Reduced-order Observer Research Articles

Observers for rectangular descriptor systems with output nonlinearities: application to secure communications and microcontroller implementation

This work considers full and reduced-order observer design for rectangular descriptor systems with application to secure communications. The output of the system is assumed to have a nonlinear term coupled with the linear part, a case that is often overlooked in the literature. The observer design is feasible under some algebraic conditions and the feasibility of a linear matrix inequality. The results are showcased through the application of secure communications, for the safe transmission and estimation of an information signal and also an encrypted image. Also, a microcontroller implementation of the master system is performed, which is the first step towards a full realisation of the design.

A Generalized Interpretation of Three Types of Disturbance-Based Controllers for Perturbed Integral Systems in Frequency Domain

It is well recognized that two-degree-of-freedom controllers are more proficient than one-degree-of-freedom controllers in overcoming uncertainty and large parameter variation. Establishing the equivalence analysis criterion among different classes of two-degree-of-freedom controllers to evaluate or compare the performance of controllers can stimulate more advanced two-degree-of-freedom controllers. We establish the equivalence analysis criterion by exploring the equivalence among proportional (P) with full-order extended state observer (FESO), P with reduced-order extended state observer (RESO) and proportional-integral (PI) with reduced-order proportional-integral observer (RPIO) in the context of a class of second-order, cascade integral systems. The equivalence analysis results are also suitable for high-order cascade integral systems. Moreover, P with FESO, P with RESO and PI with RPIO can be interpreted as a class of the generalized PI controllers, which can provide parameter tuning guidelines for the traditional PI controllers. Furthermore, the parameters of PI with RPIO cascade control can be entirely applied to tune the parameters of P with FESO cascade control and P with RESO cascade control and vice versa. Lastly, simulations in high speed permanent magnetic synchronous machine starter are provided to illustrate the theoretical results in this brief.

On reducible state variables of logical control networks

Abstract Reducible state variables are important for the study of reduced-order observer and control design of logical control networks (LCNs). This paper studies the number of reducible state variables of LCNs. Based on the upper bound of reducible state variables, several sufficient/necessary conditions are presented for the number of reducible state variables. In addition, using the regular subspace theory, the coordinate transformation as well as the swap matrix are constructed, and some new criteria are proposed to calculate reducible state variables.

Offset-free IMC with generalized disturbance models

Integral action is an essential component for offset-free response in many feedback control systems. Standard internal model control design rules ensure an offset-free response for open-loop stable plants. In this paper a linear feedback control structure is proposed that comprises an observer using an augmented plant model, state estimate feedback and disturbance estimate feedback. This allows internal model control design principles to be applied to unstable and marginally stable plants. Conditions are given for both nominal internal stability and offset-free action even in the case of plant-model mismatch. The Youla parameterization is recovered as a limiting case with reduced-order observers. The design is illustrated on a large scale non-square model with marginally stable dynamics.

DC Bus Voltage Control of Grid-Side Converter in Permanent Magnet Synchronous Generator Based on Improved Second-Order Linear Active Disturbance Rejection Control

In the permanent magnet synchronous generator (PMSG), the DC bus voltage fluctuates up and down under the influence of the load and power grid, which greatly affects the safe and reliable work of PMSG. In order to suppress the wide range fluctuation of DC bus voltage under disturbance and enhance its anti-disturbance performance, an optimized DC bus voltage control strategy is proposed by using the improved linear active disturbance rejection control (LADRC) in the voltage outer loop. By considering factors, such as load disturbance and grid voltage mutation as the total disturbance of the system, the improved reduced-order linear expansion state observer (RLSEO) is used to estimate and compensate the total disturbance, which greatly improves the stability of DC bus voltage. Firstly, the mathematical model of grid-side converter is established. On this basis, the LADRC control based on RLESO is designed, which reduces the phase lag of the linear extended state observer (LESO) and enhances the disturbance observation accuracy of the system. Then, a lead lag correction link is added to the total disturbance channel of RLESO to reduce the noise amplification effect of RLESO. Finally, the frequency domain characteristic analysis and stability proof of the improved LADRC control strategy are carried out. The simulation results show that the control strategy proposed in the article has a better control effect on the DC bus voltage.

Observer‐based fault reconstructions and fault‐tolerant control designs for uncertain switched systems with both actuator and sensor faults

This study considers the problems of the simultaneous estimations of the states, actuator and sensor faults and the design of observer-based fault-tolerant control (FTC) for a class of uncertain switched systems. First, by treating the system state, actuator fault and sensor fault as an augmented state vector, a descriptor system is constructed, where the output equation contains no faults in form. Second, the relationships between the preconditions of the original system and the descriptor system are investigated in detail, under which a reduced-order observer, which can estimate the original system states, actuator faults and sensor faults simultaneously without suffering from the influence of the disturbance, is developed. Third, based on the state estimations given by the reduced-order observer, a state-fault feedback fault-tolerant controller is designed based on an optimising H ∞ performance index and the gains are computed by linear matrix inequalities (LMIs). Finally, an electrical circuit example is given to show the effectiveness of the proposed methods.

