Observer-based Feedback Research Articles

Robust observer-based absolute stabilization for Lur’e singularly perturbed systems with state delay

This paper is concerned with the problem of robust observer-based absolute stabilization for Lur’e singularly perturbed time-delay systems. The aim is to design a suitable observer-based feedback control law such that the resulting closed-loop system is absolutely stable. First, a full-order state observer is constructed. Based on the linear matrix inequality (LMI) technique, a delay-dependent sufficient condition is presented such that the observer error system is absolutely stable. Then, for observer-based feedback control, by introducing some slack matrices, a sufficient condition for input-to-state stability (ISS) of the closed-loop system with regard to the observer error is presented. Thus, the absolute stabilization of the closed-loop system can be guaranteed based on the ISS property. In addition, the criteria presented are both independent of the small parameter and the upper bound for the absolute stability can be obtained in a workable algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the developed methods.

Adaptive neural network control for active suspension system with actuator saturation

This study investigates adaptive neural network (NN) state feedback control and robust observation for an active suspension system that considers parametric uncertainties, road disturbances and actuator saturation. An adaptive radial basis function neural network is adopted to approximate uncertain non-linear functions in the dynamic system. An auxiliary system is designed and presented to deal with the effects of actuator saturation. In addition, since it is difficult to obtain accurate states in practice, an NN observer is developed to provide state estimation using the measured input and output data of the system. The state observer-based feedback control parameters with saturated inputs are optimised by the particle swarm optimisation scheme. Furthermore, the uniformly ultimately boundedness of all the closed-loop signals is guaranteed through rigorous Lyapunov analysis. The simulation results further demonstrate that the proposed controller can effectively suppress car body vibrations and offers superior control performance despite the existence of non-linear dynamics and control input constraints.

Observer-based feedback stabilization of linear systems with event-triggered sampling and dynamic quantization

We consider the problem of output feedback stabilization in linear systems when the measured outputs and control inputs are subject to event-triggered sampling and dynamic quantization. A new sampling algorithm is proposed for outputs which does not lead to accumulation of sampling times and results in asymptotic stabilization of the system. The approach for output sampling is based on defining an event function that compares the difference between the current output and the most recently transmitted output sample not only with the current value of the output, but also takes into account a certain number of previously transmitted output samples. This allows us to reconstruct the state using an observer with sample-and-hold measurements. The estimated states are used to generate a control input, which is subjected to a different event-triggered sampling routine; hence the sampling times of inputs and outputs are asynchronous. Using Lyapunov-based approach, we prove the asymptotic stabilization of the closed-loop system and show that there exists a minimum inter-sampling time for control inputs and for outputs. To show that these sampling routines are robust with respect to transmission errors, only the quantized (in space) values of outputs and inputs are transmitted to the controller and the plant, respectively. A dynamic quantizer is adopted for this purpose, and an algorithm is proposed to update the range and the centre of the quantizer that results in an asymptotically stable closed-loop system.

Output feedback negative imaginary synthesis under structural constraints

The negative imaginary property is a property that many practical systems exhibit. This paper is concerned with the negative imaginary synthesis problem for linear time-invariant systems by output feedback control. Sufficient conditions are developed for the design of static output feedback controllers, dynamic output feedback controllers and observer-based feedback controllers. Based on the design conditions, a numerical algorithm is suggested to find the desired controllers. Structural constraints can be imposed on the controllers to reflect the practical system constraints. Also, the separation principle is shown to be valid for the observer-based design. Finally, three numerical examples are presented to illustrate the efficiency of the developed theory.

Observer-based feedback linearisation of nonlinear ultrasonic systems

At high vibration amplitudes, piezoelectric transducers exhibit nonlinear characteristics (Blackburn and Cain, J Appl Phys 100:114101, 2006; Aurelle et al., Ultrasonics 34:187–191, 1996; Hall, J Mater Sci 36:4575–4601, 2001) due to its material properties. The result is a resonance frequency shift and the occurrence of the jump phenomenon. The jump phenomenon may cause a collapse of the vibration amplitude in forced excitation systems. This nonlinear behaviour is often associated with a discrete spectrum of overtones. In order to linearise the nonlinear system a control circuit was implemented with the aim to eliminate the overtones in the response of the nonlinear system. This paper gives a theoretical and experimental study of damping higher harmonics using a discrete Luenberger observer implemented in a feedback linearisation loop. The Luenberger observer monitors the electrical charge which is proportional to the displacement and uses this information to generate a feedback voltage in order to achieve linear behaviour. Thus, the observer’s output is used to create a linearisation term added to the excitation voltage to eliminate the nonlinearity. In relation to the linearised system, there is no occurence of the jump phenomenon and the phase is linear within the operation band. This simplifies the implementation of a resonance control system.

