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1
Content available Squaring down plant model and I/O grouping strategies for a dynamic decoupling of left-invertible MIMO plants
Dworak P.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2014
|
Vol. 62, nr 3
471--479
EN
In the paper problems with dynamic decoupling of the left-invertible multi-input multi-output dynamic (MIMO) linear time invariant plants using a squaring down technique are considered. The procedure of squaring down the plant model and grouping of plant inputs and outputs are discussed. The final part of the paper includes a few examples of different strategies of synthesis of a decoupled system along with conclusions and final remarks.
2
Content available Application of adaptive multivariable Generalized Predictive Control to a HVAC system in real time
Gulan M., Salaj M., Rohal’-Ilkiv B
Archives of Control Sciences
|
2014
|
Vol. 24, no. 1
67--84
EN
This paper presents the application of a Multivariable Generalized Predictive Controller (MGPC) for simultaneous temperature and humidity control in a Heating, Ventilating and Air- Conditioning (HVAC) system. The multivariable controlled process dynamics is modeled using a set of MISO models on-line identified from measured input-output process data. The controller synthesis is based on direct optimization of selected quadratic cost function with respect to amplitude and rate input constraints. Efficacy of the proposed adaptive MGPC algorithm is experimentally demonstrated on a laboratory-scale model of HVAC system. To control the airconditioning part of system the designed multivariable predictive controller is considered in a cascade dual-rate control scheme with PID auxiliary controllers.
3
Content available Regular design equations for the discrete reduced-order Kalman filter
Hippe P.
Archives of Control Sciences
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2012
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Vol. 22, no. 2
161-174
EN
In the presence of white Gaussian noises at the input and the output of a system Kalman filters provide a minimum-variance state estimate. When part of the measurements can be regarded as noise-free, the order of the filter is reduced. The filter design can be carried out both in the time domain and in the frequency domain. In the case of full-order filters all measurements are corrupted by noise and therefore the design equations are regular. In the presence of noise-free measurements, however, they are not regular so that standard software cannot readily be applied in a time-domain design. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation causes no problems. However, the known proof of optimality of the factorization result requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for the reduced-order discrete-time Kalman filter in the time and in the frequency domains so that standard software is applicable. They also allow to formulate the conditions for the stability of the filter and to prove the optimality of the existing solutions.
4
Content available remote A study on new right/left inverses of nonsquare polynomial matrices
Hunek W. P., Latawiec K. J.
International Journal of Applied Mathematics and Computer Science
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2011
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Vol. 21, no 2
331-348
EN
This paper presents several new results on the inversion of full normal rank nonsquare polynomial matrices. New analytical right/left inverses of polynomial matrices are introduced, including the so-called [...]-inverses, [...]-inverses and, in particular, S-inverses, the latter providing the most general tool for the design of various polynomial matrix inverses. The application-oriented problem of selecting stable inverses is also solved. Applications in inverse-model control, in particular robust minimum variance control, are exploited, and possible applications in signal transmission/recovery in various types of MIMO channels are indicated.
5
Content available Regular design equations for the continuous reduced-order Kalman filter
Hippe P.
Archives of Control Sciences
|
2011
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Vol. 21, no. 4
349-361
EN
Reduced-order Kalman filters yield an optimal state estimate for linear dynamical systems, where parts of the output are not corrupted by noise. The design of such filters can either be carried out in the time domain or in the frequency domain. Different from the full-order case where all measurements are noisy, the design equations of the reduced-order filter are not regular. This is due to the rank deficient measurement covariance matrix and it can cause problems when using standard software for the solution of the Riccati equations in the time domain. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation does not cause problems. However, the known proof of optimality of the factorization result also requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for reduced-order Kalman filters in the time and in the frequency domains for linear continuous-time systems. They allow to use standard software for the design of the filter, to formulate the conditions for the stability of the filter and they also prove that the existing frequency domain solutions obtained by spectral factorization of a non-regular polynomial matrix equation are indeed optimal.
