Observer-based State Feedback Controller Research Articles

High-gain fractional disturbance observer control of uncertain dynamical systems

Disturbance observer-based control allows to compensate unknown inputs, however, in most cases, requiring their integer-order differentiability. In this paper, a novel disturbance observer-based state feedback controller is proposed to compensate a more general class of fractional-, but not necessarily integer-order, differentiable unknown inputs. The proposed fractional PI-like structure yields precise conditions for feedback gain tuning. Remarkably, the resulting controller rejects non-differentiable disturbances with a smooth controller, guaranteeing robustness, an outstanding features for tracking tasks, under a prescribed practical stability regimen. A comparison to a fractional sliding mode observer is conducted via simulations to highlight the reliability of the proposed scheme.

Distributed Observer-BasedH∞Fault-Tolerant Control for DC Microgrids With Sensor Fault

Disturbances, uncertainties, noises and device faults commonly exist in microgrids and often undermine the system stability. To meet these challenges, robust control methods have been recently employed in microgrids systems. In this paper, an active fault-tolerant control scheme is proposed for DC islanded microgrids subjected to sensor fault and external disturbance. Firstly, a distributed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> observer is designed to estimate the uncorrupted voltage and current with high accuracy. Then, an observer based state feedback controller is proposed to ensure stability of voltage regulation for the system. A consensus based control layer in the secondary level is provided to realize current sharing. For the plug-and-play operation of DC microgrids, decentralized parameters design approaches for the observer and controller are both discussed. Finally, simulation studies and experiments are carried out on a DC microgrid system to evaluate the effectiveness of the proposed fault-tolerant control scheme. The simulation and experiment results show that compared with previous works, the proposed observer based control strategy can significantly improve the reliability and resilience of DC microgrid systems.

Stabilization for switched linear systems: Hybrid observer‐based method

This paper investigates interval observer-based controller design for switched linear systems involving additional disturbance and measurement noise, whose modes need not to be cooperative. First, by giving the upper bound and the lower bound of the disturbance and the measurement noise, we construct hybrid interval observer for the considered switched linear system by means of a switched coordinate transformation, which can transform the observer error systems into cooperative ones. The interval observer can supply certain state information at any instant. Compared with the interval observer design for switched systems with arbitrary switching sequences or dwell time switching based on common Lyapunov function, the difficulty consists in characterizing the jump of the multiple Lyapunov functions. Then, by using the multiple Lyapunov functions method and average dwell time scheme, some sufficient conditions are derived and applied to build the interval observer-based state feedback controller. Finally, we provide an example to illustrate the validity of the derived results.

H∞ decentralised output feedback preview tracking control via state observer for a class of nonlinear disturbed interconnected discrete systems

ABSTRACT This paper presents an observer-based decentralized output feedback preview tracking control method for a class of nonlinear disturbed interconnected discrete systems. The considered output tracking control problem, for the first time, is transformed into a controller design problem of N augmented error subsystems. For each subsystem, the suggested control law is formulated by a combination of integral control action, observer-based state feedback control action and preview feedforward action of this subsystem. Based on the Lyapunov function approach, the auxiliary matrix variable approach, and some special mathematical manipulations, the controller feasibility conditions are established in linear matrix inequality (LMI) framework to guarantee the existence of the offered observer-based decentralized preview tracking controller. And, the gain matrices of both decentralized observation and decentralized tracking control can be searched concurrently by only one-step LMI procedure. Finally, two examples are presented to verify the effectiveness and superiority of the proposed controller.

Control of Rotary Inverted Pendulum by Using On–Off Type of Cold Gas Thrusters

This article describes the control of a rotary inverted pendulum utilizing on–off-type cold gas thrusters as the actuators, which have high similarities with thruster actuated spacecrafts with slosh dynamics. The study is completed in three phases. Firstly, a Pulse Width Modulator (PWM) design method is utilized to obtain quasi-linear thrust output from the on–off-type thrusters. Then, a single axis angle controller is designed and tested on the setup along with the PWM scheme. Finally, a pendulum is connected to the other end of the platform and a rotary inverted pendulum (Furuta Pendulum) is constructed. In this way, an inherently unstable, under-actuated, on–off driven system is obtained. For the swing-up motion of the pendulum, an energy-based method is employed. Balancing of the pendulum is achieved by an observer-based state feedback controller under small angle assumption and quasi-linear outputs from the PWM driven thrusters. All of these control methodologies are realized on a real-time target machine. The pendulum is stabilized in seven seconds after five swings, which is comparable to the systems with electric motors.

Non‐linear estimation and observer‐based output feedback control

In this study, a new observer is proposed for a class of non-linear systems which is based on an output-dependent Riccati equation. Necessary conditions for convergence of the state estimation to the system state are investigated through a theorem. Then, based on the proposed observer, two techniques are developed to solve non-linear stabilisation and non-linear tracking problems. It is shown that the separation principle between the estimation and control holds. Indeed, just like a linear system, a decentralised observer-based state feedback controller can be designed for the non-linear system while the stability of the closed-loop system is guaranteed. For the tracking problem, it is proved that the closed-loop system states converge asymptotically to the states of the desired model. Numerical simulations are given to demonstrate the effectiveness of the proposed observer and the observer-based controllers.

