scholarly journals Anti-windup design with guaranteed regions of stability for discrete-time linear systems with saturating controls

2004 ◽  
Vol 15 (1) ◽  
pp. 3-9 ◽  
Author(s):  
João Manoel Gomes da Silva Jr. ◽  
Romeu Reginatto ◽  
Sophie Tarbouriech
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Closed Loop ◽  
Basin Of Attraction ◽  
Loop System ◽  
Discrete Time System ◽  
Closed Loop System ◽  
Model Stability ◽  
Quadratic Lyapunov Functions ◽  
Time Linear

The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be modeled by a linear system connected to a deadzone nonlinearity. From this model, stability conditions based on quadratic Lyapunov functions are stated. Algorithms based on LMI schemes are proposed for computing both the anti-windup gain and an associated stability region.

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Wenping Xue ◽  
Kangji Li
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Initial State ◽  
Finite Time Stability ◽  
Time Linear

In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

scholarly journals Comparison of Disturbance Compensators for a Discrete-Time System with Parameter Uncertainty

2020 ◽  
Vol 10 (18) ◽  
pp. 6219
Author(s):  
Zhongyi Guo ◽  
Haifeng Ma ◽  
Qinghua Song
Keyword(s):  
Discrete Time ◽  
Parameter Uncertainty ◽  
Closed Loop ◽  
Sliding Mode ◽  
External Disturbance ◽  
Comparative Investigation ◽  
Industrial Applications ◽  
System Stability ◽  
Discrete Time System ◽  
Closed Loop System

The control design for many industrial applications requires compensation for parameter uncertainty and external disturbance. Reported in many previous works, the parameter uncertainty and external disturbance are combined as a lumped disturbance, which is assumed to be smooth and bounded. However, for a discrete-time sliding mode control (DSMC) system, the above assumption may not hold. Here, the parameter uncertainty, along with its compensation in the DSMC system, are reconsidered and reevaluated. The influence of parameter uncertainty on the closed-loop system stability is first addressed. Then, the comparative investigation of the performance of six state-of-the-art disturbance compensators for parameter uncertainty compensation is conducted. Simulation results show that none of these compensators can effectively observe and compensate for the parameter uncertainty.

The variable, fractional-order discrete-time PD controller in the IISv1.3 robot arm control

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Piotr Ostalczyk ◽  
Dariusz Brzezinski ◽  
Piotr Duch ◽  
Maciej Łaski ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Output Signal ◽  
Closed Loop ◽  
Loop System ◽  
Robot Arm ◽  
Pd Controller ◽  
Closed Loop System ◽  
Loop Control ◽  
Robot Arm Control

AbstractIn this paper, the discrete differentiation order functions of the variable, fractional-order PD controller (VFOPD) are considered. In the proposed VFOPD controller, a variable, fractional-order backward difference is applied to perform closed-loop, system error, discrete-time differentiation. The controller orders functions which may be related to the controller input or output signal or an input and output signal. An example of the VFOPD controller is applied to the robot arm closed-loop control due to system changes in moment of inertia. The close-loop system step responses are presented.

Use of Bilinear Structures for Modelling a Brewery Fermentation Process

1996 ◽  
Vol 29 (9) ◽  
pp. 262-265 ◽  
Author(s):  
C.R. Johnson ◽  
K.J. Burnham
Keyword(s):  
Specific Gravity ◽  
Discrete Time ◽  
Fermentation Process ◽  
Closed Loop ◽  
Loop System ◽  
Model Structure ◽  
Bilinear Model ◽  
Input Output ◽  
Closed Loop System ◽  
Model Structures

This paper presents the results of an investigative study with the aim being to obtain and assess the appropriateness of bilinear model structures for replicating the characteristics of a brewery fermentation process. Based on realtime data taken from a brewery fermentation plant, it is shown that a discrete-time twin-bilinear model, which simultaneously relates temperature to specific gravity and specific gravity to temperature, provides an adequate input/output reconstruction. The ability of the twin-bilinear model structure is discussed and possibilities for its utilization with an adaptive closed loop system are considered.

