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1

Variable structure control of second order system with acceleration constraint

Nowacka-Leverton A., Bartoszewicz A.

Mechanics / AGH University of Science and Technology

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2009

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Vol. 28, no. 3

96-100

EN

The paper presents a new sliding mode control (SMC) method for the second order system subject to acceleration constraint. The proposed method employs a time-varying switching line which initially passes through the representative point, specified by the initial conditions of the system, in the error state space. Afterwards the line moves smoothly, with a constant velocity and a constant angle of inclination to the origin of the error state space and then, having reached the origin it stops moving and remains fixed. Thus the proposed control algorithm eliminates the reaching phase and forces the representative point of the system always to stay on the switching line. Consequently, insensitivity of the system with respect to external disturbances and model uncertainties is guaranteed from the very beginning of the proposed control action. Parameters of the switching line are selected to minimize two control quality criteria - the integral absolute error (IAE) and the integral of the time multiplied by the absolute error (ITAE) - without violating the system acceleration constraint. Furthermore, the switching line is selected in such a way that the tracking error converges to zero monotonically, without overshoots or oscillations. The proposed method is verified and illustrated by a simulation example.

PL

W artykule zaprezentowano metodę projektowania ślizgowego sterowania obiektem dynamicznym drugiego rzędu przy ograniczeniu jego przyspieszenia. Wykorzystano w tym celu niestacjonarną linię przełączeń, która w chwili początkowej zawiera punkt opisujący dynamikę obiektu w przestrzeni stanu, a następnie - nie obracając się - przesuwa się ruchem jednostajnym do początku tej przestrzeni. Po osiągnięciu początku układu współrzędnych linia zatrzymuje się i w dalszej fazie procesu regulacji pozostaje nieruchoma. W ten sposób wyeliminowana zostaje konieczność osiągania ruchu ślizgowego, a dzięki temu zapewniona jest niewrażliwość obiektu na zakłócenia zewnętrzne i niedokładności określenia modelu już od samego początku trwania procesu regulacji. Linia przełączeń projektowana jest tak, aby jej parametry zapewniały minimalizację dwóch kryteriów jakości regulacji - całki modułu uchybu oraz całki iloczynu czasu i modułu uchybu - przy równoczesnym spełnieniu ograniczenia przyspieszenia obiektu. Ponadto zastosowana w układzie sterowania linia przełączeń zapewnia monotoniczną zbieżność uchybu regulacji do zera bez przeregulowań i oscylacji. Zaproponowana w artykule metoda została zilustrowana i zweryfikowana przykładem symulacyjnym.

2

Robustness of model-reference variable-structure robot control methods

Krajčí V.

Journal of Automation Mobile Robotics and Intelligent Systems

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2008

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Vol. 2, No. 2

29-34

EN

Different variations of one simple Model-Reference Variable-Structure Control (MRVSC) method are presented and used for planar robot control. The quality of trajectory tracking was tested by simulation with respect to robot parameter changes, different complex sinusoidal external disturbances and measurement noise. The results proved satisfactory robustness of all presented modified MRVSC methods.

3

Design of a sliding mode controller based on local averaged technique and applied to the buck converter

Jaen C., Pou J., Pindado R., Sala V., Zaragoza J.

Przegląd Elektrotechniczny

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2007

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R. 83, nr 10

99-102

EN

A modeling methodology applied to PWM DC-DC converters is presented in this paper. Parasitic resistors have been considered in inductor and power supply. A generalised equivalent circuit based on averaged variables is obtained for the basic structures of DC-DC converters. This circuit and the associated model are valid for continuous conduction mode and discontinuous conduction mode. This contribution contains expressions to detect changes of the converter operation mode and to estimate the value of the diode duty cycle operating under discontinuous conduction mode. A sliding mode controller for the regulation of the output voltage has been designed in terms of averaged state variables and converter parameters. The procedure is applied to a 100W Buck converter prototype. Simulations and experimental results are presented.