Reliable observer-based finite-time [formula omitted] control for networked nonlinear semi-Markovian jump systems with actuator fault and parameter uncertainties via dynamic event-triggered scheme

This paper tackles the observer-based finite-time H∞ control problem for networked nonlinear semi-Markovian jump systems (SMJSs) with actuator fault, parameter uncertainties and partly unknown transition rates via an improved dynamic event-triggered scheme (DETS). In comparison with traditional dynamic event-triggered scheme, the observer-based improved dynamic event-triggered scheme which is not restricted by real system states and could save more network resources is firstly proposed in this paper. Then, a more general actuator fault model is considered and the reliable observer-based state feedback controller is designed. Sufficient conditions are proposed to guarantee the closed-loop system is stochastically finite-time bounded with a prescribed H∞ disturbance attenuation level. Lastly, two simulation examples are given to affirm the validity of the results obtained in this paper.

New results on observer-based robust preview tracking control for Lipschitz nonlinear systems

In this article, the observer-based robust preview tracking control problem is revisited for discrete-time Lipschitz nonlinear systems. The proposed observer-based preview control scheme is composed of the integral control action, the observer-based state feedback control action, and the preview feedforward action of the reference signal. Sufficient design condition of controller and observer gains, which are able to ensure the simultaneously convergence of both the estimation error and the tracking error toward zero, is established in terms of linear matrix inequality by applying the Lyapunov function approach and several mathematical techniques. Compared with the existing result, the system model is more general, which could describe a larger range of practical processes. The observer-based preview controller design is simplified by computing the gain matrices of both observer and tracking controller simultaneously by only one-step linear matrix inequality procedure. Robustness against external disturbance is analyzed via the H∞ performance criterion to attenuate its effect on the performance signal. Finally, two numerical examples are provided to demonstrate the effectiveness of the suggested controller.

Robust Stability and Stabilization of 2D Positive System Employing Saturation

This work is concerned with the issue of stability analysis and controller synthesis for a class of Fornasini–Marchesini second-type systems with polytopic uncertainty, state delays and saturation nonlinearity. Firstly, by utilizing the co-positive Lyapunov function method, sufficient conditions in the linear programming setting are presented assuring the positivity and robust asymptotic stability of the proposed systems. Then, both the state feedback controller and the observer-based state feedback controller are considered based on the obtained results. In addition, the design schemes of the related controller gain matrices are also explicitly provided. Finally, two illustrative examples are given to demonstrate the effectiveness of the method outlined in this paper.

Unknown Input Reconstruction via Interval Observer and State and Unknown Input Compensation Feedback Controller Designs

In this paper, we investigate the state estimation, unknown input and measurement noise reconstruction problems and the feedback controller design issues for a linear discrete-time system with both unknown inputs and measurement noises. First, an augmented system is constructed and the state vector of the augmented system consists of the original system state and the measurement noise, and the preconditions between the original system and the augmented system is discussed in detail. Second, for the augmented system, a reduced-order observer is designed so that the original system state estimates and the measurement noise reconstruction can be obtained. Third, in order to get the asymptotical unknown input reconstruction, an interval observer for part of the measurable output is proposed and an unknown input reconstruction method based on the interval observer is developed. Finally, an observer-based state feedback and unknown input controller is designed and the closed-loop system stability is analyzed. We point out that the closed-loop system satisfies the so-called separation property. At last, two simulation examples are given to verify the effectiveness of the proposed methods.

Observer-Based Finite-Region Dissipative Control for 2-D Continuous-Discrete Systems over Networks

This work is concerned with the problem of finite-region dissipativity-based control for a class of two-dimensional (2-D) continuous-discrete systems in Roesser model over networks, in which the time delays and missing measurements are both involved. Sufficient conditions ensuring the finite-region boundedness and finite-region (T,S,R)-σ-dissipativity for the resulting closed-loop system are derived via utilizing Lyapunov function approach and special recursive formulas. Further, based on the obtained finite-region (T,S,R)-σ-dissipativity conditions, the observer-based state feedback controller is designed. Finally, a simulation example is given to illustrate the effectiveness of the proposed controller design result.

Interval observer-based event-triggered control for switched linear systems

This paper studies the interval observer-based event-triggered controller design for switched systems involving additive disturbance and measurement noise. We first extend the definition of asymptotic interval observers for general non-switched systems into switched ones. Then, by giving the bound of the disturbance and the measurement noise and adopting the multiple Lyapunov function method, some sufficient conditions are derived and applied to build the interval observer, which supply certain information at any instant: an upper bound and a lower bound are provided for each component of the states. Next, we propose an event-triggered sampling mechanism and design an interval observer-based state feedback controller for the considered switched systems. Finally, we afford two examples to illustrate the validity of the derived results.

Finite-time H∞ control for a class of singular Markovian jump systems subject to actuator saturation

This work considers the finite-time control problem for a class singular Markovian jump delayed systems subject to saturating actuators. By employing local sector conditions and an appropriate Lyapunov function, a observer-based state feedback controller is designed to guarantee that the resulted closed-loop constrained system is mean-square locally finite-time stabilizable. Some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness of proposed method.

