Proportional Integral Observer Research Articles

Design of finite‐time convergent functional observer for descriptor systems: Application to fault estimation

AbstractIn this paper, a finite‐time functional observer design for linear time‐invariant descriptor systems is presented. A generalized observer based on additional degrees of freedom is developed. This observer can be considered of a general structure since the existing proportional observer (PO) and proportional‐integral observer (PIO) constitute its particular cases. The main contribution is to generate a finite‐time convergent functional observer for descriptor systems by combining two generalized functional observers. The obtained results are applied to the simultaneous state, sensor, and actuator faults estimation. A numerical example is given to illustrate the approach. The obtained results show that the observer is robust in presence of uncertainties, compared to its particular cases.

Design of unknown input integral sliding‐mode discrete observer for linear systems

AbstractThis paper considers the problem of the observer design to estimate the state and reconstruct the unknown inputs for linear discrete‐time systems in the presence of uncertainties. By appropriate use of system transformation and the integral term in the sliding‐surface design, we propose a novel output injection term in its structure to achieve convergence of the sliding‐manifold. The dimension of the designed observer is independent of the number of additive uncertainties in the model of the plant. A numerical simulation demonstrates the design procedure and compares the proposed observer with the standard proportional integral observer (PIO) design.

Proportional integral observer‐based robust fault‐tolerant consensus for nonlinear two‐time‐scale‐agent systems with heterogeneous sensor faults

AbstractThis article studies the fault‐tolerant consensus issue of a class of nonlinear two‐time‐scale‐agent systems with heterogeneous sensor faults and external disturbances. First, the decentralized proportional integral (PI) observer for each agent is constructed to estimate the states and sensor faults simultaneously. Then, a distributed adaptive protocol based on the decentralized PI observer is designed to guarantee the consensus of the underlying systems. Some sufficient existence conditions are given in terms of linear matrix inequalities (LMIs) for the decentralized PI observer and the fault tolerant consensus protocol. Note that performance index is employed to attenuate the influence of sensor faults and disturbances on state estimation and the consensus of the underlying systems. Finally, the effectiveness and superiority of the proposed method are demonstrated by an application example and a numerical example.

An improved sliding mode speed controller for PMSM based on new terminal reaching law with generalized proportional integral observer

A compound sliding mode controller for permanent magnet synchronous motor (PMSM) based on an adaptive terminal sliding mode reaching law with generalized proportional integral observer is proposed. First, an adaptive terminal reaching law is proposed to solve the defects of large chattering in commonly used sliding mode control, which consists of a piecewise function and a terminal term of state variables. The reaching law could adjust the gain according to the distance between the system state and the equilibrium point. On the premise of reducing chattering, a higher reaching speed is guaranteed. The convergence time has an upper bound and is not concerned with the initial value of the sliding mode variable. Based on the reaching law, an adaptive sliding mode controller is established. Second, to reduce the sliding mode gain and enhance the antidisturbance ability of the PMSM, a generalized proportional integral observer is established to evaluate the perturbations in PMSM and compensate them to the speed controller in real time. Simulations and experiments verify that the new compound control method has a faster-approaching speed, smaller chattering, and stronger antidisturbance ability than other methods.

A Multiple-Sensor Fault-Tolerant Control of a Single-Phase Pulse-Width Modulated Rectifier Based on MRAS and GPI Observers

Due to their advantages in ensuring low harmonic distortion and high power factors, single-phase Pulse-Width Modulated (PWM) rectifiers are widely employed in several industrial applications. Generally, the conventional control loop of a single-phase PWM rectifier uses both voltage and current sensors. Hence, in case of sensor fault, the performance and the availability of the converter can be seriously compromised. Therefore, diagnosis approaches and fault-tolerant control (FTC) strategies are mandatory to monitor these systems. Accordingly, this paper introduces a novel multiple-sensor FTC scheme for a single-phase PWM rectifier. The proposed fault diagnosis approach relies on joining several Generalized Proportional Integral (GPI) and Model Reference Adaptive System (MRAS) observers with a residual generation technique to detect and isolate sensor faults in a simple and reliable manner. While conventional sensor FTC methods dedicated to PWM rectifiers can only deal with single faults, the suggested approach guarantees a very good effectiveness level of sensor fault detection, isolation (FDI) and FTC of multiple-sensor fault occurrence scenarios. Consequently, the single-phase PWM rectifier can work with only the survivable single sensor with the guarantee of very good performance as in healthy operation mode. The effectiveness of the proposed sensor FDI approach and its control reconfiguration performance are demonstrated through both extensive simulation and experimental results.

