Robust state derivative feedback LMI-based designs for discretized systems.

2020 ◽  
Author(s):  
Marco A. C. Leandro ◽  
Renan L. Pereira ◽  
Karl H. Kienitz
Keyword(s):  
Discrete Time ◽  
Cartesian Product ◽  
Stable Region ◽  
Space Representation ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
Time Model ◽  
State Space Representation ◽  
Augmented System ◽  
Discretized Systems

This work addresses novel Linear Matrix Inequality (LMI)-based conditions for thedesign of discrete-time state derivative feedback controllers. The main contribution of this work consists of an augmented discretized model formulated in terms of the state derivative, such that uncertain sampling periods and parametric uncertainties in polytopic form can be propagated from the original continuous-time state space representation. The resulting discrete-time model is composed of homogeneous polynomial matrices with parameters lying in the Cartesian product of simplexes, plus an additive norm-bounded term representing the residual discretization error. Moreover, the referred condition allows for the closed-loop poles allocation of the augmented system in a D-stable region. Finally, numerical simulations illustrate the effectiveness of the proposed method.

scholarly journals Neural-Network-Based Discrete-Time Fuzzy Control of Continuous-Time Nonlinear Systems with Dither

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Zhi-Ren Tsai ◽  
Jiing-Dong Hwang
Keyword(s):  
Neural Network ◽  
Nonlinear System ◽  
Discrete Time ◽  
Continuous Time ◽  
Fuzzy Controller ◽  
Sampling Frequency ◽  
Space Representation ◽  
Linear Matrix ◽  
State Space Representation ◽  
Ct System

This study presents an effective approach to stabilizing a continuous-time (CT) nonlinear system using dithers and a discrete-time (DT) fuzzy controller. A CT nonlinear system is first discretized to a DT nonlinear system. Then, a Neural-Network (NN) system is established to approximate a DT nonlinear system. Next, a Linear Difference Inclusion state-space representation is established for the dynamics of the NN system. Subsequently, a Takagi-Sugeno DT fuzzy controller is designed to stabilize this NN system. If the DT fuzzy controller cannot stabilize the NN system, a dither, as an auxiliary of the controller, is simultaneously introduced to stabilize the closed-loop CT nonlinear system by using the Simplex optimization and the linear matrix inequality method. This dither can be injected into the original CT nonlinear system by the proposed injecting procedure, and this NN system is established to approximate this dithered system. When the discretized frequency or sampling frequency of the CT system is sufficiently high, the DT system can maintain the dynamic of the CT system. We can design the sampling frequency, so the trajectory of the DT system and the relaxed CT system can be made as close as desired.

L2 gain state derivative feedback control of uncertain vehicle suspension systems

2017 ◽  
Vol 24 (16) ◽  
pp. 3779-3794 ◽  
Author(s):  
Hakan Yazici ◽  
Mert Sever
Keyword(s):  
Ride Comfort ◽  
Controller Design ◽  
Parametric Uncertainty ◽  
Feedback Controller ◽  
Vehicle Suspension ◽  
Space Representation ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
State Space Representation ◽  
Tire Stiffness

This paper is concerned with the design of a robust L2 gain state derivative feedback controller for an active suspension system. An uncertain quarter vehicle model is used to analyze vehicle suspension performance. Parametric uncertainty is assumed to exist in sprung mass, tire stiffness and suspension damping coefficients. Polytopic type state space representation is used to enable robust controller design via a linear matrix inequalities (LMIs) framework. Then nominal and robust L2 gain state derivative feedback controllers having bounded controller gains and robust L2 gain state feedback controllers are tested against ISO2631 random road disturbances with different road grades and vehicle horizontal velocities. Simulation results show that the proposed robust L2 gain state derivative feedback controller is very effective in improving ride comfort without deterioration on road holding ability.

Discrete-time Inversion Model Control of a Double-damper System with Uncertain Parameters

2017 ◽  
Vol 6 (3) ◽  
pp. 168
Author(s):  
Marwa Hannachi ◽  
Ikbel Bencheikh Ahmed ◽  
Dhaou Soudani
Keyword(s):  
Discrete Time ◽  
Algebraic Approach ◽  
Building Blocks ◽  
Internal Model Control ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Inversion ◽  
Time Model ◽  
Model Control ◽  
The Stability

<span>This paper addresses the control at discrete time of physical complex systems multi-inputs multi-outputs with variables parameters. Classified among the robust control laws the Internal Model Control (IMC) is adopted in this work to ensure the desired performances adjacent to the complexities of the system. However, the application of this control strategy requires that these different building blocks be open loop stable, which invites us, on the one hand, to apply the algebraic approach of Kharitinov for delimiting the summits stability domain’s system. On the other case, the Linear Matrix Inequalities (LMI) approach is applied to determine the corrector’s stability conditions obtained by a specific inversion of the chosen model. It is in this sense that we contribute by this work to execute the command by inversion the discrete-time model in order to ensure the stability and to maintain the performances the stability conditions of required for the double damper system with variable parameters.</span>

scholarly journals Design of a Discrete Tracking Controller for a Magnetic Levitation System: A Nonlinear Rational Model Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Fernando Gómez-Salas ◽  
Yongji Wang ◽  
Quanmin Zhu
Keyword(s):  
Discrete Time ◽  
Magnetic Levitation ◽  
Approximate Model ◽  
Space Representation ◽  
State Space Representation ◽  
Classical State ◽  
System A ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Model Approach

This work proposes a discrete-time nonlinear rational approximate model for the unstable magnetic levitation system. Based on this model and as an application of the input-output linearization technique, a discrete-time tracking control design will be derived using the corresponding classical state space representation of the model. A simulation example illustrates the efficiency of the proposed methodology.

scholarly journals Stabilization of discrete-time LTI positive systems

2017 ◽  
Vol 27 (4) ◽  
pp. 575-594 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Linear Matrix ◽  
Positive System ◽  
Matrix Inequalities ◽  
Positive Systems ◽  
Feedback Controllers ◽  
Associated Solutions ◽  
State Observers ◽  
Time Linear

AbstractThe paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the state-feedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.

FUZZY LOGIC DERIVATION OF NEURAL NETWORK MODELS WITH TIME DELAYS IN SUBSYSTEMS

2005 ◽  
Vol 14 (06) ◽  
pp. 967-974 ◽  
Author(s):  
CHEN-YUAN CHEN ◽  
JOHN RONG-CHUNG HSU ◽  
CHENG-WU CHEN
Keyword(s):  
Time Delays ◽  
Fuzzy Model ◽  
Network Models ◽  
Space Representation ◽  
Linear Matrix ◽  
Neural Network Models ◽  
Lmi Optimization ◽  
Common Solution ◽  
State Space Representation ◽  
The Stability

This paper extends the Takagi-Sugeno (T-S) fuzzy model representation to analyze the stability of interconnected systems in which there exist time delays in subsystems. A novel stability criterion which can be solved numerically is presented in terms of Lyapunov's theory for fuzzy interconnected models. In this paper, we use linear difference inclusion (LDI) state-space representation to represent the fuzzy model. Then, the linear matrix inequality (LMI) optimization algorithm is employed to find common solution and then guarantee the asymptotic stability.

Sign in / Sign up

Export Citation Format

Share Document