Event-triggered control for linear continuous switched singular systems

Event-triggered control is an effective control scheme, which can reduce the number of samplings without affecting a desirable system performance. The state-based and observer-based state feedback control are studied for linear switched singular systems in continuous-time case. Firstly, we provide an improved event-triggered sampling mechanism. Next, a set of co-design methods are presented, namely, the construction of switching laws, event-triggered scheme and the choice of controller parameters are jointly discussed. Furthermore, the stability conditions are achieved in terms of global E-uniform boundedness providing that the average dwell time is satisfied for considered systems. In our paper, the improved event-triggered mechanism is adopted and obtained results have less conservatism than existing results. Finally, we illustrate the feasibility via numerical examples.

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

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.

Mitigation of Quantization Effect in Observer-based State-feedback Control with Quantized Observation

This paper studies observer-based state-feedback control of a linear system, where the observation signal is corrupted by the quantization error of an error feedback quantizer that consists of a uniform quantizer and a feedback filter. To mitigate the efect of the quantization error on the system output, we minimize the H2 norm of the transfer function from the round-off error of the uniform quantizer to the system output with respect to the observer gain and the feedback filter alternatively. The minimization with respect to the observer gain is formulated into an optimization under a linear matrix inequality and a bilinear matrix inequality, whose minimum is numerically found by an XY-centering algorithm. The minimization with respect to the feedback filter is a convex optimization whose solution can be obtained numerically. The two minimization problems are iteratively solved, until the H2 norm converges. A numerical example is provided to see the performance of our method.

Extended state observer based indirect-type ILC for single-input single-output batch processes with time- and batch-varying uncertainties

In this paper, a set-point related indirect-type iterative learning control (ILC) design is proposed for industrial batch processes with time-varying uncertainties and external disturbances. Different from the existing robust feedforward ILC methods solely focusing on error convergence along the batch direction, the proposed design has a double-loop control structure to conduct also dynamic control performance in the time direction as required in many engineering applications, where the inner loop is a generalized extended state observer based feedback control structure designed to ensure set-point tracking with robust stability in the time direction, and the outer loop consists of a simple proportional-type learning controller to update only the set-point command such that the tracking performance can be gradually improved along the batch direction. A tractable linear matrix inequality based sufficient condition is established to simultaneously guarantee bounded output tracking error and system input against time- and batch-varying uncertainties. An industrial injection molding process model is used to demonstrate the effectiveness and advantages of the new design in comparison to the recently developed robust feedforward ILC and indirect-type ILC designs.

Robust H∞ state-feedback control for path following of autonomous ground vehicle based on lateral velocity estimation

A robust [Formula: see text] observer-based static state-feedback controller is designed for the path following of autonomous ground vehicles in this paper. Considering the lateral velocity of vehicle is usually difficult to measure, an observer is designed to estimate the value of lateral velocity first. Then, a robust controller is proposed to cope with the modeling uncertainty and disturbance, such as the variation of road coefficient and lateral disturbance. Numerical simulations using a high-fidelity and full-vehicle model based on a CarSim–Simulink joint platform have verified the effectiveness of the proposed approach.

Finite-time event-triggered non-fragile control and fault detection for switched networked systems with random packet losses

This paper investigates the problem of event-triggered observer-based fault detection for a class of uncertain switched nonlinear network control systems (SNNCSs) with random communication packet losses and infinite distributed delay. The main objective of this work is to design an event-triggered state feedback non-fragile H∞ controller such that the resulting closed-loop form of the considered SNNCSs is robustly finite-time bounded and satisfies a prescribed H∞ performance constraint in the finite-time interval. By employing average dwell time approach, the problem of finite-time boundedness and residual H∞ performance analysis is discussed. Specifically, a new set of conditions in the form of LMIs are derived to ensure the finite-time boundedness with the prescribed residual H∞ performance for the relevant closed-loop system. Moreover, the desired observer-based state feedback controller gain matrices and residual weighting matrices can be expressed in an explicit form. Finally, the applicability and effectiveness of the developed results are examined via numerical examples with simulation results.

Observer-based state-feedback robust control for path following of autonomous ground vehicles

In this article, a robust [Formula: see text] observer-based static state-feedback controller is designed for the path following of autonomous ground vehicles. The Takagi–Sugeno fuzzy modeling technique is used for modeling of vehicle dynamics with varying longitudinal velocity first. Then considering the high cost of direct lateral velocity measurement, an observer is designed to estimate the value of lateral velocity. Meanwhile, a robust controller is proposed to deal with the parameter uncertainties and external disturbances simultaneously, including the variation of the tire-cornering stiffness of both front and rear tires. Afterward, the condition of designing such an observer-based controller is transformed into the feasible problem of linear matrix inequalities. Numerical simulations using a high-fidelity and full vehicle model are performed based on a Carsim–Simulink joint platform. Simulation results under different conditions and comparison with other controller show that the proposed controller is effective irrespective of the variation in the road condition, the change in the vehicle longitudinal velocity and the external disturbances.