6
Adaptive output feedback control of MIMO AUV with unknown gain matrix
Nambisan P. R., Singh S. N.
Systems Science
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2009
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Vol. 35, no 2
5-10
EN
This paper presents a model reference adaptive control (MRAC) system for the dive plane control of a multi-input, multi-output (MIMO) autonomous underwater vehicle (AUV). The vehicle is equipped with a bow and a stern hydroplane for the purpose of control. It is assumed that the system parameters including the high-frequency gain matrix are unknown. Based on the Lyapunov stability theory, an adaptive output feedback control law is derived for the trajectory control of the depth and pitch angle. For the design of the control law, SDU decomposition of the high-frequency gain matrix is used, and only the measured output variables (the depth and pitch angle) are used for the synthesis of the controller. Simulation results are presented which show that in the closed-loop system, depth and pitch angle trajectory tracking is accomplished in spite of the presence of parameter uncertainties.
7
Content available remote On directional change and anti-windup compensation in multivariable control systems
Horla D.
International Journal of Applied Mathematics and Computer Science
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2009
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Vol. 19, no 2
281-289
EN
The paper presents a novel description of the interplay between the windup phenomenon and directional change in controls for multivariable systems (including plants with an uneven number of inputs and outputs), usually omitted in the literature. The paper also proposes a new classification of anti-windup compensators with respect to the method of generating the constrained control signal.
8
Content available remote Minimum variance control of discrete-time and continuous-time LTI MIMO systems - a new unified framework
Hunek W. P., Latawiec K. J.
Control and Cybernetics
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2009
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Vol. 38, no 3
609-624
EN
This paper presents a new uniform framework for solving the problem of minimum variance control of both discrete-time and continuous-time linear time-invariant multi-input multi-output systems described by general input-output models. Rather surprisingly, it is shown that the continuous-time case can be analyzed and synthesized without the necessity of involving the celebrated (and rather complex) theory of output predictor emulation, so that quite similar, simple solution is obtained like for the well-known discrete-time case.
9
Content available On decoupling of LTI MIMO systems with guaranteed stability
Bańka S., Dworak P.
Pomiary Automatyka Kontrola
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2007
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R. 53, nr 6
46-51
EN
In the paper methods for decoupling of dynamic multivariable systems are presented. There is discussed both static and dynamic decoupling of systems for open-loop control. The designed elements of the system provides elimination of interactions between specific plants inputs and outputs in a steady and transition state respectively. Results of considerations are illustrated by a numerical example.
PL
W artykule omawia się sposoby odsprzęgania dynamicznych wielowymiarowych układów liniowych do celów sterowania nimi w otwartej pętli. Rozważa się zarówno odsprzęganie statyczne eliminujące interakcje między poszczególnymi wyjściami obiektu w stanach ustalonych jak i odsprzęganie dynamiczne pozwalające na eliminację tych oddziaływań również w stanach przejściowych. Rozważania zilustrowano przykładem obliczeniowym.
10
Content available remote The steering of the ship motion: a Μ-synthesis approach
Gierusz W.
Archives of Control Sciences
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2006
|
Vol. 16, no. 1
87-109
EN
The main goal of this task was synthesis of the multivariable regulator for precise steering of the real, training ship. However such object is strongly nonlinear and its characteristics depends on current work conditions. Therefore one of possible ways to build a proper ship's controller can be the robust control theory approach. It enables the introduction of the effects of the modeling errors, unknown nonlinearities, unawareness of the particular object phenomena into the controller synthesis process. First part of the paper describes the meaning of the weighting functions in the system, the conditions for computing of the H∞ controller and the parametric and nonparametric uncertainties. The next part presents the requirements which should be fulfilled by regulator to the robust one and it describes the way how to calculate the multivariable robust controller via D-K iteration. In the last part of the paper exemplary results of the steering process from simulation and the real-time illustrates the control quality of the obtained closed-loop system.
11
Content available remote Control zeros and maximum-accuracy / maximum-speed control of LTI MIMO discrete-time systems
Latawiec K. J.
