scholarly journals A New Anti-Windup Compensator Based on Quantitative Feedback Theory for an Uncertain Linear System with Input Saturation

2019 ◽  
Vol 9 (15) ◽  
pp. 2958 ◽  
Author(s):  
R. Jeyasenthil ◽  
Seung-Bok Choi
Keyword(s):  
Robust Stability ◽  
Actuator Saturation ◽  
Linear Time ◽  
Input Saturation ◽  
Design Procedure ◽  
Feedback System ◽  
Linear Matrix ◽  
Quantitative Feedback Theory ◽  
Uncertain Linear System ◽  
Effective Manner

This paper devotes to the robust stability problem for an uncertain linear time invariant (LTI) feedback system with actuator saturation nonlinearity. Based on a three degree of freedom (DOF) non-interfering control structure, the robust stability is enforced with the describing function (DF) approach for an uncertain LTI system to avoid the limit cycle. A new type of anti-windup (AW) compensator is designed using the quantitative feedback theory (QFT) graphical method, which results in a simple design procedure and low-order AW control system. One of the most significant benefits of the proposed method is free of the non-convexity (intractable) drawback of the linear matrix inequality (LMI)-based approach. The analysis conducted on the benchmark problem clearly reveals that the proposed QFT-based anti-windup design is able to handle both saturation and uncertainty in a very effective manner.

A QFT Framework for Antiwindup Control Systems Design

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
J. C. Moreno ◽  
A. Baños ◽  
M. Berenguel
Keyword(s):  
Control Systems ◽  
Robust Stability ◽  
Stability Problem ◽  
Degrees Of Freedom ◽  
Actuator Saturation ◽  
Linear Time ◽  
Design Method ◽  
Systems Design ◽  
Linear Matrix ◽  
Single Input Single Output

The paper is devoted to the robust stability problem of linear time invariant feedback control systems with actuator saturation, especially in those cases with potentially large parametric uncertainty. The main motivation of the work has been twofold: First, most of the existing robust antiwindup techniques use a conservative plant uncertainty description, and second, previous quantitative feedback theory (QFT) results for control systems with actuator saturation are not suitable to achieve robust stability specifications when the control system is saturated. Traditionally, in the literature, this type of problems has been solved in terms of linear matrix inequalities (LMIs), using less structured uncertainty descriptions as given by the QFT templates. The problem is formulated for single input single output systems in an input-output (I/O) stability sense, and is approached by using a generic three degrees of freedom control structure. In this work, a QFT-based design method is proposed in order to solve the robust stability problem of antiwindup design methods. The main limitation is that the plant has poles in the closed left half plane, and at most, has one integrator. The work investigates robust adaptations of the Zames–Falb stability multipliers result, and it may be generalized to any compensation scheme that admits a decomposition as a feedback interconnection of linear and nonlinear blocks (Lur’e type system), being antiwindup systems as a particular case. In addition, an example will be shown, making explicit the advantages of the proposed method in relation to previous approaches.

scholarly journals T-S Fuzzy-Based Optimal Control for Minimally Invasive Robotic Surgery with Input Saturation

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Faguang Wang ◽  
Hongmei Wang ◽  
Yong Zhang ◽  
Xijin Guo
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Actuator Saturation ◽  
Input Saturation ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Invariant Ellipsoid ◽  
Minimally Invasive Robotic Surgery ◽  
Takagi Sugeno

A minimally invasive surgery robot is difficult to control when actuator saturation exists. In this paper, a Takagi-Sugeno fuzzy model-based controller is designed for a minimally invasive surgery robot with actuator saturation, which is difficult to control. The contractively invariant ellipsoid theorem is applied for the actuator saturation. The proposed scheme can be derived using the H-infinity control theorem and parallel distributed compensation. The result is rebuilt in the form of linear matrix inequalities for easier calculation by computer. Meanwhile, the uniformly ultimately bounded stable and the prescribed H-infinity control performance can be guaranteed. The proposed scheme is simulated in a Novint Falcon haptic device system.