High bandwidth control of slow sampling rate nonlinear systems using alternating predictive GPIOs

This paper investigates the problem of robust output feedback control tracking for a class of nonlinear dual-rate sample-data systems subject to time-varying disturbances. These dual-rate systems, known as slow measurement fast control (SMFC) systems, are characterised by a slow sampling rate of the sensor and a fast updating rate of the controller. To facilitate high-frequency signal tracking, this paper introduces an alternating predictive generalised proportional integral observer (APGPIO). The proposed control method not only effectively restores the system state and captures disturbance changes between samples but also enhances the control bandwidth and anti-disturbance ability, enabling effective tracking of high-frequency reference outputs. By combining it with a fast updating sample-data feedback controller, APGPIO utilises predictive methods to increase the sampling rate of the system's sensors, matching the update frequency of the controller. Stability analysis demonstrates that the tracking error of this hybrid nonlinear system converges to a bounded region centred at the origin. Finally, the designed method's high control bandwidth and anti-disturbance ability are demonstrated through multiple sets of simulations using a real system.

Disturbance rejection-based non-fragile hybrid-triggered control design for repeated scalar nonlinear systems

This article features the composite disturbance estimation and non-fragile hybrid-triggered control problems for continuous-time repeated scalar nonlinear systems prone to external disturbances. Priorly, the proportional integral observer comprising of both proportional and integral loops is incorporated to obtain better state estimations. Further, the external disturbance weakening the system performance is carefully estimated by deploying an improved equivalent-input-disturbance technique. Then, the availed disturbance estimate is blended into the control algorithm to exterminate the influence of the disturbance acting upon the proffered system. Next, a hybrid-triggered control comprised of a transition among event and time triggered paradigms are considered to reduce the network transmittance and also to simultaneously enhances the system outcomes. On top of that, the perturbations in controller gain matrix are taken into concern in order to make the controller more resilient towards redundant changes. Following that, utilising the Lyapunov theory, we obtain the mean-square asymptotic stability requirements for the developed system with the use of linear matrix inequalities and configure the gain matrices. Successively, the credibility of the synthesised control system is portrayed by exhibiting two numerical examples.

Proportional-Integral Observer-Based State Estimation for Markov Memristive Neural Networks With Sensor Saturations.

This article investigates the resilient proportional-integral observer (PIO) problem for Markov switching memristive neural networks (MSMNNs) with randomly occurring sensor saturation within a finite-time interval. The Markov switching of memristive neural networks is regulated by a higher level deterministic switching signal, whose transition probabilities are piecewise time-varying and can be depicted by the average dwell-time strategy. Meanwhile, a Bernoulli stochastic process associated with an uncertain packet arriving rate is adopted to describe the randomly occurring sensor saturation. The aim is to design a resilient PIO such that the augmented dynamic has the property of stochastic finite-time boundedness while meeting the desired performance index. By applying the Lyapunov method and the average dwell-time scheme, sufficient criteria are established for MSMNNs, and a unified design method is presented for the existence of the PIO. Lastly, the attained theoretical results are validated via a numerical simulation.

Distributed platooning control of automated vehicles subject to replay attacks based on proportional integral observers

Secure platooning control plays an important role in enhancing the cooperative driving safety of automated vehicles subject to various security vulnerabilities. This paper focuses on the distributed secure control issue of automated vehicles affected by replay attacks. A proportional-integral-observer (PIO) with predetermined forgetting parameters is first constructed to acquire the dynamical information of vehicles. Then, a time-varying parameter and two positive scalars are employed to describe the temporal behavior of replay attacks. In light of such a scheme and the common properties of Laplace matrices, the closed-loop system with PIO-based controllers is transformed into a switched and time-delayed one. Furthermore, some sufficient conditions are derived to achieve the desired platooning performance by the view of the Lyapunov stability theory. The controller gains are analytically determined by resorting to the solution of certain matrix inequalities only dependent on maximum and minimum eigenvalues of communication topologies. Finally, a simulation example is provided to illustrate the effectiveness of the proposed control strategy.

Partial-Neurons-Based Proportional-Integral Observer Design for Artificial Neural Networks: A Multiple Description Encoding Scheme.

This article is concerned with a new partial-neurons-based proportional-integral observer (PIO) design problem for a class of artificial neural networks (ANNs) subject to bounded disturbances. For the purpose of improving the reliability of the data transmission, the multiple description encoding mechanisms are exploited to encode the measurement data into two identically important descriptions, and the encoded data are then transmitted to the decoders via two individual communication channels susceptible to packet dropouts, where Bernoulli-distributed stochastic variables are utilized to characterize the random occurrence of the packet dropouts. An explicit relationship is discovered that quantifies the influences of the packet dropouts on the decoding accuracy, and a sufficient condition is provided to assess the boundedness of the estimation error dynamics. Furthermore, the desired PIO parameters are calculated by solving two optimization problems based on two metrics (i.e., the smallest ultimate bound and the fastest decay rate) characterizing the estimation performance. Finally, the applicability and advantage of the proposed PIO design strategy are verified by means of an illustrative example.