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.

Reduced-Order Observer Based-Fault Estimation for Markovian Jump Systems With Time-Varying Generally Uncertain Transition Rates

This paper addresses such problem for simultaneous estimations of the actuator fault, output disturbance and sensor fault for a type of Markovian jump systems, which takes on time-varying generally uncertain transition rates. In order to perform estimations for faults, a new reduced-order observer is proposed, of which the gain matrix is designed to fully decouple the unknown input for the system. As for the solution to time-varying generally uncertain transition rates, an offline quantization mechanism is developed, which can help to prove, to a large extent, the observer error system to be stable. The proposed method is able to guarantee the exact estimations of the states and faults in spite of the existence of external disturbances and the time-varying stochastic switching. Furthermore, a numerical example is brought to testify the correctness of the designed fault estimation method.

Observer-based fault detection and diagnosis strategy for industrial processes

This study presents the design of a fault detection and diagnosis (FDD) scheme, composed from a bank of two types of observers, applied to linear parameter varying (LPV) systems. The first one uses a combination of reduced-order LPV observers to detect, isolate and estimate actuators faults, and the second one consists of a set of full-order LPV unknown input observers (UIO) to detect, isolate and estimate sensors faults. The observers’ design, convergence and its stability conditions are guaranteed in terms of linear matrix inequalities (LMI). Therefore, the main purpose of this work is to provide a novelty model-based observers’ technique to detect and diagnose faults upon non-linear systems. Simulation results, based on two typical chemical industrial processes, are given to illustrate and discuss the implementation and performance of such an approach.

A Note on Adaptive Observer Design Method for One-Sided Lipschitz Systems

The design problem of adaptive observer for one-sided Lipschitz systems with unknown parameters is addressed. The research focuses on the nonlinear system dynamics which only satisfies one-sided Lipschitz, but not quadratic inner-boundedness. Firstly, an adaptive full-order observer is constructed. Specially, when the one-sided Lipschitz constant is negative, this observer can also be designed. By using the decomposition method, a reduced-order observer is constructed under the same assumptions. The validity of designed observers is illustrated via two examples at last.

Nonlinear observer design based on immersion and invariance method: an insight to chaotic systems

This paper presents some use of reduced order observers for two classes of chaotic systems. The first class includes rod-type plasma torch and Arneodo systems and the second class contains Lorenz and Chen systems. In this regard, a recently developed approach called immersion and invariance method is employed. During the estimation the first state of the system is assumed measured. Implementation of the proposed nonlinear observer is simple and does not need high gain to estimate unavailable state in comparison with conventional methods by rendering manifold observer design inspired form sliding mode theory. An important point of this design is to find appropriate mapping that give rise to exponential stability of observer dynamic. It is worth mentioning that the problem of designing a reduced order observer can be turned into the problem of finding a proper invariant manifold. Stability of the proposed scheme is proven via Lyapunov theorem whilst the simulation results confirm the significance of the proposed immersion and invariance observer.

Event-triggered finite-time consensus for stochastic multi-agent systems

This paper studies a consensus problem for a kind of stochastic multi-agent systems (SMAS). First, a reduced-order observer is designed to estimate unknown states in SMASs. Second, an event-triggered adaptive output feedback control method is presented. It can reduce the controller updates and communication burden. Moreover, the radial basis function neural networks are applied to approximate the unknown functions in systems. Finally, it is demonstrated that the proposed control scheme can achieve finite-time practical consensus for SMASs. Simulation results are provided to illustrate the effectiveness of the theoretical analysis.

Active Disturbance Rejection Control for a Fluid-Driven Hand Rehabilitation Device

This article proposes a new hand rehabilitation device to help therapists repetitively perform hand group stretching training for poststroke patients. The actuator of the proposed device is made of elastomeric materials, driven by fluid pressure, and put onto the surface of a glove. Compared to the traditional rigid exoskeletons for hand rehabilitation, the proposed device is soft, lightweight, and low cost. Because the exact and explicit model is hard to be built for the proposed device and the unconscious tremors occurred during hand rehabilitation, the active disturbance rejection control (ADRC) algorithm, based on the extended state observer (ESO), is adopted to achieve the control purpose. This article analyzes the transient and steady-state performances of the controller based on some reasonable assumptions, and shows its better disturbance rejection ability compared to the widely used proportional-integral-differential control method. In addition, the ADRC algorithm with the reduced-order extended state observer (RESO) has been studied as well. The parameters of the RESO can be obtained by the parameters of the previously determined ESO instead of the trial and error approach, which can ensure the control performance of the ADRC with the RESO does not degrade. Finally, clinical tests have been conducted to verify the functional correctness of the proposed device, and these theoretical results have also been verified by experiments and comparisons.

Interval Functional Observers Design for Time-Delay Systems Under Stealthy Attacks

This study considers stealthy attacks in the design of interval functional observers for time-delay systems. We are interested in the case where a malicious agent compromises the sensors of the systems. We first design reduced-order observers to estimate bounds of the attack signals. Then by using the information on the bounds of the attack signals, we design novel interval functional observers for the systems. We derive conditions for the existence of the interval observers and formulate them in terms of linear programmings which are very efficient computational techniques. Two illustrative examples with extensive simulations are given to show correctness and effectiveness of the proposed method.