Robust Control of Automotive Active Seat-Suspension System Subject to Actuator Saturation

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Zhou Gu ◽  
Shumin Fei ◽  
Yaqin Zhao ◽  
Engang Tian
Keyword(s):  
Controller Design ◽  
Actuator Saturation ◽  
Input Saturation ◽  
Output Feedback Control ◽  
Suspension System ◽  
Linear Matrix ◽  
Control Input ◽  
State Variables ◽  
Sampled Data ◽  
Seat Suspension

This paper deals with the problem of robust sampled-data control for an automotive seat-suspension system subject to control input saturation. By using the nature of the sector nonlinearity, a sampled-data based control input saturation in the control design is studied. A passenger dynamic behavior is considered in the modeling of seat-suspension system, which makes the model more precisely and brings about uncertainties as well in the developed model. Robust output feedback control strategy is adopted since some state variables, such as, body acceleration and body deflection, are unavailable. The desired controller can be achieved by solving the corresponding linear matrix inequalities (LMIs). Finally, a design example has been given to demonstrate the effectiveness and advantages of the proposed controller design approach.

scholarly journals MIMO PI Controllers for LTI Systems with Multiple Time Delays Based on ILMIs and Sensitivity Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-25 ◽  
Author(s):  
Wajdi Belhaj ◽  
Olfa Boubaker
Keyword(s):  
Time Delays ◽  
Linear Time ◽  
Design Procedure ◽  
Internal Model Control ◽  
Linear Matrix ◽  
Multiple Time ◽  
Sensitivity Functions ◽  
Multiple Time Delays ◽  
Model Control ◽  
Pi Controllers

In this paper, a MIMO PI design procedure is proposed for linear time invariant (LTI) systems with multiple time delays. The controller tuning is established in two stages and guarantees performances for set-point changes, disturbance variations, and parametric uncertainties. In the first stage, an iterative linear matrix inequality (ILMI) approach is extended to design PI controllers for systems with multiple time delays without performance guarantee, a priori. The second stage is devoted to improve the closed-loop performances by minimizing sensitivity functions. Simulations results carried out on the unstable distillation column, the stable industrial scale polymerization (ISP) reactor, and the non-minimum phase 4-tank benchmark prove the efficiency of the proposed approach. A comparative analysis with the conventional internal model control (IMC) approach, a multiloop IMC-PI approach, and a previous ILMI PID approach proves the superiority of the proposed approach compared to the related ones.

Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zahra Sadat Aghayan ◽  
Alireza Alfi ◽  
J. A. Tenreiro Machado
Keyword(s):  
Fractional Order ◽  
Robust Stability ◽  
Input Saturation ◽  
Neutral Type ◽  
Domain Of Attraction ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Nonlinear Perturbations ◽  
Robust Stability Analysis ◽  
Delay Dependent

Abstract In this article, we address the delay-dependent robust stability of uncertain fractional order neutral-type (FONT) systems with distributed delays, nonlinear perturbations, and input saturation. With the aid of the Lyapunov–Krasovskii functional, criteria on asymptotic robust stability of FONT, expressed in terms of linear matrix inequalities, are constructed to compute the state-feedback controller gains. The controller gains are determined subject to maximizing the domain of attraction via the cone complementarity linearization algorithm. The theoretical results are validated using numerical simulations.

scholarly journals Robust Quasi–LPV Model Reference FTC of a Quadrotor Uav Subject to Actuator Faults

2015 ◽  
Vol 25 (1) ◽  
pp. 7-22 ◽  
Author(s):  
Damiano Rotondo ◽  
Fatiha Nejjari ◽  
Vicenç Puig
Keyword(s):  
Reference Model ◽  
Fault Tolerant ◽  
Linear Time ◽  
Design Procedure ◽  
Pole Placement ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Reference Trajectory ◽  
Model Reference ◽  
Error Models