The active disturbance rejection control of the rotating disk–beam system with boundary input disturbances

ABSTRACTThis paper deals with the stabilisation of the rotating disk–beam system, where the control ends of beam and disk are suffered from disturbances, respectively. The active disturbance rejection control (ADRC) approach is adopted in investigation. The disturbances are first estimated by the extended state observers, and the observer-based feedback control laws are then designed to cancel the disturbances. When the angular velocity of the disk is less than the square root of the first nature frequency of the beam, it is shown that the feedback control laws are robust to the external disturbances, that is, the vibration of the beam can be suppressed while the disk rotating with a desired angular velocity in presence of the disturbances. Finally, the simulation results are provided to illustrate the effectiveness of ADRC approach.

Observer-Based Sequential Control of a Nonlinear Two-Time-Scale System with Multiple Slow and Fast States

Abstract: This paper extends the method of sequential control of a two-time-scale system with multiple slow and fast states from full-state feedback to observer-based feedback. It provides a guideline for the number and role of the observers needed, and proposes a Lyapunov design method for the selection of observer dynamics. The use of lower-order reduced subsystems simplifies the observer design. Using an extension of the existing composite Lyapunov analysis the stability of the full-order system including the controller and the observer in the loop is investigated. The procedure is demonstrated on a nonlinear two-time-scale system which is a combination of two springs, two masses and two dampers. Results in the paper demonstrate that the observer design methodology for a nonlinear system with one slow and one fast state can be extended to a system with multiple slow and fast states. The extended composite Lyapunov analysis is proposed to find an upper bound of the perturbation parameter up to which the full-order closed-loop system including the controller and the observer is stable.

Observer-Based Feedback Control of Networked Control Systems With Delays and Packet Dropouts

The observer-based feedback controller of a new linear networked control system (NCS) with both delays and packet dropouts is designed when the state information is not fully available. With the effects of transmission delays, NCSs are modeled as a discrete-time system with time-varying parameter. The occurrence of packet dropouts is modeled as a Bernoulli event in the NCSs. Under certain conditions, the observer-based controller is proved to render the corresponding NCSs exponentially mean-square stable based on Lyapunov stability theorem and matrix inequality theory. Finally, numerical simulations are included to demonstrate the theoretical results.

New sufficient conditions for observer-based control of fractional-order uncertain systems

New simple linear matrix inequalities are proposed to ensure the stability of a class of uncertain fractional-order linear systems by means of a fractional-order deterministic observer. It is shown that the conditions of existence of an observer-based feedback can be split into a set of linear matrix inequalities that are numerically tractable. The presented results show that it is possible to decouple the conditions containing the bilinear variables into separate conditions without imposing equality constraints or considering an iterative search of the controller and the observer gains. Simulations results are given to approve the efficiency and the straightforwardness of the proposed design.

Observer-Based Sliding Mode Control of Rijke-Type Combustion Instability

Observer-based sliding mode control of combustion instability in a Rijke-type thermoacoustic system is considered. A commonly used thermoacoustic model with sensors and monopole-like actuators is linearized and formulated in a state-space form. It is assumed that the velocity or pressure sensor locations are chosen to assure the observability of the system. An observer-based sliding mode controller is then implemented to tune the actuators so that the system is asymptotically stable. The effectiveness of the controller is illustrated through a simulation example involving two modes and one sensor. The successful demonstration indicates that the observer-based feedback controller can be applied to a real combustion system with multiple modes.

Robust Disturbance Observer-Based Feedback Linearization Control for a Research Reactor Considering a Power Change Rate Constraint

This paper presents a robust disturbance observer-based feedback linearization control method using a fuzzy-based power change rate limiting method for a research reactor. The proposed controller has been designed for a nonlinear model of the reactor. Compared to the conventional control methods, the proposed scheme shows better control performance as it provides effective compensation for the steady-state error, due to a specific type of unmodeled dynamics. To cope with system uncertainties such as parameter uncertainties, unmodeled dynamics, and even external disturbance, we propose a robust disturbance observer-based feedback linearization controller. Moreover, the fuzzy-based power change rate limiting method is proposed, which is practically required for safe operation to limit the power change rate within a pre-designed safety range. In addition, a motor control input is considered and obtained by using the inverse model for the power control system. We show by numerical simulation that the proposed control law guarantees asymptotic stability as well as improved performance even in the presence of disturbance.

Observer-Based Feedback Controller Design for a Class of Stochastic Systems With Non-Gaussian Variables

In this note, the observer-based feedback control problem is investigated for a class of non-Gaussian stochastic systems. The proposed control strategy is the optimal control under a performance function measuring a sort of entropy of the state deviation. Sufficient conditions under which the closed-loop system is locally and ultimately bounded in the mean-square sense are presented. Simulation results demonstrate the effectiveness of the proposed design method.

