2011 (Volume 21)
An iterative method for time optimal control of dynamic systems
|N. Kashiri, M.H. Ghasemi, M. Dardel|
(Babol University of Technology, Iran)
An iterative method for time optimal control of a general type of dynamic systems is proposed, subject to limited control inputs. This method uses the indirect solution of open-loop optimal control problem. The necessary conditions for optimality are derived from Pontryagin's minimum principle and the obtained equations lead to a nonlinear two point boundary value problem (TPBVP). Since there are many difficulties in finding the switching points and in solving the resulted TPBVP, a simple iterative method based on solving the minimum energy solution is proposed. The method does not need finding the switching point so that the resulted TPBVP can be solved by usual algorithms such as shooting and collocation. Also, since the solution of TPBVPs is sensitive to initial guess, a short procedure for making the proper initial guess is introduced. To this end, the accuracy and efficiency of the proposed method is demonstrated using time optimal solution of some systems: harmonic oscillator, robotic arm, double spring-mass problem with coulomb friction and F-8 aircraft.
keywords: dynamic systems, optimal control, time optimal control, Pontryagin's minimum principle, bounded control inputs
Nonlinear multiple model particle filters algorithm for tracking multiple targets
|A. Sebbagh, H. Tebbikh|
(Laboratoire d'Automatique and Informatique de Guelma (LAIG), Algeria)
The paper addresses multiple targets tracking problem encountered in number of situations in signal and image processing. In this paper, we present an efficient filtering algorithm to perform accurate estimation in jump Markov nonlinear systems, which we aim to contribute in solving the problem of multiple targets tracking using bearings-only measurements. The idea of this algorithm consists of the combination between the multiple model approach and particle filtering methods, which give a nonlinear multiple model particle filters algorithm. This algorithm is used to estimate the trajectories of multiple targets assumed to be nonlinear, from their noisy bearings.
keywords: estimation, particle filter, multiple targets tracking, multiple model approach
Dead-time compensation in continuous-review perishable inventory systems with a remote supply source
|P. Ignaciuk, A. Bartoszewicz|
(Technical University of Lodz, Poland)
In this paper we address the problem of efficient control of continuous-review perishable inventory systems. In the considered systems the goods at a distribution center used to fulfill unknown, variable demand deteriorate at a constant rate, and are replenished with delay from a remote supply source. We develop a new supply policy which incorporates the Smith predictor for dead-time compensation. A number of properties of the designed policy is formulated, and strictly proved. In particular, we show that the policy guarantees that the assigned storage space at the distribution center is never exceeded which means that the cost of emergency storage is eliminated. Moreover, we show that with appropriately chosen controller parameters all of the demand imposed at the distribution center is realized from the readily available resources, thus ensuring the maximum service level.
keywords: inventory control, perishable inventory systems, time-delay systems, Smith predictor
About a certain relation between two polynomials of the same degree
(Cracow Uniwersity of Technology, Poland)
This article presents several different methods for solving the problem of how to find a certain relation defined in chapter 2. The first method deals with the identities known in the theory of symmetric polynomials as the elements of a certain vector space. The second method is designed around the matrix transformations between symmetric polynomials. The third method is designed around the property of a linear operator and its characteristic polynomial. The fourth method is designed in the area of complex numbers, and introduces the multiplication group of 'complex roots of one'. Significant improvement in the third and fourth method is made by introducing so called 'block method'. It facilitates all calculations by making them much shorter. The article ends with an example showing symmetry and regularity of all procedures. Finally, the article shows how to solve the problem for any degree n of the polynomial, and for any degree k. At the end of the paper solutions for n <= 5 and k <= 5 are tabulated.
keywords: roots of polynomials, symmetric polynomials, companion matrix, eigenvalues, transformations
Use of asymmetrical currents waveforms to detect and localize open switch faults for two level voltage source inverter three-phase shunt active power filter
|T. Benslimane, B. Chetate|
(Laboratory of Automation and Electrification of Industrial Enterprises, University of Boumerdes, University of Msila, Algeria)
(Applied Research Unit on Renewable Energies, Industrial zone, Ghardaia, Algeria)
This paper proposes an open switch faults detection and localization algorithm for shunt three phase active filter topology. It mainly details converter configuration and examines a simple and reliable optimized fault diagnosis method. The converter topology is based on classical three-leg active power filter topology. New fault diagnosis method is proposed, based on classical currents measurements. It includes combinatory logic to analyze and validate error signals. Hysteresis control is applied before and after fault detection, which avoids any controller reconfiguration. Simulation results obtained with Matlab/Simulink/Plecs tools prove the effectiveness of this method.
keywords: active power filter, fault detection, two level there phase voltage source inverter, current mean value
Stability of continuous-discrete linear systems with delays in state vector
|T. Kaczorek, L. Sajewski|
(Bialystok University of Technology, Poland)
A new class of positive continuous-discrete linear systems with delays in state vector described by the model based on 2D general model is addressed. Necessary and sufficient conditions for the positivity and asymptotic stability of this class of linear systems are established. A procedure for checking the asymptotic stability is proposed. The effectiveness of the procedure is demonstrated on a numerical example.
keywords: stability, positivity, continuous-discrete, delays, state vector