Linear Matrix Inequality Robust Tracking Control Conditions for Nonlinear Disturbed Interconnected Systems

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Ali Sghaier Tlili
Keyword(s):  
Tracking Control ◽  
Design Method ◽  
Performance Criterion ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Robust Tracking Control ◽  
External Disturbances ◽  
Control Approach ◽  
Control Gain ◽  
And Control

The objective of this paper is to develop a robust decentralized observer-based feedback model reference tracking control approach for a class of nonlinear disturbed interconnected systems. The proposed H∞ control and observation design method is formulated within an optimization problem involving linear matrix inequalities (LMIs), efficiently solved by a one-step LMI procedure, to compute the decentralized observation and control gain matrices of each subsystem, and to attenuate the external disturbances affecting the subsystems by minimizing a H∞ performance criterion. A numerical simulation is highlighted on a power system with three-interconnected machines to demonstrate the effectiveness of the developed control approach despite the interconnections between different generators, nonlinearities in the system, and external disturbances.

scholarly journals Control of a Variable Blade Pitch Wind Turbine Subject to Gust Wind and Actuators Saturation

2021 ◽  
Vol 11 (17) ◽  
pp. 7865
Author(s):  
Chokri Sendi
Keyword(s):  
Wind Turbine ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
External Disturbances ◽  
Control Gain ◽  
Dynamics And Control ◽  
Takagi Sugeno ◽  
And Control ◽  
The Mathematical Model

This paper examines the dynamics and control of a variable blade pitch wind turbine during extreme gust wind and subject to actuators saturation. The mathematical model of the wind turbine is derived using the Lagrange dynamics. The controller is formulated using the Takagi–Sugeno fuzzy model and utilizes the parallel distributor compensator to obtain the feedback control gain. The controller’s objective is to obtain the generator electromagnetic torque and the blade pitch angle to attenuate the external disturbances. The (T–S) fuzzy controller with disturbances rejection properties is developed using the linear matrix inequalities technic and solved as an optimization problem. The efficacy of the proposed (T–S) fuzzy controller is illustrated via numerical simulations.

Robust control design of electric helicopter tail reduction system: Fuzzy and optimal view

2020 ◽  
Vol 26 (9-10) ◽  
pp. 814-829
Author(s):  
Yinfei Zhu ◽  
Han Zhao ◽  
Hao Sun ◽  
Shengchao Zhen ◽  
Zicheng Zhu
Keyword(s):  
Robust Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Control Cost ◽  
Robust Controller ◽  
External Disturbances ◽  
Control Approach ◽  
Reduction System ◽  
Control Gain ◽  
Robust Control Design

The optimal robust control with a fuzzy approach is applied to design the electric helicopter tail reduction system in this article. Firstly, the fuzzy dynamical model of the electric helicopter tail reduction system with uncertainties and external disturbances is established, which may be time varying. Then, we propose a deterministic robust controller (differing from IF-THEN rules in traditional fuzzy control) to solve the uncertain problem in electric helicopter tail reduction systems. The electromechanical system with the proposed controller is proved to be stable via the Lyapunov function. The control gain with an optimal design is considered, which minimizes a fuzzy performance index associated with both the control error and the control cost. Furthermore, simulations compared with linear-matrix-inequality control are made to validate the effectiveness and stability of the optimal robust controller. All results show that the performance of the fuzzy electric helicopter tail reduction system can be always guaranteed by this optimal robust control approach.

scholarly journals Suboptimal Disturbance Observer Design Using All Stabilizing Q Filter for Precise Tracking Control

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1434 ◽  
Author(s):  
Wonhee Kim ◽  
Sangmin Suh
Keyword(s):  
Design Method ◽  
Industrial Applications ◽  
Point Of View ◽  
Observer Design ◽  
Linear Matrix ◽  
External Disturbances ◽  
Closed Loop Systems ◽  
Control Target ◽  
The Stability ◽  
Unified Index

For several decades, disturbance observers (DOs) have been widely utilized to enhance tracking performance by reducing external disturbances in different industrial applications. However, although a DO is a verified control structure, a conventional DO does not guarantee stability. This paper proposes a stability-guaranteed design method, while maintaining the DO structure. The proposed design method uses a linear matrix inequality (LMI)-based H∞ control because the LMI-based control guarantees the stability of closed loop systems. However, applying the DO design to the LMI framework is not trivial because there are two control targets, whereas the standard LMI stabilizes a single control target. In this study, the problem is first resolved by building a single fictitious model because the two models are serial and can be considered as a single model from the Q-filter point of view. Using the proposed design framework, all-stabilizing Q filters are calculated. In addition, for the stability and robustness of the DO, two metrics are proposed to quantify the stability and robustness and combined into a single unified index to satisfy both metrics. Based on an application example, it is verified that the proposed method is effective, with a performance improvement of 10.8%.

