Sampled-data mixed H∞ and passive control for attitude stabilization and vibration suppression of flexible spacecrafts with input delay

2018 ◽  
Vol 24 (22) ◽  
pp. 5401-5417 ◽  
Author(s):  
Baolong Zhu ◽  
Zhiping Zhang ◽  
Mingliang Suo ◽  
Ying Chen ◽  
Shunli Li
Keyword(s):  
Closed Loop ◽  
Passive Control ◽  
Vibration Suppression ◽  
Design Method ◽  
Performance Criterion ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Sampled Data ◽  
Closed Loop System

This paper deals with the problem of mixed [Formula: see text] and passive control for flexible spacecrafts subject to nonuniform sampling and time-varying delay in the input channel. An impulsive observer-based controller is introduced and the resulting closed-loop system is a hybrid system consisting of a continuous time-delay subsystem and an impulsive differential subsystem. As a first result, we derive a generalized bounded real lemma (GBRL), that is, a generalized [Formula: see text] performance criterion, for the impulsive differential subsystem by constructing a time-varying Lyapunov functional. Then, on the basis of this GBRL and utilizing the Lyapunov–Krasovskii approach, a sufficient condition is derived to asymptotically stabilize the closed-loop system and simultaneously guarantee a prescribed mixed [Formula: see text] and passivity performance index. A design method is proposed for the desired controller, which can be readily constructed by solving a convex optimization problem with linear matrix inequalities (LMIs) constraints. Finally, numerical experiments are provided to support the theoretical results, and comparisons with former approaches are also discussed.

Event-triggered Hꝏ control for NCS with time-delay and packet losses

2019 ◽  
Vol 37 (3) ◽  
pp. 918-934
Author(s):  
Jing Bai ◽  
Ying Wang ◽  
Li-Ying Zhao
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Discrete Event ◽  
Sufficient Conditions ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Closed Loop System ◽  
Packet Losses ◽  
Event Triggered

Abstract This paper is concerned with the discrete event-triggered dynamic output-feedback ${H}_{\infty }$ control problem for the uncertain networked control system, where the time-varying sampling, network-induced delay and packet losses are taken into account simultaneously. The random packet losses are described via the Bernoulli distribution. And then, the closed-loop system is modelled as an augmented time-delay system with interval time-varying delay. By using the Lyapunov stability theory and the augmented state space method, the sufficient conditions for the asymptotic stability of the closed-loop system are proposed in the form of linear matrix inequalities. At the same time, the design method of the ${H}_{\infty }$ controller is created. Finally, a numerical example is employed to illustrate the effectiveness of the proposed method.

A Novel Delay-Independent Robust Adaptive Controller Design for Uncertain Nonlinear Systems With Time-Varying State Delay

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Hadi Azmi ◽  
Alireza Yazdizadeh
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Closed Loop ◽  
Controller Design ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
System Delay ◽  
Closed Loop System

Abstract In this paper, two novel adaptive control strategies are presented based on the linear matrix inequality for nonlinear Lipschitz systems. The proposed approaches are developed by creatively using Krasovskii stability theory to compensate parametric uncertainty, unknown time-varying internal delay, and bounded matched or mismatched disturbance effects in closed-loop system of nonlinear systems. The online adaptive tuning controllers are designed such that reference input tracking and asymptotic stability of the closed-loop system are guaranteed. A novel structural algorithm is developed based on linear matrix inequality (LMI) and boundaries of the system delay or uncertainty. The capabilities of the proposed tracking and regulation methods are verified by simulation of three physical uncertain nonlinear system with real practical parameters subject to internal or state time delay and disturbance.

Stabilization of Nonlinear Strict-Feedback Systems With Time-Varying Delayed Integrators

2011 ◽  
Author(s):  
Nikolaos Bekiaris-Liberis ◽  
Miroslav Krstic
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Loop System ◽  
Time Varying ◽  
Feedback Systems ◽  
Closed Loop System ◽  
Feedback Form ◽  
Globally Asymptotically Stable ◽  
Strict Feedback

We consider nonlinear systems in the strict-feedback form with simultaneous time-varying input and state delays, for which we design a predictor-based feedback controller. Our design is based on time-varying, infinite-dimensional backstepping transformations that we introduce, to convert the system to a globally asymptotically stable system. The solutions of the closed-loop system in the transformed variables can be found explicitly, which allows us to establish its global asymptotic stability. Based on the invertibility of the backstepping transformation, we prove global asymptotic stability of the closed-loop system in the original variables. Our design is illustrated by a numerical example.