Control and Cybernetics
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2005
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Vol. 34, no 2
453-475
EN
Based on new definitions of "control zeros" and minimum phase property for possibly nonsquare LTI MIMO discrete-time systems, generalizations of perfect regulation and perfect filtering are presented both for polynomial matrix and state space models. Consequently, general equivalence results are announced for multi-step and single-step optimal controls as well as for maximum-accuracy and maximum-speed controls for LTI MIMO discrete-time systems. The latter is made visible after the introduction of a new-category of time-optimal control, namely infimum-time control. The equivalence conditions refer to the system's right-invertibility and the (newly-defined) minimum phase behavior, which demonstrates the usefulness of the new approach to zeros of multi variable systems.
12
Content available remote A power system application of a robust decentralized controller design methodology
Vesely V., Kozakova A.
Archives of Control Sciences
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2005
|
Vol. 15, no. 2
187-198
EN
The paper deals with the frequency domain design of a robust power system stabilizer (PSS) foe a multivariable power system. The proposed PSS design procedure is based on a novel approach that applies the independent design methodology along with the well-known small gain theory and the robust stability conditions in the M-D setup to the so-called equivalent subsystems. Theoretical results have been applied to the design of a robust multivariable PSS for a part of the Power System of the Slovak Republic.
13
On controllability and observability of linear systems: multiple eigenvalue case
Yaici M., Belmehdi A.
Systems Science
|
2004
|
Vol. 30, no 2
11-20
EN
This paper presents a method to verify the controllability and observability of linear multivariable systems with multiple modes using eigenprojectors or constituent matrices. Eigenprojectors are obtained by the partial fraction expansion of the numerator of the transfer function matrix of the system and the constituent matrices are obtained from the spectral decomposition of the state matrix. Eigenprojectors inform on the properties of the corresponding mode separately from the others, so controllability and observability of each mode are checked. A previous paper has dealt with linear systems with single eigenvalues, and the same method gave good results. Numerical examples are given to illustrate this method.
14
Content available Sterowanie adaptacyjne w wielowymiarowych układach dynamicznych
Bańka S., Dworak P.
Pomiary Automatyka Kontrola
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2004
|
R. 50, nr 1
19-24
PL
W pracy omawia się problemy wystepujące przy projektowaniu i realizacji w dziedzinie czasowej adaptacyjnych układów sterowania w wielowymiarowych układach dynamicznych ze sprzężeniem zwrotnym, wykorzystujących technikę lokowania biegunów (z ang. Pole Placement). Na tle ogólnych wymagań stawianych wielowymiarowym układom ze sprzężeniem zwrotnym rozpatruje się przypadki sterowania modalnego z wykorzystaniem obserwatorów Luenbergera pełnego rzędu i obserwatorów funkcjonalnych zredukowanego rzędu. Podaje się sposoby projektowania regulatorów modalnych w dziedzinach operatorowych "s" lub "z" oraz ich realizacji w dziedzinach czasowych, przydatnych do celów sterowania adaptacyjnego. Całość rozważań ilustruje przykład obliczeniowy przeprowadzony dla obiektu 4 rzędu o 3 wejściach i 2 wyjściach.
EN
The paper deals with problems encountered when designing and implementing (in time domain) adaptive control systems in feedback multivariable dynamic systems employing the pole placement approach. Some cases of modal control using full-order functional reduced-order Luenberger observers are considered against the backgroung of general requirements that are imposed on multivariable feedback-based systems. Techniques for designing modal controllers in the s-domain or z-domain and their implementation in time-domain beging suitable for adaptive conterol are given. The considerations are illustrated by an example of the design procedure carried out for a control plant of the 4th order with 3 inputs and 2 outputs.
15
Content available High Precision State Feedback Robust Control System for Ship Track-Keeping
Łozowicki A.
