Robust Full-Order and Reduced-Order Observers for a Class of Uncertain Switched Systems

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Junqi Yang ◽  
Fanglai Zhu ◽  
Xingguo Tan ◽  
Yunjian Wang
Keyword(s):  
Sliding Mode ◽  
Average Dwell Time ◽  
Switched System ◽  
Linear Matrix ◽  
Asymptotic State ◽  
State Transformation ◽  
State Estimate ◽  
Reduced Order ◽  
Unknown Inputs ◽  
Tank System

This paper deals with the problem of robust state estimation for a class of switched linear systems with unknown inputs under average dwell time (ADT) switching, where the switching of the observers is synchronous with that of the estimated system. First, based on the feasibility of an optimization problem with linear matrix inequality (LMI) constraint, a robust sliding-mode switched observer is developed such that the asymptotic state reconstruction is guaranteed even if the switched system is with unknown inputs. Second, a reduced-order switched system which avoids the influence of unknown inputs is constructed by the technique of state transformation, and a reduced-order switched observer is proposed to estimate the continuous states of the original switched system. Next, the conditions under which a full-order switched observer exists also guarantee the existence of a reduced-order switched observer. The convergence of the state estimate is proved to be exponential by appropriate Lyapunov analysis. Finally, the simulation results confirm the predicted performance and applicability by a simplified three-tank system.

Robust adaptive state estimation for uncertain nonlinear switched systems with unknown inputs

2016 ◽  
Vol 40 (4) ◽  
pp. 1082-1091 ◽  
Author(s):  
Junqi Yang ◽  
Yantao Chen ◽  
Zheng Zheng ◽  
Wei Qian
Keyword(s):  
State Estimation ◽  
Switched Systems ◽  
Dwell Time ◽  
Sliding Mode ◽  
Lipschitz Constant ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Nonlinear Switched Systems ◽  
Continuous State

This paper discusses the issue of the continuous state estimation for a class of uncertain nonlinear switched systems under the two cases of both average dwell time and mode-dependent average dwell time. A robust and adaptive switched observer is developed such that the states of an original nonlinear switched system can be asymptotically estimated, where the Lipschitz constant of the nonlinear term may be unknown since the designed adaptation law can adaptively adjust it. Based on the feasible solution of an optimization problem with a linear matrix inequality constraint, the observer gain matrices are obtained and guarantee the existence of a robust switched observer. Meanwhile, the switching signals are designed such that the observer error dynamics is globally uniformly exponentially stable, and the sufficient conditions of the existence of a robust sliding-mode switched observer are derived. Finally, the effectiveness of the proposed approaches is illustrated by a numerical example and switched Rössler chaotic dynamics.

scholarly journals Observer-Based Robust Passive Control for a Class of Uncertain Neutral Systems: An Integral Sliding Mode Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Ruiping Xu ◽  
Zhen Liu ◽  
Cunchen Gao ◽  
Huimin Xiao
Keyword(s):  
Passive Control ◽  
Sliding Mode ◽  
External Disturbance ◽  
The State ◽  
Linear Matrix ◽  
Neutral Systems ◽  
State Estimate ◽  
Integral Sliding Mode ◽  
Time Varying Delay ◽  
System States

The problem of integral sliding mode control (ISMC) with passivity is investigated for a class of uncertain neutral systems with time-varying delay (NTSTD) and external disturbance. The system states are unavailable. An ISMC strategy is proposed based on the state estimate. By employing a novel sliding functional, a new sufficient criterion of robust asymptotic stability and passivity for both the error system and the sliding mode (SM) dynamic system is derived via linear matrix inequality (LMI) technique. Then, a SM controller is synthesized to guarantee the reachability of the sliding surface predefined in the state estimate space. Finally, a numerical example shows the feasibility and superiority of the obtained result.

scholarly journals Robust fault estimation of a blade pitch and drivetrain system in wind turbine model

2020 ◽  
pp. 107754632092627
Author(s):  
Seyedeh Hamideh Sedigh Ziyabari ◽  
Mahdi Aliyari Shoorehdeli ◽  
Madjid Karimirad
Keyword(s):  
Wind Turbine ◽  
Wind Turbines ◽  
Sliding Mode ◽  
Sliding Mode Observer ◽  
Fault Estimation ◽  
Unknown Input ◽  
Unknown Input Observer ◽  
Reduced Order ◽  
Unknown Inputs ◽  
Estimation Scheme

