scholarly journals LMI–Based Robust Control of Uncertain Nonlinear Systems via Polytopes of Polynomials

2019 ◽  
Vol 29 (2) ◽  
pp. 275-283 ◽  
Author(s):  
Marcelino Sánchez ◽  
Miguel Bernal
Keyword(s):  
Nonlinear Systems ◽  
Space Representation ◽  
Linear Matrix ◽  
Uncertain Nonlinear Systems ◽  
Linear Parameter Varying ◽  
Analysis And Design ◽  
Linear Parameter Varying Systems ◽  
State Space Representation ◽  
The Subject ◽  
And Control

Abstract This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a generalisation of the characteristic polynomial, which proves to outperform former results on the subject. Moreover, the derived conditions have the advantage of being cast as linear matrix inequalities under mild assumptions.

Modeling, Actuation, and Control of an Active Fluid Vibration Isolator

1997 ◽  
Vol 119 (1) ◽  
pp. 52-59 ◽  
Author(s):  
M. J. Panza ◽  
D. P. McGuire ◽  
P. J. Jones
Keyword(s):  
Electrical Power ◽  
Fluid Pressure ◽  
Space Representation ◽  
Vibration Isolator ◽  
Mass System ◽  
Integral Control ◽  
Active Fluid ◽  
State Space Representation ◽  
In Series ◽  
And Control

An integrated mathematical model for the dynamics, actuation, and control of an active fluid/elastomeric tuned vibration isolator in a two mass system is presented. The derivation is based on the application of physical principles for mechanics, fluid continuity, and electromagnetic circuits. Improvement of the passive isolator performance is obtained with a feedback scheme consisting of a frequency shaped notch compensator in series with integral control of output acceleration and combined with proportional control of the fluid pressure in the isolator. The control is applied via an electromagnetic actuator for excitation of the fluid in the track connecting the two pressure chambers of the isolator. Closed loop system equations are transformed to a nondimensional state space representation and a key dimensionless parameter for isolator-actuator interaction is defined. A numerical example is presented to show the effect of actuator parameter selection on system damping, the performance improvement of the active over the passive isolator, the robustness of the control scheme to parameter variation, and the electrical power requirements for the actuator.

Modeling, Actuation, and Control of an Active Fluid Vibration Isolator

1995 ◽  
Author(s):  
Michael J. Panza ◽  
Dennis P. McGuire ◽  
Peter J. Jones
Keyword(s):  
Electrical Power ◽  
Fluid Pressure ◽  
Space Representation ◽  
Vibration Isolator ◽  
Mass System ◽  
Integral Control ◽  
Active Fluid ◽  
State Space Representation ◽  
In Series ◽  
And Control

Abstract An integrated mathematical model for the dynamics, actuation, and control of an active fluid/elastomeric tuned vibration isolator in a two mass system is presented. The derivation is based on the application of physical principles for mechanics, fluid continuity, and electromagnetic circuits. Improvement of the passive isolator performance is obtained with a feedback scheme consisting of a frequency shaped notch compensator in series with integral control of output acceleration and combined with proportional control of the fluid pressure in the isolator. The control is applied via an electromagnetic actuator for excitation of the fluid in the track connecting the two pressure chambers of the isolator. Closed loop system equations are transformed to a nondimensional state space representation and a key dimensionless parameter for isolator-actuator interaction is defined. A numerical example is presented to show the effect of actuator parameter selection on system damping, the performance improvement of the active over the passive isolator, the robustness of the control scheme to parameter variation, and the electrical power requirements for the actuator.

scholarly journals A vibroacoustic application of modeling and control of linear parameter-varying systems

2010 ◽  
Vol 32 (4) ◽  
pp. 409-419 ◽  
Author(s):  
Jan De Caigny ◽  
Juan Francisco Camino ◽  
Ricardo C L F de Oliveira ◽  
Pedro Luis D Peres ◽  
Jan Swevers
Keyword(s):  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Modeling And Control ◽  
Linear Parameter Varying Systems ◽  
Parameter Varying ◽  
And Control

State estimation for a class of Linear Parameter-Varying systems with parametric uncertainties

2020 ◽  
Vol 42 (15) ◽  
pp. 3035-3042
Author(s):  
Zhongwei He ◽  
Wei Xie
Keyword(s):  
State Estimation ◽  
Sufficient Conditions ◽  
Estimation Methods ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Observation Error ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Linear Parameter Varying Systems ◽  
Parameter Varying

This paper is concerned with interval state estimation for a class of Linear Parameter-Varying systems with parametric uncertainties. Firstly, sufficient conditions to guarantee both the cooperativity and stability of observation error dynamics are presented in terms of parameterized matrix inequality formulations. Secondly, a novel method for scheduled controller law design is proposed in the framework of interval observer design. Under the assumptions that scheduled parameters have a polytopic structure property, the problems of the existence conditions of observers and scheduled controller design are transformed into finite linear matrix inequalities ones, which can be solved by convex optimization algorithms. The validity of the proposed state estimation methods is illustrated through a simple example.

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.

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