness of the suggested optimal fractional PID control is demonstrated with a suitable robot with three degrees of freedom as an illustrative example.

Optimal conventional and fractional PID control algorithm for a robotic system with three degrees of freedom driven by DC motors

The paper presents the new algorithms of PID control based on fractional calculus (FC) and optimal procedure in the position and tracking control of robotic system with 3 DOFs driven by DC motors. The objective of this work is to find out optimal settings for a fractional PIαDβ controller in order to fulfill proposed design specifications for the closed-loop system, taking advantage of the fractional orders, α and β. Finally, the effectiveness of suggested optimal fractional PID control is demonstrated with a suitable robot with three degrees of freedom as the illustrative example.□