scholarly journals Controlling the Chaotic Motions of an Airfoil with a Nonlinear Stiffness Using Closed-Loop Harmonic Parametric Excitation

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 165
Author(s):  
Robert Bruce Alstrom
Keyword(s):  
Parametric Excitation ◽  
Closed Loop ◽  
Vibration Suppression ◽  
Preliminary Investigation ◽  
Random Excitation ◽  
Loop System ◽  
Nonlinear Stiffness ◽  
Resonance Capture ◽  
Closed Loop System ◽  
Chaotic Motions

The purpose of this research is to conduct a preliminary investigation into the possibility of suppressing the flutter and post-flutter (chaotic) responses of a two-dimensional self-excited airfoil with a cubic nonlinear stiffness (in torsion) and linear viscous damping via closed-loop harmonic parametric excitation. It was found that the initial configuration of the proposed control scheme caused the torsional/pitch dynamics to act as a nonlinear energy sink; as a result, it was identified that the mechanisms of vibration suppression are the resonance capture cascade and the short duration or isolated resonance capture. It is the isolated resonance capture that is responsible for the second-order-like damping and full vibration suppression of the aeroelastic system. The unforced and closed-loop system was subjected to random excitation to simulate aerodynamic turbulence. It was found that the random excitation suppresses the phase-coherent chaotic response, and the closed-loop system is susceptible to random excitation.

scholarly journals Robust LFC Strategy for Wind Integrated Time-Delay Power System Using EID Compensation

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3223 ◽  
Author(s):  
Liu ◽  
Zhang ◽  
Zou
Keyword(s):  
Time Delay ◽  
Power System ◽  
Closed Loop ◽  
Frequency Control ◽  
Loop System ◽  
Load Frequency Control ◽  
System Stability ◽  
Linear Matrix ◽  
Closed Loop System ◽  
The Stability

This paper presents an active disturbance rejection control (ADRC) technique for load frequency control of a wind integrated power system when communication delays are considered. To improve the stability of frequency control, equivalent input disturbances (EID) compensation is used to eliminate the influence of the load variation. In wind integrated power systems, two area controllers are designed to guarantee the stability of the overall closed-loop system. First, a simplified frequency response model of the wind integrated time-delay power system was established. Then the state-space model of the closed-loop system was built by employing state observers. The system stability conditions and controller parameters can be solved by some linear matrix inequalities (LMIs) forms. Finally, the case studies were tested using MATLAB/SIMULINK software and the simulation results show its robustness and effectiveness to maintain power-system stability.

Gain Scheduled Control of Gas Turbine Engines: Stability and Verification

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Mehrdad Pakmehr ◽  
Nathan Fitzgerald ◽  
Eric M. Feron ◽  
Jeff S. Shamma ◽  
Alireza Behbahani
Keyword(s):  
Convex Optimization ◽  
Gas Turbine ◽  
Closed Loop ◽  
Gas Turbine Engine ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Turbine Engine ◽  
Gain Scheduled Controller ◽  
Gain Scheduled

A stable gain scheduled controller for a gas turbine engine that drives a variable pitch propeller is developed and described. A stability proof is developed for gain scheduled closed-loop system using global linearization and linear matrix inequality (LMI) techniques. Using convex optimization tools, a single quadratic Lyapunov function is computed for multiple linearizations near equilibrium and nonequilibrium points of the nonlinear closed-loop system. This approach guarantees stability of the closed-loop gas turbine engine system. To verify the stability of the closed-loop system on-line, an optimization problem is proposed, which is solvable using convex optimization tools. Simulation results show that the developed gain scheduled controller is capable to regulate a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance.

Application of Approximate I/O Linearization to Aircraft Flight Control

1994 ◽  
Vol 116 (3) ◽  
pp. 429-436 ◽  
Author(s):  
A. W. Lee ◽  
J. K. Hedrick
Keyword(s):  
Control Problem ◽  
Flight Control ◽  
Closed Loop ◽  
Performance Enhancement ◽  
Design Method ◽  
Loop System ◽  
Closed Loop System ◽  
Aircraft Flight Control ◽  
Original Plant ◽  
Control Saturation

This paper examines the performance enhancement of a statically unstable aircraft subject to the input and state constraints. Under control saturation, i/o linearizability is destroyed and the state trajectories may not be attracted to the sliding surface. If the reference signals are sufficiently large and the zero-dynamics is lightly damped, the i/o linearizing control may become unreasonably large in magnitude, making the closed-loop system susceptible to the damaging effects of control saturation. In addition to performance degradations such as increased tracking errors, control saturation can drive the closed-loop system to instability. In this paper, a new design method called approximate i/o linearization is presented to enhance the performance of the SISO longitudinal flight control problem under saturation. The new approximate i/o linearization law is obtained by solving a pointwise minimization problem. The function to be minimized consists of a surface whose relative degree is one, its derivative, and weighted square of the input u. The advantages of the approximate i/o linearization is that the adverse effects of control saturation can be minimized by properly selecting the weight on the usage of the control. The only requirement for the new technique is that the original plant be locally i/o linearizable. Thus approximate i/o linearization does not impose additional strict requirements on the plant. In the remaining sections of the paper, stability and bounded tracking properties of the approximate i/o linearization are proven. Finally, a longitudinal flight control problem is used to demonstrate the application of approximate i/o linearization.