Robust Tracking Control for Takagi–Sugeno Fuzzy Systems With Unmeasurable Premise Variables: Application to Tank System

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
H. Ghorbel ◽  
A. El Hajjaji ◽  
M. Souissi ◽  
M. Chaabane
Keyword(s):  
Tracking Control ◽  
Fuzzy Systems ◽  
Design Procedure ◽  
Control Design ◽  
Linear Matrix ◽  
Robust Tracking Control ◽  
Fuzzy Observer ◽  
Tank System ◽  
System States ◽  
Takagi Sugeno

In this paper, a robust fuzzy observer-based tracking controller for continuous-time nonlinear systems presented by Takagi–Sugeno (TS) models with unmeasurable premise variables, is synthesized. Using the H∞ norm and Lyapunov approach, the control design for TS fuzzy systems with both unmeasurable premises and system states is developed to guarantee tracking performance of closed loop systems. Sufficient relaxed conditions for synthesis of the fuzzy observer and the fuzzy control are driven in terms of linear matrix inequalities (LMIs) constraints. The proposed method allows simplifying the design procedure and gives the observer and controller gains in only one step. Numerical simulation on a two tank system is provided to illustrate the tracking control design procedure and to confirm the efficiency of the proposed method.

scholarly journals Observer-Based Decentralized Tracking Control with Preview Action for a Class of Nonlinear Interconnected Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Xiao Yu
Keyword(s):  
Tracking Control ◽  
Controller Design ◽  
Tracking Error ◽  
State Feedback Control ◽  
Control Action ◽  
Linear Matrix ◽  
Reference Trajectory ◽  
Integral Control ◽  
Control Approach ◽  
Output Tracking Control

In this paper, for the first time, the observer-based decentralized output tracking control problem with preview action for a class of interconnected nonlinear systems is converted into a regulation problem for N augmented error subsystems composed of the tracking error dynamics, the difference equation of the state observer, and the available future reference trajectory dynamics associated with each individual subsystem. The developed innovative formulation of an observer-based decentralized preview tracking control scheme consists of the integral control action, the observer-based state feedback control action, and the preview action of the desired trajectory. The controller design feasibility conditions are formulated in terms of a linear matrix inequality (LMI) by using the Lyapunov function approach to ensure the existence of the suggested observer-based decentralized control strategy. Furthermore, both decentralized observer gain matrices and decentralized tracking controller gain matrices can be efficiently and simultaneously computed through a one-step LMI procedure. Stability analysis of the closed-loop augmented subsystem is carried out to illustrate that all tracking errors asymptotically converge toward zero. Finally, a numerical example is provided to demonstrate the effectiveness of the suggested control approach.

On the controllers' design to stabilize ground resonance helicopter

2019 ◽  
Vol 25 (23-24) ◽  
pp. 2894-2909
Author(s):  
José A. Ignácio da Silva ◽  
Douglas D. Bueno ◽  
Gustavo L. C. M. de Abreu
Keyword(s):  
Broad Class ◽  
Linear Matrix ◽  
Rotor Speed ◽  
Control Approach ◽  
Control Gain ◽  
Controller Gain ◽  
Ground Resonance ◽  
Speed Range ◽  
Alternative Methodology ◽  
Operational Envelope

Ground resonance (GR) in helicopters is a potentially catastrophic instability commonly caused by coalescence of the regressive cyclic blade lag mode with the fuselage motion in certain rotor speed ranges. It can limit the helicopter operational envelope and the design of this type of vehicle can become a difficult task. Although a broad class of actuators allows the use of active and semi-active techniques to design feedback-based control systems, a limited number of works in the literature introduce formulations to compute the controller gain to suppress this phenomenon. Also, commonly, a control approach defines a feedback, particularly to a specific rotor speed. In this context, this work introduces an alternative methodology to design an active control system to stabilize GR of a helicopter. The proposed approach can suppress this instability in all rotor speed ranges by using only one control gain. Two strategies are proposed based on linear matrix inequalities (LMIs). The Lyapunov stability criteria are used and the unstable rotor speed is considered as an uncertain parameter to define an associated convex space. Using convex optimization, a robust control gain is computed until all the unstable rotor speed range is stabilized. Numerical simulations are carried out to demonstrate the effectiveness of this methodology. The results confirm the viability of the proposed approach to design active and semi-active controllers.

scholarly journals Robust Tracking Control for Rendezvous in Near-Circular Orbits

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Neng Wan ◽  
Ming Liu ◽  
Hamid Reza Karimi
Keyword(s):  
Tracking Control ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Robust Tracking ◽  
Robust Tracking Control ◽  
Circular Orbits ◽  
Two Body Problem ◽  
Guaranteed Cost ◽  
Tracking Controller

This paper investigates a robust guaranteed cost tracking control problem for thrust-limited spacecraft rendezvous in near-circular orbits. Relative motion model is established based on the two-body problem with noncircularity of the target orbit described as a parameter uncertainty. A guaranteed cost tracking controller with input saturation is designed via a linear matrix inequality (LMI) method, and sufficient conditions for the existence of the robust tracking controller are derived, which is more concise and less conservative compared with the previous works. Numerical examples are provided for both time-invariant and time-variant reference signals to illustrate the effectiveness of the proposed control scheme when applied to the terminal rendezvous and other astronautic missions with scheduled states signal.

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