2018 (vol. 28) - Number 1

*I. Duleba, I. Karcz-Duleba:*

A comparison of methods solving repeatable inverse kinematics for robot manipulators

*A. Niederliński:*

A new approach for modelling uncertainty in expert systems knowledge bases

*T.T. Tuan, L.D. Tufa, M.I.A. Mutalib, N.M. Ramli :*

Optimal operation of a process by integrating dynamic economic optimization and model predictive control formulated with empirical model

*M. Kaleta:*

Network winner determination problem

*A. Kowalewski:*

Extremal problems for parabolic systems with time-varying lags

*T. Rybus, K. Seweryn, J.Z. S±siadek:*

Application of predictive control for manipulator mounted on a satellite

*T. Kaczorek:*

Reachability and observability of positive discrete-time linear systems with integer positive and negative powers of the state Frobenius matrices

*G. Grassi, A. Ouannas, V-T. Pham:*

A general unified approach to chaos synchronization in~continuous-time systems (with or without equilibrium points) as well as in discrete-time systems

*D. Pazderski:*

A robust smooth controller for a unicycle-like robot

ACS Abstract:

**2013 (Volume 23)**

Number 3

Optimal boundary control problems of retarded parabolic systems

A. Kowalewski, A. Krakowiak(AGH University of Science and Technology, Krakow, Poland) |

Optimal boundary control problems of retarded parabolic systems are presented. Necessary and sufficient conditions of optimality are derived for the Neumann problem. A simple example of application is also presented.

**keywords:** boundary control, parabolic systems, time delays, linear quadratic problem, quadratic programming method

Delay-dependent dissipative control for stochastic singular systems with state delay

Chunyan Ding(Yantai Engineering & Technology College, Yantai, China) | Qin Li(Yantai University, Yantai, China) |

The problem of delay-dependent dissipative analysis and control for stochastic singular systems with state delay is investigated in this paper. Delay-dependent dissipative condition for the stochastic singular systems with state delay is obtained by employing singular stochastic Lyapunov and LMI-based methods. Based on this condition, a delay-dependent dissipative controller is presented. A numerical example is provided to demonstrate the effectiveness of the proposed approach.

**keywords:** stochastic singular system, dissipative control, delay-dependent, state delay, linear matrix inequality (LMI)

Steady-state analysis for a class of hyperbolic systems with boundary inputs

K. Bartecki(Opole University of Technology, Poland) |

Results of a steady-state analysis performed for a class of distributed parameter systems described by hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of the system with two state variables and two boundary inputs, the analytical expressions for the steady-state distribution of the state variables are derived, both in the exponential and in the hyperbolic form. The influence of the location of the boundary inputs on the steady-state response is demonstrated. The considerations are illustrated with a practical example of a shell and tube heat exchanger operating in parallel- and countercurrent-flow modes.

**keywords:** distributed parameter system, partial differential equation, hyperbolic system, steady-state solution, heat exchanger

Design and experimentation of a self-tuning PID control applied to the 3DOF helicopter

A. Boubakir, S. Labiod(University of Jijel, Algeria) | F. Boudjema(National Polytechnic School, Algeria) | F. Plestan(Ecole Centrale de Nantes, France) |

The paper presents design and experimental validation of a stable self-tuning PID controller for three degrees of freedom (3-DOF) helicopter. At first, it is proposed a self-tuned proportional-integral-derivative (PID) controller for a class of uncertain second order multi-input multi-output nonlinear dynamic systems to which the 3-DOF helicopter dynamic model belongs. Within this scheme, the PID controller is employed to approximate unknown ideal controller that can achieve control objectives. PID controller gains are the adjustable parameters and they are updated online with a stable adaptation mechanism designed to minimize the error between the unknown ideal controller and the used by PID controller. The stability analysis of the closed-loop system is performed using Lyapunov approach. It is proven that all signals in the closed-loop system are uniformly ultimately bounded. The proposed approach can be regarded as a simple and effective model-free control since the mathematical model of the system is assumed unknown. Experimental results are presented to verify the effectiveness of the proposed controller.

**keywords:** 3-DOF helicopter, PID control, adaptive control, model-free control, MIMO nonlinear systems

Discrete-time switching state-space controller of DC drive

G. Sieklucki, A. Bisztyga, R. Sykulski, A. Zdrojewski, T. Orzechowski(AGH University of Science and Technology, Krakow, Poland) |

Control synthesis with state variables constraints for the DC drive is considered. Constraints are defined for the specific operating states of the DC motor during starting and braking in the presence of selected specific conditions. The control signal is based on the reference values and current state of the motor. The inverse dynamics method is applied. Closed-loop control law is realized by means of switching state-space controller.

**keywords:** DC drive, state variable constraints, switching gain matrix controller, state variables controller

A structured mathematical model of PHA biopolymer production process

J. Finkeova, P. Hrncirik, J. Mares, J. Vovsik, O. Hudecek, J. Nahlik(Institute of Chemical Technology, Prague, Czech Rep.) |

The paper describes a mathematical model of PHA biopolymer production process by {\em Pseudomonas putida} KT2442 where the octanoic acid is used as a substrate. The process is modeled using mass balances for fed-batch cultivation. Proper fitting to experimental data is obtained by identification of the model parameters. The model exhibits good agreement with experiments and its possible application for control is considered in the paper.

**keywords:** mathematical model, fed-batch cultivation, biopolymer production, process identification, model verification, physiological situations, Pseudomonas putida KT2442

Improved direct torque control of induction motors using adaptive observer and sliding mode control

D. Kouchih(University Saad Dahlab, Algeria) | M. Tadjine, M.S. Boucherit(Automatic Control Department, ENP, Algeria) |

This paper presents the synthesis of an adaptive observer which is used for the improvement of the direct torque control of induction motor drives. The observer detects stator flux components in two-phase stationary reference frame, rotor speed and stator resistance by measure of the stator terminal voltages and currents. The observer is adapted using a simple algorithm which does not imply a high computational load. Stability analysis based on Lyapunov theory is performed in order to guarantee the closed loop stability. Simulation tests under load disturbance and stator resistance variation are provided to evaluate the consistency and performance of the proposed control technique in the low and high speeds.

**keywords:** adaptive observer, direct torque control, induction motor, sensorless, sliding mode control

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