Modeling and Control of an Automotive All-Wheel Drive Clutch as a Piecewise Affine System

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Shiming Duan ◽  
Jun Ni ◽  
A. Galip Ulsoy
Keyword(s):  
Closed Loop ◽  
Open Loop ◽  
Lyapunov Theory ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Modeling And Control ◽  
Piecewise Affine ◽  
Wheel Drive ◽  
And Control

Piecewise affine (PWA) systems belong to a subclass of switched systems and provide good flexibility and traceability for modeling a variety of nonlinear systems. In this paper, application of the PWA system framework to the modeling and control of an automotive all-wheel drive (AWD) clutch system is presented. The open-loop system is first modeled as a PWA system, followed by the design of a piecewise linear (i.e., switched) feedback controller. The stability of the closed-loop system, including model uncertainty and time delays, is examined using linear matrix inequalities based on Lyapunov theory. Finally, the responses of the closed-loop system under step and sine reference signals and temperature disturbance signals are simulated to illustrate the effectiveness of the design.

Robust nonfragile observer-based H2/H∞ controller

2016 ◽  
Vol 24 (4) ◽  
pp. 722-738 ◽  
Author(s):  
Atta Oveisi ◽  
Tamara Nestorović
Keyword(s):  
Control System ◽  
Real Time ◽  
Closed Loop ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Real Time System ◽  
Structured Uncertainty

A robust nonfragile observer-based controller for a linear time-invariant system with structured uncertainty is introduced. The [Formula: see text] robust stability of the closed-loop system is guaranteed by use of the Lyapunov theorem in the presence of undesirable disturbance. For the sake of addressing the fragility problem, independent sets of time-dependent gain-uncertainties are assumed to be existing for the controller and the observer elements. In order to satisfy the arbitrary H2-normed constraints for the control system and to enable automatic determination of the optimal [Formula: see text] bound of the performance functions in disturbance rejection control, additional necessary and sufficient conditions are presented in a linear matrix equality/inequality framework. The [Formula: see text] observer-based controller is then transformed into an optimization problem of coupled set of linear matrix equalities/inequality that can be solved iteratively by use of numerical software such as Scilab. Finally, concerning the evaluation of the performance of the controller, the control system is implemented in real time on a mechanical system, aiming at vibration suppression. The plant under study is a multi-input single-output clamped-free piezo-laminated smart beam. The nominal mathematical reduced-order model of the beam with piezo-actuators is used to design the proposed controller and then the control system is implemented experimentally on the full-order real-time system. The results show that the closed-loop system has a robust performance in rejecting the disturbance in the presence of the structured uncertainty and in the presence of the unmodeled dynamics.

Output feedback boundary control of a flexible marine riser system

2017 ◽  
Vol 24 (16) ◽  
pp. 3617-3630 ◽  
Author(s):  
Yu Liu ◽  
Fang Guo
Keyword(s):  
Boundary Control ◽  
Closed Loop ◽  
Vibration Suppression ◽  
High Gain ◽  
Loop System ◽  
System State ◽  
Marine Riser ◽  
Closed Loop System ◽  
Observer Error ◽  
System States

This paper is concerned with the design of boundary control for globally stabilizing a flexible marine riser system. The dynamics of the riser system are represented in the form of hybrid partial–ordinary differential equations. Firstly, when the system state available for feedback is unmeasurable, an observer backstepping method is employed to reconstruct the system state and then design the boundary control for vibration suppression of the riser system. Subsequently, for the case that the system states in the designed control law cannot be accurately obtained, the high-gain observers are utilized to estimate those unmeasurable system states. With the proposed control, the uniformly ultimately bounded stability of the closed-loop system is demonstrated by the use of Lyapunov’s synthetic method and the state observer error is converged exponentially to zero as time approaches to infinity. In addition, the disturbance observer is introduced to track external environmental disturbance. Finally, the control performance of the closed-loop system is validated by carrying out numerical simulation.

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