Abstract A solution for fault tolerant control (FTC) of a quadrotor unmanned aerial vehicle (UAV) is proposed. It relies on model reference-based control, where a reference model generates the desired trajectory. Depending on the type of reference model used for generating the reference trajectory, and on the assumptions about the availability and uncertainty of fault estimation, different error models are obtained. These error models are suitable for passive FTC, active FTC and hybrid FTC, the latter being able to merge the benefits of active and passive FTC while reducing their respective drawbacks. The controller is generated using results from the robust linear parameter varying (LPV) polytopic framework, where the vector of varying parameters is used to schedule between uncertain linear time invariant (LTI) systems. The design procedure relies on solving a set of linear matrix inequalities (LMIs) in order to achieve regional pole placement and H∞ norm bounding constraints. Simulation results are used to compare the different FTC strategies.

scholarly journals Computation of a Reference Model for Robust Fault Detection and Isolation Residual Generation

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Emmanuel Mazars ◽  
Imad M. Jaimoukha ◽  
Zhenhai Li
Keyword(s):  
Fault Detection ◽  
Reference Model ◽  
Linear Time ◽  
Design Procedure ◽  
Fault Detection And Isolation ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lmi Optimization ◽  
Linear Time Invariant ◽  
Robust Fault Detection

This paper considers matrix inequality procedures to address the robust fault detection and isolation (FDI) problem for linear time-invariant systems subject to disturbances, faults, and polytopic or norm-bounded uncertainties. We propose a design procedure for an FDI filter that aims to minimize a weighted combination of the sensitivity of the residual signal to disturbances and modeling errors, and the deviation of the faults to residual dynamics from a fault to residual reference model, using theℋ∞-norm as a measure. A key step in our procedure is the design of an optimal fault reference model. We show that the optimal design requires the solution of a quadratic matrix inequality (QMI) optimization problem. Since the solution of the optimal problem is intractable, we propose a linearization technique to derive a numerically tractable suboptimal design procedure that requires the solution of a linear matrix inequality (LMI) optimization. A jet engine example is employed to demonstrate the effectiveness of the proposed approach.

scholarly journals On the estimation of robust stability regions for nonlinear systems with saturation

2004 ◽  
Vol 15 (3) ◽  
pp. 269-278 ◽  
Author(s):  
Daniel F. Coutinho ◽  
Daniel J. Pagano ◽  
Alexandre Trofino
Keyword(s):  
Nonlinear Systems ◽  
Robust Stability ◽  
Actuator Saturation ◽  
Quadratic Function ◽  
Differential Algebraic Equations ◽  
The State ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Algebraic Equations ◽  
Stability Regions

This paper addresses the problem of determining robust stability regions for a class of nonlinear systems with time-invariant uncertainties subject to actuator saturation. The unforced nonlinear system is represented by differential-algebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters, and the saturation nonlinearity is modelled by a sector bound condition. For this class of systems, local stability conditions in terms of linear matrix inequalities are derived based on polynomial Lyapunov functions in which the Lyapunov matrix is a quadratic function of the state and uncertain parameters. To estimate a robust stability region is considered the largest level surface of the Lyapunov function belonging to a given polytopic region of state. A numerical example is used to demonstrate the approach.

Synchronization of coupled reaction–diffusion neural networks via intermittent control and saturated impulses

2021 ◽  
pp. 2150398
Author(s):  
Zhengran Cao ◽  
Chuandong Li ◽  
Zhilong He ◽  
Xiaoyu Zhang
Keyword(s):  
Neural Networks ◽  
Actuator Saturation ◽  
Impulsive Control ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
Intermittent Control ◽  
Coupled Neural Networks ◽  
Hybrid Controller

The impulsive synchronization of coupled neural networks with input saturation and the term of reaction–diffusion via a hybrid control strategy is investigated. In this paper, a hybrid controller is proposed, including impulsive controller with input saturation and intermittent controller. This type of hybrid controller can not only solve the periodic and aperiodic intermittent control, lower the update frequency of the controller, but also avoid the saturation phenomenon of impulsive control. Based on linear matrix inequalities (LMIs), and Jensen’s inequality, under a proposed suitable Lyapunov function, a series of sufficient conditions are established to guarantee the stability of the error system. Compared with the recent relevant impulsive saturation results, the polytopic representation method dealing with actuator saturation may make the synchronization criterion more universal and less restrictive. Finally, a numerical example is provided to verify the correctness and feasibility of the theoretical results.

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