In this article, a novel robust fault estimation scheme to ensure efficient and reliable operation of wind turbines has been presented. Wind turbines are complex systems with large flexible structures that work under very turbulent and unpredictable environmental conditions for a variable electrical grid. The proposed observer-based estimation scheme consists of a set of possible faults affecting the dynamics, sensors, and actuators of wind turbines. First, the pitch and drivetrain system faults occur simultaneously with process and sensor disturbances that are called unknown input signals. Second, through a series of coordinate transformations, the faulty subsystem is decoupled from the rest of the system. The first subsystem is affected by unknown inputs, and the second one is affected by faults. A reduced-order unknown input observer is designed to reconstruct states accurately, whereas a reduced-order sliding mode observer is designed for the second subsystem such that it is robust against unknown inputs and faults. Moreover, the reduced-order unknown input observer guarantees the asymptotic stability of the error dynamics using the Lyapunov theory method and completely removes unknown inputs; on the other hand, the reduced-order sliding mode observer is designed to reconstruct faults for the faulty subsystem accurately. Until now, authors only focused on an unknown input signal in the dynamics of the system, especially in nonlinear systems. The estimated fault will be adequate to accommodate the control loop, and sufficient conditions are developed to guarantee the stability of the state estimation error. In the next step, to figure the effectiveness of the proposed approach, a wind turbine benchmark system model is considered with faults and unknown inputs scenarios. The simulation results are used to validate the robustness of the proposed algorithms under noise conditions, and the results show that the algorithm could classify faults robustly.

Reduced-Order Observer Design for Discrete-Time Descriptor Systems With Unknown Inputs: An Linear Matrix Inequality Approach

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Shenghui Guo ◽  
Fanglai Zhu
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Observer Design ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Unknown Input ◽  
Matrix Inequality ◽  
Reduced Order ◽  
Unknown Inputs ◽  
Reduced Order Observer

Reduced-order observer design methods for both linear and nonlinear discrete-time descriptor systems based on the linear matrix inequality (LMI) approach are investigated. We conclude that the conditions under which a full-order observer exists can also guarantee the existence of a reduced-order observer. By choosing a special reduced-order observer gain matrix, a reduced-order unknown input observer is proposed for linear system with unknown inputs, and then an unknown input reconstruction is provided for some special cases. We also extend above results to the cases of nonlinear systems. Finally, three numerical comparative simulation examples are given to illustrate the effectiveness and merits of proposed methods.

scholarly journals Bumpless Transfer of Uncertain Switched System and Its Application to Turbofan Engines

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5204
Author(s):  
Penghui Sun ◽  
Xi Wang ◽  
Shubo Yang ◽  
Bei Yang ◽  
Huairong Chen ◽  
...  
Keyword(s):  
Sliding Mode ◽  
Average Dwell Time ◽  
Transient Behavior ◽  
Switched System ◽  
Control Input ◽  
Nonlinear Controller ◽  
Turbofan Engines ◽  
Nonlinear Control Problems ◽  
Bumpless Transfer ◽  
Flight Envelope

Nonlinear control problems in turbofan engines are challenging. No single nonlinear controller can achieve desired control effects in a full flight envelope, but in the case of multiple controllers, there exist problems in the bumpless transfer between different controllers. To this end, this paper presents a bumpless transfer mechanism for an uncertain switched system based on integral sliding mode control (ISMC), and the mechanism can be used for the speed control of turbofan engines. The uncertain switched system is used to describe the turbofan engine dynamics. Then, the ISMC controller is derived for subsystems of the uncertain switched system. A resetting scheme is introduced for the ISMC controller to ensure the continuity of control inputs during the controller transition, as well as the bumpless transfer. In view of the transient behavior caused by controller switching, the global stability of the switched system is analyzed using the multiple Lyapunov function approach and average dwell time condition. Simulation results validate that the designed resetting scheme can ensure the continuity of control input signals and avoid the instability caused by high-frequency controller switching, and increase the control effectiveness of the proposed ISMC method within the full flight envelope.

scholarly journals Robust Tracker of Hybrid Microgrids by the Invariant-Ellipsoid Set

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1794
Author(s):  
Hilmy Awad ◽  
Ehab H. E. Bayoumi ◽  
Hisham M. Soliman ◽  
Michele De Santis
Keyword(s):  
Sliding Mode ◽  
Tracking Error ◽  
Nonlinear Dynamical System ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Nonlinear Dynamical ◽  
Load Variations ◽  
Invariant Ellipsoid ◽  
Steady State Responses ◽  
Linearized Model

This paper introduces a new ellipsoidal-based tracker design to control a grid-connected hybrid direct current/alternating current (DC/AC) microgrid (MG). The proposed controller is robust against both parameters and load variations. The studied hybrid MG is modelled as a nonlinear dynamical system. A linearized model around an operating point is developed. The parameter changes are modelled as norm-bounded uncertainties. We apply the new extended version of the attractive (or invariant) ellipsoid for this tracking problem. Convex optimization is used to obtain the region’s minimal size where the tracking error between the state trajectories and the reference states converges. The sufficient conditions for stability are derived and solved based on linear matrix inequalities (LMIs). The proposed controller’s validity is shown via simulating the hybrid MG with various operational scenarios. In each scenario, the performance of the controller is compared with a recently proposed sliding mode controller. The comparison clearly illustrates the superiority of the developed controller in terms of transient and steady-state responses.

Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

2021 ◽  
pp. 107754632198920
Author(s):  
Zeinab Fallah ◽  
Mahdi Baradarannia ◽  
Hamed Kharrati ◽  
Farzad Hashemzadeh
Keyword(s):  
Transition Probabilities ◽  
Sliding Mode ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Singular Markovian Jump Systems

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.

Sign in / Sign up

Export Citation Format

Share Document