Pomiary Automatyka Kontrola
|
2004
|
R. 50, nr 1
25-28
EN
In the paper the problem of ship trajectory tracking with ε-accuracy is considered. A three-degrees-of-freedom ship model full dynamic interaction between motions in roll, sway and yaw is assumed. The aim of the paper is to determine the robust control for ship trajectory tracking with ε-accuracy. Such control is obtained by means of a state feedback (called Tytus feedback) system characterised by an arbitrarily high gain. For this purpose a non-linear as well as linearised stable and unstable ship model is used. the simulation results confirm that a high precision performance can be achieved by the proposed control scheme.
PL
W pracy rozważa się problem sterowania ruchem statku po zadanej trajektorii z dowolnie małą ε-dokładnością. W rozważaniach przyjęto model statku o trzech stopniach swobody i pełnym opisie zależności dynamicznych pomiędzy przechyłami bocznymi, kołysaniem wzdłużnym i kursem statku. Celem pracy jest wyznaczenie odpornego układu sterowania ruchem statku po zadanej trajektorii z ε-dokładnością. Układem spełniającym powyższe warunki jest układ ze sprzężeniem zwrotnym od stanu i dostatecznie dużym wzmocnieniem. Opisany układ ze sprzężeniem zwrotnym wykorzystano do sterowania nieliniowego modelu statku jak również dla sterowania zlinearyzowanego, stabilnego i niestabilnego modelu statku. Wyniki symulacji w srodowisku MATLAB-SIMULINK potwierdzają wysoką jakość sterowania jaka może być uzyskana dzięki wykorzystaniu zaproponowanego układu.
16
Content available remote Some Algorithmic Aspects of Subspace Identification With Inputs
Chiuso A., Picci G.
International Journal of Applied Mathematics and Computer Science
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2001
|
Vol. 11, no 1
55-75
EN
It has been experimentally verified that most commonly used subspace methods for identification of linear state-space systems with exogenous inputs may, in certain experimental conditions, run into ill-conditioning and lead to ambiguous results. An analysis of the critical situations has lead us to propose a new algorithmic structure which could be used either to test difficult cases and/or to implement a suitable combination of new and old algorithms presented in the literature to help fixing the problem.
17
Content available remote An outline of the linear control system synthesis by a proper, stable rational functions approach
Ładziński R.
Archives of Control Sciences
|
1998
|
Vol. 7, no. 3/4
241-265
EN
In the process of designing controllers for linear multivariable plants specially effective are algebraic methods which require from the transfer matrices of both, the plant and the controller to be presented in coprime fractional form with factorization carried on with respect to the ring of exponentially-stable, proper real-rational functions. The main objective of the paper is to show that this form of representation with simultaneous parametrization of all linear controllers that provide internal stability of the closed-loop system can be achieved in the simplest and most natural way by analysing the system shown in Fig. 3 - the so-called basic structure. Problems of choosing the parameter to meet some important design specifications, viz. a robust asymptotic tracking of the reference signal with disturbance and noise rejection are also considered and illustrated by two representative examples covering the area of continuous- and discrete-time systems.
18
Content available remote Generating a self-organizing fuzzy controller from human skill performance for multivariable systems
Lekova A., Boyadjiev D.
Applied Mathematics and Computer Science
|
1998
|
Vol. 8, no 3
633-645
EN
The paper presents a learning concept for creating of a self-organizing fuzzy controller for multivariable systems by explicit use of human skill performance during the control of a complex technological process. When such processes cannot be entirely controlled automatically, a natural way to achieve flexible and adaptive control is a combination of human resources and information technologies. The main idea is the decomposition of a multivariable control system into several subsystems with two inputs and multiple outputs. The number of sub-systems corresponds to the number of all orthogonal projections of an N-dimensional input vector in the two-dimensional pIane. Thus the method for generating fuzzy if-then rules from numerical data in the two-dimensional pIane which is already available, can be used. Fuzzy rules with variable fuzzy regions are generated automatically. An aggregation operator for calculating the connectivity degree of membership functions which connects the whole set of the generated fuzzy rules in all decomposed subsystems is found.
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