Robust stability of positive discrete-time linear systems of fractional order

2010 ◽  
Vol 58 (4) ◽  
pp. 567-572 ◽  
Author(s):  
M. Busłowicz
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Robust Stability ◽  
Discrete Time ◽  
Natural Order ◽  
Discrete Time System ◽  
Uncertainty Structure ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Robust stability of positive discrete-time linear systems of fractional orderThe paper is devoted to the problem of robust stability of linear positive discrete-time systems of fractional order with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of linear uncertainty structure with unity rank uncertainty structure and with non-negative perturbation matrices, are established. It is shown that robust stability of the positive discrete-time fractional system is equivalent to: 1) robust stability of the corresponding positive discrete-time system of natural order - in the general case, 2) robust stability of the corresponding finite family of positive discrete-time systems of natural order - in the case of linear unity rank uncertainty structure, 3) asymptotic stability of only one corresponding positive discrete-time system of natural order - in the case of linear uncertainty structure with non-negative perturbation matrices. Moreover, simple necessary and sufficient condition for robust stability of the positive interval discrete-time linear systems of fractional order is given. The considerations are illustrated by numerical examples.

scholarly journals Decomposition of the pairs (A, B) and (A, C) of positive discrete-time linear systems

2010 ◽  
Vol 20 (3) ◽  
pp. 341-361 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Transfer Matrix ◽  
Discrete Time ◽  
Positive System ◽  
Discrete Time System ◽  
Time System ◽  
Time Linear

Decomposition of the pairs (A, B) and (A, C) of positive discrete-time linear systemsA new test for checking the reachability (observability) of positive discrete-time linear systems is proposed. Conditions are established under which the unreachable pair (A, B) and the unobservable pair (A, C) of positive discrete-time system can be decomposed into reachable and unreachable parts and observable and unobservable parts, respectively. It is shown that the transfer matrix of the positive system is equal to the transfer matrix of its reachable (observable) part.

Discrete-Time Closed-Loop Model Identification of Fixed-Structure Unstable Multivariable Systems

2007 ◽  
Author(s):  
Huzefa Shakir ◽  
Won-Jong Kim
Keyword(s):  
System Identification ◽  
Discrete Time ◽  
Closed Loop ◽  
Model Identification ◽  
Order Reduction ◽  
Loop System ◽  
Loop Model ◽  
Frequency Range ◽  
Closed Loop System ◽  
Closed Loop Identification

This paper presents improved empirical representations of a general class of open-loop unstable systems using closed-loop system identification. A multi-axis magnetic-levitation (maglev) nanopositioning system with an extended translational travel range is used as a test bed to verify the closed-loop system-identification method proposed in this paper. A closed-loop identification technique employing the Box-Jenkins (BJ) method and a known controller structure is developed for model identification and validation. Direct and coupling transfer functions (TFs) are then derived from the experimental input-output time sequences and the knowledge of controller dynamics. A persistently excited signal with a frequency range of [0, 2500] Hz is used as a reference input. An order-reduction algorithm is applied to obtain TFs with predefined orders, which give a close match in the frequency range of interest without missing any significant plant dynamics. The entire analysis is performed in the discrete-time domain in order to avoid any errors due to continuous-to-discrete-time conversion and vice versa. Continuous-time TFs are used only for order-reduction and performance analysis of the identified plant TFs. Experimental results in the time as well as frequency domains verified the accuracy of the plant TFs and demonstrated the effectiveness of the closed-loop identification and order-reduction methods.

Adaptive robust stabilization of a class of uncertain non-linear systems with mismatched time-varying parameters

2011 ◽  
Vol 226 (2) ◽  
pp. 204-214 ◽  
Author(s):  
M M Arefi ◽  
M R Jahed-Motlagh
Keyword(s):  
Linear Systems ◽  
Closed Loop ◽  
Robust Stabilization ◽  
Lyapunov Theory ◽  
Loop System ◽  
Time Varying ◽  
Closed Loop System ◽  
Mismatched Uncertainties ◽  
Non Linear ◽  
Non Linear Systems

In this paper, an adaptive robust stabilization algorithm is presented for a class of non-linear systems with mismatched uncertainties. In this regard, a new controller based on the Lyapunov theory is proposed in order to overcome the problem of stabilizing non-linear time-varying systems with mismatched uncertainties. This method is such that the stability of the closed-loop system is guaranteed in the absence of the triangularity assumption. The proposed approach leads to asymptotic convergence of the states of the closed-loop system to zero for unknown but bounded uncertainties. Subsequently, this method is modified so that all the signals in the closed-loop system are uniformly ultimately bounded. Eventually, numerical simulations support the effectiveness of the given algorithm.

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