Coordinated output regulation of heterogeneous linear systems under switching topologies

In this paper, we construct a framework to describe and study the coordinated output regulation problem for multiple heterogeneous linear systems. Each agent is modeled as a general linear multiple-input multiple-output system with an autonomous exosystem which represents the individual offset from the group reference for the agent. The multi-agent system as a whole has a group exogenous state which represents the tracking reference for the whole group. Under the constraints that the group exogenous output is only locally available to each agent and that the agents have only access to their neighbors’ information, we propose observer-based feedback controllers to solve the coordinated output regulation problem using output feedback information. A high-gain approach is used and the information interactions are allowed to be switching over a finite set of networks containing both graphs that have a directed spanning tree and graphs that do not. Simulations are shown to validate the theoretical results.

Robust Observer-Based Feedback Control for Lipschitz Singularly Perturbed Systems

The observer-based feedback control for singularly perturbed systems (SPSs) with Lipschitz constraint is addressed. A sufficient condition, independent of the perturbation parameter, for a full-order observer is presented in terms of linear matrix inequality (LMI) such that observation error is exponentially stable for all sufficiently small perturbation parameters. Then, for observer-based feedback control, a proper controller is constructed to guarantee the input-to-state stability of the system with regard to the observation error. Considering the convergence of observation error, the stability of the system can be obtained based on the input-to-state stability property. It is shown that the proposed method is simple and easy to operate. Moreover, the upper bound of the small perturbation parameter for stability of systems can be explicitly estimated with a workable computation way. Finally, two numerical examples show the effectiveness of the proposed method.

Robust fault estimation and compensation for LPV systems under actuator and sensor faults

We propose a fault tolerant control scheme that compensates for actuator and sensor faults in linear parameter varying (LPV) systems by adjusting controller and observer gains based on estimates of the fault magnitude. The scheme consists of a plant in closed loop with an observer-based feedback tracking controller, which is adapted to the fault situation diagnosed by a fault detection and isolation (FDI) algorithm. Assuming the presence of unknown but bounded process and measurement disturbances, invariant sets are derived for the relevant system variables, and these sets are used to obtain error bounds in the fault estimate. Using these bounds, we provide conditions that ensure correct FDI and robust stability of the compensated closed-loop system even under errors in the fault magnitude estimation.

Observer-based state feedback H-infinity control for networked control systems

Observer-based state feedback H-infinity control for networked control systems

Application of Dual Youla Parameterization Based Adaptive Wide-Area Damping Control for Power System Oscillations

An adaptive damping control scheme based on the dual Youla parameterization is proposed in this paper for inter-area low frequency oscillations. First, a set of observer-based feedback controllers are pre-designed using ${\rm H}_{2} /{\rm H}_{\infty}$ robust control method for a set of nominal operating conditions. Second, the power system and controllers are parameterized using Youla method, respectively. Finally, online measurements are utilized to identify the changing dynamics and adjust the parameterized controllers to adapt to changing operating conditions through the updated Youla parameters. A 127-bus equivalent of the Western Electricity Coordinating Council (WECC) system with three additional controllers of energy storage system is employed as a test system. The results of frequency domain and time domain of different contingences demonstrate the effectiveness and robustness of the Youla based adaptive control scheme.

An Observer-Based Robust Load Frequency Control

A full-order observer-based state feedback linear controller design approach for a single area load frequency problem is presented. The load frequency control model incorporates integral control for improved command tracking response and disturbance rejection. A full state feedback is implemented through full-order state observer design. State feedback with integral controllers design is carried out through a pole-placement technique using symmetrical root locus method. Parametric model uncertainty has been considered and stability robustness study has been carried out assigning a bound on the deviations in parameters of single area load frequency model. The proposed design methodology achieves performance satisfying the specified stability margins. The methodology provides a control over peak values of the frequency and control signal deviations which may be utilized to meet hardware constraints. A numerical example illustrates the effectiveness of the developed methodology.

Relative Orbit Stabilization Control for the Agile Satellite under Stochastic Disturbance

This paper investigates the relative orbit control problem for a space communication satellite network. An observer-based state feedback control scheme is developed under the circumstance of faults and disturbance occurring in the sensors and actuators. The validity of sliding mode observer for the satellites’ network is deduced and the analysis and proof of the relative orbit stabilization control are completed.

Observer-based bang-bang control for a class of nonlinear stochastic systems

This paper is about the bang-bang control strategy for a class of nonlinear stochastic systems. The goal is to give a new approach to stabilize the considered systems which are affected by multiplicative noises by using a state feedback control at first, then an observer-based feedback control in a second time. The so called bang-bang controller permits to ensure the almost sure exponential stability of the closed loop stochastic system.