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2017 (vol. 27) - Number 4


M. Kaczmarek, W. Domski, A. Mazur:

Position-force control of mobile manipulator - nonadaptive and adaptive case



Zhong Cao, Wenjing Zhao, Xiaorong Hou:

Adaptive robust simultaneous stabilization controller with tuning parameters design for two dissipative Hamiltonian systems



J. Duda:

A Lyapunov functional for a system with both lumped and distributed delay



Sundarapandian Vaidyanathan, Aceng Sambas, Mustafa Mamat, Mada Sanjaya WS:

A new three-dimensional chaotic system with a hidden attractor,  circuit design and application in wireless mobile robot



J. Ratajczak, K. Tcho˝:

On dynamically consistent Jacobian inverse for non-holonomic robotic systems



D. Krokavec, A. Filasova:

Stabilization of discrete-time LTI positive systems



P. Tatjewski:

Offset-free nonlinear Model Predictive Control with state-space process models




ACS Abstract:

2017 (Volume 27)
Number 4
1.

Position-force control of mobile manipulator - nonadaptive and adaptive case

2.

Adaptive robust simultaneous stabilization controller with tuning parameters design for two dissipative Hamiltonian systems

3.

A Lyapunov functional for a system with both lumped and distributed delay

4.

A new three-dimensional chaotic system with a hidden attractor,  circuit design and application in wireless mobile robot

5.

On dynamically consistent Jacobian inverse for non-holonomic robotic systems

6.

Stabilization of discrete-time LTI positive systems

7.

Offset-free nonlinear Model Predictive Control with state-space process models



Position-force control of mobile manipulator - nonadaptive and adaptive case

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M. Kaczmarek, W. Domski, A. Mazur
(Wroclaw University of Technology, Poland)

This article presents a control algorithm for nonholonomic mobile manipulators with a simple, geometric holonomic constraint imposed on the robot's arm. A mathematical model in generalized, auxiliary and linearized coordinates is presented, as well as the constrained dynamics of the robotic system. A position-force control law is proposed, both for the fully known robot's model, as well as for the model with parametric uncertainty in the dynamics. Theoretical considerations are supported by the results of computer simulations.

keywords: holonomic constraint, nonholonomic constraint, parametric uncertainty, adaptive control

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Adaptive robust simultaneous stabilization controller with tuning parameters design for two dissipative Hamiltonian systems

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Zhong Cao, Wenjing Zhao
(Guangzhou University, China)
Xiaorong Hou
(University of Electronic Science and Technology of China, Chengdu, China)

This paper investigates the problem of adaptive robust simultaneous stabilization (ARSS) of two dissipative Hamiltonian systems (DHSs), and proposes a number of results on the controller parameterization design. Firstly, an adaptive H∞ control design approach is presented by using the dissipative Hamiltonian structural for the case that there are both external disturbances and parametric uncertainties in two DHSs. Secondly, an algorithm for solving tuning parameters of the controller is proposed using symbolic computation. The proposed controller parameterization method avoids solving Hamilton-Jacobi-Issacs (HJI) equations and the obtained controller is easier as compared to some existing ones. Finally, an illustrative example is presented to show that the ARSS controller obtained in this paper works very well.

keywords: ARSS control, DHSs, symbolic computation, controller parameterization, tuning parameters

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A Lyapunov functional for a system with both lumped and distributed delay

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J. Duda
(AGH University of Science and Technology, Poland)

In the paper construction of a Lyapunov functional for time delay system with both lumped and distributed delay is presented. The Lyapunov functional is determined by means of the Lyapunov matrix. The method of determination of the Lyapunov matrix for time delay system with both lumped and distributed delay is presented. It is given the example illustrating the method.

keywords: time-delay system, Lyapunov matrix, Lyapunov functional

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A new three-dimensional chaotic system with a hidden attractor,  circuit design and application in wireless mobile robot

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Sundarapandian Vaidyanathan
(Vel Tech University, India)
Aceng Sambas
(Universiti Sultan Zainal Abidin, Malaysia and Universitas Muhammadiyah Tasikmalaya, Indonesia)
Mustafa Mamat
(Universiti Sultan Zainal Abidin, Malaysia)
Mada Sanjaya WS
(UIN Sunan Gunung Jati Bandung, Indonesia)

This research work proposes a new three-dimensional chaotic system with a hidden attractor. The proposed chaotic system consists of only two quadratic nonlinearities and the system possesses no critical points. The phase portraits and basic qualitative properties of the new chaotic system such as Lyapunov exponents and Lyapunov dimension have been described in detail. Finally, we give some engineering applications of the new chaotic system like circuit simulation and control of wireless mobile robot.

keywords: chaos, chaotic systems, hidden attractors, circuit simulation

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On dynamically consistent Jacobian inverse for non-holonomic robotic systems

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J. Ratajczak, K. Tcho˝
(Wroclaw University of Technology, Poland)

This paper presents the dynamically consistent Jacobian inverse for non-holonomic robotic system, and its application to solving the motion planning problem.  The system's kinematics are represented by a driftless control system, and defined in terms of its input-output map in accordance with the endogenous configuration space approach. The dynamically consistent Jacobian inverse (DCJI) has been introduced by means of a Riemannian metric in the endogenous configuration space, exploiting the reduced inertia matrix of the system's dynamics.  The consistency condition is formulated as the commutativity property of a diagram of maps. Singular configurations of DCJI are studied, and shown to coincide with the kinematic singularities. A parametric form of DCJI is derived, and used for solving example motion planning problems for the trident snake mobile robot. Some advantages in performance of DCJI in comparison to the Jacobian pseudoinverse are discovered.

keywords: non-holonomic system, motion, Jacobian inverse, dynamic consistency, metric, motion planning

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Stabilization of discrete-time LTI positive systems

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D. Krokavec, A. Filasova
(University of Kosice, Slovakia)

The paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteeing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the state-feedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.

keywords: state feedback stabilization, positive discrete-time observers, linear discrete-time positive systems, linear matrix inequalities, asymptotic stability

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Offset-free nonlinear Model Predictive Control with state-space process models

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P. Tatjewski
(Warsaw University of Technology, Poland)

Offset-free model predictive control (MPC) algorithms for nonlinear state-space process models, with modeling errors and under asymptotically constant external disturbances, is the subject of the paper. The main result of the paper is the presentation of a novel technique based on constant state disturbance prediction. It was introduced originally by the author for linear state-space models and is generalized to the nonlinear case in the paper. First the case with measured state is considered, in this case the technique allows to avoid disturbance estimation at all. For the cases with process outputs measured only and thus the necessity of state estimation, the technique allows the process state estimation only - as opposed to conventional approach of extended process-and-disturbance state estimation. This leads to simpler design with state observer/filter of lower order and, moreover, without the need of a decision of disturbance placement in the model (under certain restrictions), as in the conventional approach. A theoretical analysis of the proposed algorithm is provided, under applicability conditions which are weaker than in the conventional approach. The presented theory is illustrated by simulation results of nonlinear processes, showing competitiveness of the proposed algorithms.

keywords: nonlinear control, predictive control, offset-free control, state-space model, state estimation

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