Reduced order finite time observers and output feedback for time-varying nonlinear systems

We provide finite time reduced order observers for a class of nonlinear time-varying continuous-time systems. We use the observers to design globally asymptotically stabilizing output feedback controls. We illustrate our work in tracking dynamics for a nonholonomic system in chained form.

Active disturbance rejection position servo control of PMSLM based on reduced-order extended state observer

To enhance the control accuracy of permanent magnet synchronous linear motor (PMSLM) servo systems affected by disturbances, such as time-varying parameters and abrupt load changes, an active disturbance rejection control (ADRC) algorithm based on a reduced-order extended state observer (ESO) is adopted to suppress the disturbances on the control system. First, the system's ability to estimate disturbances is enhanced by linearizing the ESO. Second, the pole placement method is used for the construction of a reduced-order ESO that can reduce the influence of the number of adjustment parameters and the phase lag. The parameters of the reduced-order ADRC are adjusted, the optimal control parameters are selected, and the stability of controller is proved. Finally, practical experiments prove that the proposed method can improve control accuracy under multiple working conditions and features strong anti-interference ability. There is a smaller steady-state error, and no overshoot is observed.

Global finite-time stabilisation for a class of nonlinear systems in the p-normal form via output feedback

In this paper, a finite-time output feedback control scheme is presented for a class of nonlinear systems in the p-normal form. The nonlinear functions in the systems are assumed to be bounded by both low-order and high-order nonlinearities multiplied by a polynomial-type output-dependent growth rate, which are able to cover a more general ones. A reduced-order observer is constructed to estimate unmeasurable states, and a finite-time output feedback controller is proposed for the considered system by constructing a new Lyapunov function and using the adding a power integration technique. Two simulation examples are given to verify the effectiveness of the proposed scheme.

Reduced-Order Observer-Based Dynamic Event-Triggered Adaptive NN Control for Stochastic Nonlinear Systems Subject to Unknown Input Saturation.

In this article, a dynamic event-triggered control scheme for a class of stochastic nonlinear systems with unknown input saturation and partially unmeasured states is presented. First, a dynamic event-triggered mechanism (DEM) is designed to reduce some unnecessary transmissions from controller to actuator so as to achieve better resource efficiency. Unlike most existing event-triggered mechanisms, in which the threshold parameters are always fixed, the threshold parameter in the developed event-triggered condition is dynamically adjusted according to a dynamic rule. Second, an improved neural network that considers the reconstructed error is introduced to approximate the unknown nonlinear terms existed in the considered systems. Third, an auxiliary system with the same order as the considered system is constructed to deal with the influence of asymmetric input saturation, which is distinct from most existing methods for nonlinear systems with input saturation. Assuming that the partial state is unavailable in the system, a reduced-order observer is presented to estimate them. Furthermore, it is theoretically proven that the obtained control scheme can achieve the desired objects. Finally, a one-link manipulator system and a three-degree-of-freedom ship maneuvering system are presented to illustrate the effectiveness of the proposed control method.

Distributed Adaptive Output Feedback Control for Multiagent Systems With Unknown Dynamics

In this article, we present a novel distributed adaptive output feedback control for the cooperative output regulation problem of linear multiagent systems. The agent plant is general in the sense that those interesting practical issues such as unknown dynamics, directed network graph, and agents with nonidentical relative degrees are taken into account simultaneously. The obtained controller consists of the reduced-order observer, the internal model, as well as the adaptive control law, all of which are shown to be fully distributed without using the knowledge of Laplacian matrix of the network graph. It is of interest to see that, in our recursive design, each agent does not need to estimate the unknown parameters from the neighbors, giving rise to a merely two-dimensional adaptive law with quite a simple structure. It is also this feature that our design has the capability of handling the agents with arbitrary nonidentical high relative degrees.

Variable structure control for mismatched uncertain systems using output variables with finite-time convergence

ABSTRACT In this paper, a novel variable structure control (VSC) approach is investigated for a class of mismatched uncertain systems. The VSC approach, which includes output variables only, shows finite-time convergence of the sliding mode, complete invariance to the matched uncertainties, the asymptotic stability property, and is free of the chattering phenomenon. A suitable reduced-order observer (ROO) is constructed to estimate the unmeasured variables. Additionally, a novel finite-time sliding-mode controller (FTSMC), based on the constructed ROO and the output variables, is proposed to stabilize a class of mismatched uncertain systems. To ensure finite-time stability and chattering removal, a discontinuous FTSMC is replaced by a continuous FTSMC utilizing a tanh function. Moreover, a new linear matrix inequality (LMI) condition is derived so that the system in the sliding mode is not only completely invariant to matched uncertainties but also asymptotically stable. Finally, a numerical example is presented, which demonstrates the effectiveness and advantages of this method.