Algebraic PI observer for velocity and displacement in civil structures from acceleration measurement

This study aims to deal with the velocity and displacement estimation problem in civil structures through acceleration measurements. Nowadays, different schemes have been proposed to solve this problem, however, most proposed observer schemes generally require the Luenberger structure and sometimes any base transformation. In contrast, this paper provides a novel algebraic Proportional Integral (PI) observer based on the Algebraic Observability Condition (AOC), which allows the representation of the velocity and displacement terms as a function of the acceleration measurements, does not need a coordinate transformation, and uses proportional and integral correction of the estimation error. Moreover, a simple criterion for the observer gains selection is provided in order to ensure asymptotic convergence which leads to the fact that the gains can be assigned without using any numerical method to calculate them. An advantage of this observer is that it can be easily implemented for practical purposes. Finally, the effectiveness and accuracy of this estimation method are demonstrated experimentally via a reduced-scale five-story building prototype.

H∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

AbstractThis study explores the development of  dynamic observer (HDO) for discrete‐time nonlinear systems (DTNLS) with time‐varying delay (TVD) and disturbances. The approach is to construct an augmented Lyapunov–Krasovskii function (LKF) with double summation terms, using the generalized reciprocally convex matrix inequality (GRCMI), as well as the Jensen‐based inequality (JBI) and the Wirtinger‐based inequality (WBI). These lead to less conservative time‐dependent conditions, represented as a set of linear matrix inequalities (LMIs) that can be efficiently solved using the LMI or YALMIP toolboxes. In addition, the proposed observer includes the widely used proportional observer (PO) and proportional integral observer (PIO) as specific cases. Two examples are presented to demonstrate the validity and effectiveness of the results.

Proportional-Integral Observer-Based State Estimation for Singularly Perturbed Complex Networks With Cyberattacks.

This article investigates the asynchronous proportional-integral observer (PIO) design issue for singularly perturbed complex networks (SPCNs) subject to cyberattacks. The switching topology of SPCNs is regulated by a nonhomogeneous Markov switching process, whose time-varying transition probabilities are polytope structured. Besides, the multiple scalar Winner processes are applied to character the stochastic disturbances of the inner linking strengths. Two mutually independent Bernoulli stochastic variables are exploited to characterize the random occurrences of cyberattacks. In a practical viewpoint, by resorting to the hidden nonhomogeneous Markov model, an asynchronous PIO is formulated. Under such a framework, by applying the Lyapunov theory, sufficient conditions are established such that the augmented dynamic is mean-square exponentially ultimately bounded. Finally, the effectiveness of the theoretical results is verified by two numerical simulations.

Single-Loop Robust Model Predictive Speed Regulation of PMSM Based on Exogenous Signal Preview

Speed regulation problem of permanent magnet synchronous motor (PMSM) with overcurrent protection is addressed in this paper by using a single-loop robust model predictive control (MPC) approach. The unique feature of this new disturbance rejection MPC method is the utilization of the preview information of lumped exogenous signal. Different from most of the existing disturbance observer-based MPC approaches, the reference inputs, the lumped disturbances in PMSM, and their higher-order differences are explicitly considered as a part of this new concept of lumped exogenous signal by exploiting output regulation theory. Preview of the possible future behaviors of this exogenous signal is conducted based upon the development of two generalized proportional integral observers (GPIOs). An accuracy enhanced prediction model is obtained by exploiting the estimation and preview of the exogenous signal during the prediction horizon. Speed regulation problem of the PMSM is transformed into an error stabilization problem by means of regulator equations and preview information where the faster time-varying exogenous signal is considered. The overcurrent protection problem is also taken into account throughout the receding horizon optimization process. Experimental studies show that the proposed method achieves effective functionality in overcurrent protection, and much better dynamic performance against time-varying exogenous inputs.

