Design of an Optimal Preview Controller for Linear Discrete-Time Descriptor Noncausal Multirate Systems

The linear discrete-time descriptor noncausal multirate system is considered for the presentation of a new design approach for optimal preview control. First, according to the characteristics of causal controllability and causal observability, the descriptor noncausal system is constructed into a descriptor causal closed-loop system. Second, by using the characteristics of the causal system and elementary transformation, the descriptor causal closed-loop system is transformed into a normal system. Then, taking advantage of the discrete lifting technique, the normal multirate system is converted to a single-rate system. By making use of the standard preview control method, we construct the descriptor augmented error system. The quadratic performance index for the multirate system is given, which can be changed into one for the single-rate system. In addition, a new single-rate system is obtained, the optimal control law of which is given. Returning to the original system, the optimal preview controller for linear discrete-time descriptor noncausal multirate systems is derived. The stabilizability and detectability of the lifted single-rate system are discussed in detail. The optimal preview control design techniques are illustrated by simulation results for a simple example.

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

Open Physics ◽

10.2478/s11534-013-0254-9 ◽

2013 ◽

Vol 11 (6) ◽

Cited By ~ 5

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.

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Use of Bilinear Structures for Modelling a Brewery Fermentation Process

Measurement and Control ◽

10.1177/002029409602900902 ◽

1996 ◽

Vol 29 (9) ◽

pp. 262-265 ◽

Cited By ~ 1

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.

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

Volume 9: Mechanical Systems and Control, Parts A, B, and C ◽

10.1115/imece2007-41834 ◽

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.

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

Sba Controle & Automação Sociedade Brasileira de Automatica ◽

10.1590/s0103-17592004000100002 ◽

2004 ◽

Vol 15 (1) ◽

pp. 3-9 ◽

Cited By ~ 3

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.

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LMI Pole Regions for a Robust Discrete-Time Pole Placement Controller Design

Algorithms ◽

10.3390/a12080167 ◽

2019 ◽

Vol 12 (8) ◽

pp. 167

Author(s):

Danica Rosinová ◽

Mária Hypiusová

Keyword(s):

Discrete Time ◽

Closed Loop ◽

Controller Design ◽

Loop System ◽

Pole Placement ◽

Linear Matrix ◽

Closed Loop System ◽

Robust Controller ◽

Pole Placement Controller ◽

Robust Controller Design

Herein, robust pole placement controller design for linear uncertain discrete time dynamic systems is addressed. The adopted approach uses the so called “D regions” where the closed loop system poles are determined to lie. The discrete time pole regions corresponding to the prescribed damping of the resulting closed loop system are studied. The key issue is to determine the appropriate convex approximation to the originally non-convex discrete-time system pole region, so that numerically efficient robust controller design algorithms based on Linear Matrix Inequalities (LMI) can be used. Several alternatives for relatively simple inner approximations and their corresponding LMI descriptions are presented. The developed LMI region for the prescribed damping can be arbitrarily combined with other LMI pole limitations (e.g., stability degree). Simple algorithms to calculate the matrices for LMI representation of the proposed convex pole regions are provided in a concise way. The results and their use in a robust controller design are illustrated on a case study of a laboratory magnetic levitation system.

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Analysis and Design of Networked Control Systems with Random Markovian Delays and Uncertain Transition Probabilities

Abstract and Applied Analysis ◽

10.1155/2014/486978 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Li Qiu ◽

Chengxiang Liu ◽

Fengqi Yao ◽

Gang Xu

Keyword(s):

Control Systems ◽

Discrete Time ◽

Closed Loop ◽

Networked Control Systems ◽

Transition Probabilities ◽

Lyapunov Stability Theory ◽

Loop System ◽

Networked Control ◽

Closed Loop System ◽

Analysis And Design

This paper focuses on the stability issue of discrete-time networked control systems with random Markovian delays and uncertain transition probabilities, wherein the random time delays exist in the sensor-to-controller and controller-to-actuator. The resulting closed-loop system is modeled as a discrete-time Markovian delays system governed by two Markov chains. Using Lyapunov stability theory, a result is established on the Markovian structure and ensured that the closed-loop system is stochastically stable. A simulation example illustrates the validity and feasibility of the results.

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Design of a stabilizing controller for discrete-time switched delay systems with affine parametric uncertainties

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217748191 ◽

2018 ◽

Vol 41 (1) ◽

pp. 14-22 ◽

Cited By ~ 5

Author(s):

NA Baleghi ◽

MH Shafiei

Keyword(s):

Discrete Time ◽

Closed Loop ◽

Sufficient Conditions ◽

Average Dwell Time ◽

Loop System ◽

Delay Systems ◽

Linear Matrix ◽

Parametric Uncertainties ◽

Closed Loop System ◽

Stabilizing Controller

This paper studies the stabilization problem of discrete-time switched systems in the presence of a time-varying delay and parametric uncertainties. The main goal is to provide a state feedback controller to guarantee the stability of the closed-loop system with an evaluated average dwell time. In this regard, an appropriate Lyapunov–Krasovskii functional is constructed and the sufficient conditions for stability of the closed-loop system are developed in terms of feasibility testing of proposed linear matrix inequalities. These conditions only depend on the upper bounds of the time delay and uncertain parameters. Additionally, a numerical example is provided to verify the theoretical results.

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