PL

W artykule przedstawiono metodologię modelowania przekształtników PWM napięcia stałego (DC-DC) z uwzględnieniem rezystancji pasożytniczych cewki indukcyjnej i źródła zasilenia. Na podstawie uśrednionych zmiennych stanu opracowano ogólny schemat zastępczy podstawowych struktur przekształtników DC-DC. Ten schemat oraz odpowiedni model są słuszne przy przewodzeniu ciągłym i impulsowym. Obydwa tryby przewodzenia łączą wyrażenia, wykrywające zmiany w działaniu przekształtnika oraz pozwalające oszacować wartości cyklu pracy diody przy przewodzeniu impulsowym. Zaprojektowany dla uśrednionych zmiennych stanu z uwzględnieniem parametrów przekształtnika regulator ślizgowy napięcia wyjściowego został zastosowany w prototypie przekształtnika typu Buck o mocy 100W. Artykuł zawiera wyniki badań symulacyjnych i eksperymentalnych.

4

A time-varying switching plane design for variable structure control of the third order system with input constraint

Bartoszewicz A., Nowacka A.

Archives of Control Sciences

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2004

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Vol. 14, no. 2

201-213

EN

In this paper a new sliding mode control algorithm for the third order ucertain, nonlinear and time-varying dynamic system subject to unknown disturbance and input constraints is proposed. The algorithm employs a time-varying switching plane. At the initial time t=t0, the plane passes through the point determined by the system initial conditions in the error state space. Afterwards, the moves with a constant velocity to the origin of the space. the plane is selected in such a way that the integral of the absolute value of the system error over the whole period of the control action is minimized and the input constraint is satisfied. By this means, the reaching phase is eliminated, insensitivity of the system to the external disturbance is guaranteed from the very beginning of the proposed control action and fast, monotonic error convergence to zero is achieved.

5

Robust variable structure model following controller for load frequency control

Patre B.M., Bandyopadhyay B., Unbehauen H.

Systems Science

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2002

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Vol. 28, nr 4

43-59

EN

A systematic procedure for design of variable structure model following load frequency controller for a single-area power system has been presented. The variable structure model following control (VSMFC) technique presented in this paper not only guarantees invariance to a class of parameter variations and disturbances but also possesses other attractive features of variable structure systems (VSS) such as robustness to unknown disturbances, simplicity in design, and reduced order dynamics when in sliding mode. The simulation results of the variable structure model following control strategy to load frequency control are presented by changing all parameters by 30% to 50% from their nominal values. These results show that systems performance is robust to parameter variations and disturbances.

6

On the effect of chattering in the sliding mode control systems.

Bartoszewicz A.

Systems Science

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2000

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Vol. 26, nr 1

29-42

EN

Variable structure control systems with the ideal sliding motion are perfectly robust with respect to matched disturbance and parameter uncertainty. However, this mode of operation is not achieved in practice. Thus, in this paper the non-ideal sliding motion actually taking place in variable structure systems is investigated. The phenomenon of chattering, i.e., high frequency oscillations which inevitably occur in the systems with ideal relays, is analysed. It is shown that the oscillations are caused by fast usually neglected dynamics of the system, for instance, unmodelled delay or inertia. The describing function method is used to predict the amplitude and the frequency of the oscillations. Furthermore, a simple method is given to determine how the ideal relay input-output characteristics should be modified to eliminate the chattering without introducing excessive control errors. Simulation results confirming the theoretical analysis presented.

7

Chattering attenuation in sliding mode control systems

Bartoszewicz A.

Control and Cybernetics

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2000

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Vol. 29, no 2

585-584

EN

In this paper sliding mode control systems are considered and a new technique to attenuate chattering is proposed. The technique employs simple, first-order dynamical devices, i.e. an integrator or a low-pass filter, to compensate in part for unknown and changing disturbance. As a result of this compensation, the magnitude of the discontinuous control term is essentially reduced. The term does not depend on the admissible disturbance or its change rate, but only on the uncertainty of the disturbance at the initial time t = t[sub o]. The technique proposed in this paper attenuates the undesirable chattering without any deterioration of the system performance.