Disturbance suppression based quantized tracking control for periodic piecewise polynomial systems

The investigation presented here deals with the issue of disturbance suppression and the design of robust tracking control with quantization mechanism for periodic piecewise polynomial systems prone to parameter uncertainties, time delays and external disturbances by means of a proportional integral observer (PIO)-based parallel equivalent input disturbance (PEID) approach. Primarily, in the PEID technique, in order to reduce estimate errors, the PEID notion has been put forward, wherein these errors are perceived as artificial disturbances and a chain of EID compensators has been employed to make amends for them. Meanwhile, PIO’s integrating part aids in blending a relaxing variable into the system’s layout, which allows for greater flexibility in the system’s framework while rendering the system more robust. Subsequently, with the information of estimates from PEID and PIO, disturbance suppression-based quantized tracking control is designed, which simultaneously makes the system states follow the reference states and mitigates the disturbances from the system. Further, the input signals are quantized before being sent as a result of the limited capacity of the channel via which the data is transmitted. Subsequently, through configuring a periodic piecewise polynomial matrix and blending Lyapunov stability theory with the matrix polynomial lemma, adequate requirements are derived in the framework of linear matrix inequalities which ensure the desired outcomes. After which, the requisite controller and observer gain matrices are generated by solving the stated linear matrix inequality-based relations. Ultimately, the simulation portion offers a numerical example that verifies the potential of the acquired findings.

A current dynamics model and proportional–integral observer for state-of-charge estimation of lithium-ion battery

Compared with the battery voltage error, in this article, the battery current error between the predicted current and the measured, is used as the input of the observer to estimate the state-of-charge. The current-based observer for the state-of-charge estimation requires a current dynamics model to formulate the lithium-ion battery, making its differential equation contain a load-like variation of the state-of-charge more importantly. Combining the current differential equation with the equivalent circuit model for the lithium-ion battery, a novel current dynamics model is formulated and utilized to predict the battery current. Then, a proportional-integral observer is designed to estimate the state-of-charge by the battery current error, and both the battery model parameters and the battery nominal capacity are updated in real time. The current-based proportional-integral observer algorithm is downloaded into a battery management system and tested in a battery electric vehicle. Some comparative experiments are carried out among the current-based observer, the current-integral method, and the extended Kalman filter. According to the experimental results and the statistical analyses, it is shown that the proportional-integral observer based on the current dynamics model is a good candidate for the accurate estimation of the state-of-charge.

State Feedback Control with Integral Action Applied to a Knee Rehabilitation Robot

The main objective of this paper is to describe the design of a state feedback controller with integral action based on a proportional integral observer with Takagi-Sugeno structure, for trajectory tracking of a rehabilitation routine applied to a knee rehabilitation robot. The stability analysis of the controller is addressed by Lyapunov, a constraint is applied to the controller input.

Proportional Integral Observer-Based Controller for an H2AT System under the Takagi-Sugeno Representation

In this article the main objective is the design of a proportional integral (PI) observer that allows estimate the nonmeasurable states of an H2AT pendulum, who represents a person with spinal cord injury and contributes to a better understanding of the behavior of individuals with spinal cord injury. Based on the PI observer, a state feedback controller is designed for a system T-S representation.

Saturated formation containment control for a heterogeneous multi-agent system with unknown perturbations

This work addresses formation containment control for a heterogeneous multi-agent system composed of first-order (FO) and second-order (SO) agents that can be either leader or follower agents. It is assumed that unknown but bounded disturbances perturb its dynamical model. An error-based version of a generalized proportional–integral observer (GPIO) is proposed to estimate these perturbations, and saturation functions, based on position measurement and estimated velocity errors, are designed to achieve the control objective. Specifically, it is shown that the leader agents converge to a desired geometric pattern following a desired trajectory simultaneously. Furthermore, the follower agents converge to the convex hull spanned by the leaders. The result applies to a group of robots in which a directed spanning tree gives the communication topology among the leaders with a root in the main leader. At the same time, each follower receives information from at least one leader agent, and the communication is directed. Real-time experiments and a comparison with a robust control technique exhibit the excellent performance of the proposed GPIO and control strategy in achieving formation containment control.

Reference management-based resilient control for delayed periodic piecewise polynomial systems under proportional integral observer

This article examines the proportional integral observer (PIO)-based resilient tracking control problem for periodic piecewise polynomial systems (PPPSs) in the presence of time delay and disturbances. To be precise, the PPPSs are formulated by dividing the fundamental period of periodic systems into numerous subintervals, each of which is defined using matrix polynomial functions. Further, the PIO strategy is employed to estimate the states of the undertaken system with high precision wherein the integral term in PIO enhances the system's design flexibility and also increases its robustness. Taking advantage of these characteristics, a PIO-based tracking control is configured with gain perturbations to track the desired reference states. Moreover, to attenuate the implications made by disturbances in considered system design, H ∞ performance is employed. Furthermore, in order to establish adequate conditions in the form of linear matrix inequalities, the time-varying polynomial Lyapunov–Krasovskii functional is implemented. Then, the time-varying gain matrices of the control scheme and PIO configuration are computed by solving the obtained criteria through the MATLAB platform. Concludingly, to evidence for the discoveries' potential and usefulness, a numerical example is offered.