Nonlinear High-gain Observer Research Articles

Cascade Control of Grid-Connected NPC Converters via Sliding Mode Technique

This paper proposes a two-stage control strategy including an adaptive sliding mode control (ASMC) and a nonlinear high-gain observer (HGO) for the three-level neutral-point-clamped (NPC) converter in dc microgrids. In the outer loop, an ASMC is utilized to regulate the dc-link voltage. By introducing an adapted gain, the tradeoff between the chattering and dynamic performance of the classic sliding mode control is overcome, thus the transient response of the NPC converter can be further enhanced without increasing the chattering. In addition, a nonlinear HGO is cooperated with the ASMC method to reject exogenous disturbance for the NPC converter, which not only assures a high disturbance rejection capacity but also accommodates the inevitable measurement noise in the actual applications. For the inner loop, in consideration of the parameter uncertainty, a high-gain observer-based second-order sliding mode (SOSM) control is adopted to assure the steady state performance and the robustness of the NPC converter. Finally, a set of comparative experimental results confirm the effectiveness and superiority of the proposed control scheme implemented in the NPC converter. Additionally, the robustness under parameter variation of the proposed method is also validated.

Activity recognition using a combination of high gain observer and deep learning computer vision algorithms

Inertial sensors have become increasingly popular in human activity classification due to their ease of use and affordability. This paper proposes a novel algorithm for human activity recognition that is a combination of a high-gain observer and deep learning computer vision classification algorithms. The nonlinear high-gain observer designed using Lyapunov analysis accurately estimates the attitude of the chest of a human subject using measurements from a single Inertial Measurement Unit (IMU). The signals processed by the observer are then converted into spectrograms to obtain “images” of the frequency response of the signals. The images for activities from a dataset of 7 human subjects are annotated and used for training/ fine-tuning of several well-known deep learning algorithms for image processing. The results from the best combination of our algorithms shows an exceptional accuracy of 98% for activity recognition. Using deep learning computer vision algorithms, this paper shows how to perform transfer learning from networks pre-trained on millions of images, thus showing how we can train a powerful deep learning network for activity recognition even with just small datasets. The algorithm that uses the high gain observer is shown to perform significantly better than an algorithm based on raw accelerometer and gyro signals.

A nonlinear observer for bilinear systems in block form

This paper presents the design of a high-gain nonlinear observer for bilinear systems in the block form. We prove the uniform exponential stability of the observer error by finding a concrete exponential bound. In particular, we extend the result of O. I. Goncharov on the exponential stability of high-gain bilinear observers into observers of block forms. Our work results in a generalization of that work. We also study and simulate two examples of observers for bioreactor systems in two and three dimensions. Finally, the results show the effectiveness of the proposed approach.

Velocity Estimation of Robot Manipulators: An Experimental Comparison

Accurate velocity information is often essential to the control of robot manipulators, especially for precise tracking of fast trajectories. However, joint velocities are rarely directly measured and instead estimated to save costs. While many approaches have been proposed for the velocity estimation of robot joints, no comprehensive experimental evaluation exists, making it difficult to choose the appropriate method. This paper compares multiple estimation methods running on a six degrees-of-freedom manipulator. We evaluate: 1) the estimation error using a ground-truth signal, 2) the closed-loop tracking error, 3) convergence behavior, 4) sensor fault tolerance, 5) implementation and tuning effort. To ensure a fair comparison, we optimally tune the estimators using a genetic algorithm. All estimation methods have a similar estimation error and similar closed-loop tracking performance, except for the nonlinear high-gain observer, which is not accurate enough. Sliding-mode observers can provide a precise velocity estimation despite sensor faults.

A Nonlinear State Observer for the Bi-Hormonal Intraperitoneal Artificial Pancreas.

Currently, continuous glucose monitoring sensors are used in the artificial pancreas to monitor blood glucose levels. However, insulin and glucagon concentrations in different parts of the body cannot be measured in real-time, and determining body glucagon sensitivity is not feasible. Estimating these states provides more information about the current system status, facilitating improved decision-making by the model-based controller. In this regard, the aim of this paper is to design a nonlinear high-gain observer for a bi-hormonal artificial pancreas in the presence of measurement noises, model uncertainties, and disturbances. The model used in the observer is based on an existing intraperitoneal nonlinear animal model in the literature. This model is modified by assuming that insulin can directly transfer from the peritoneal cavity to the bloodstream. Based on a set of realistic assumptions, one model is considered after each hormone infusion, and two observers are separately designed. The model is divided into the insulin-phase and glucagon-phase models based on a set of realistic assumptions. Thereafter, two high-gain observers are designed separately for these phases contributing to estimating the non-measurable states. The observer error is proven to be locally uniformly ultimately bounded, and it is verified that any asymptotically stable control laws remain stable in the presence of the observer. The performance of the observers with different gains is evaluated for a scenario with multiple insulin and glucagon infusions. The proposed observer converges to a finite error, according to the results. Clinical relevance- In Type 1 diabetic patients, the developed observer can be employed in a closed-loop artificial pan-creas to improve the performance of model-based controllers. It estimates the key states, which are necessary for forecasting the body's response to insulin and glucagon boluses.

Observer-based virtual sensors for microalgae cultures monitoring

In this paper, a nonlinear observer design is presented for simultaneous parameter estimation and state variables estimation. The case of study is microalgae cultures for biodiesel generation, where reaction rates, biomass concentration, intracellular quota and nitrogen concentration are critical variables that provide information about the state of the process. However, these variables might be difficult to measure due to the lack of specific instruments, high sensor costs or infeasibility of installation in the process. Therefore, two observer-based virtual sensors are presented in this paper as an analytical alternative to perform estimation of the main important variables or parameters of the process: a nonlinear adaptive observer and a nonlinear high-gain observer. The observers are based on the Droop´s mathematical model that describes the ability of microalgae to store nutrients and the decoupling between substrate uptake and biomass growth. Numerical simulations are made in order to evaluate the performance of the proposed observers.

Secured transmission design schemes based on chaotic synchronization and optimal high gain observers

The distinguishing feature of the proposed secured transmission design scheme is the use of chaotic nonlinear systems and optimal high gain observers for the encryption/decryption operation and their application in image cryptography. The primary concern in this work is to develop an innovative algorithm for optimizing the high gain observer performances. Therefore, the proposed strategy uses a nonlinear chaotic system in the plain-text encryption phase and the optimal high gain observer in the decryption phase with no interdependence between these two operations. Practically, the chaotic system is suitable to be used as a block cipher as it has a random nature depending on its initial conditions. In addition, it is possible to present the proposed block cipher method as an enhancement of the existing block cipher involving short keys. For the decryption, a challenging design combining a high gain observer and non-dominated sorting genetic algorithms (NSGA-II) for optimizing the observation gain is developed. Efficiency and substantial performances of the synchronization method, tested with nonlinear unified chaotic system and optimal high gain observer, are demonstrated by several numerical simulation scenarios on a prominent QR (Quick Response) code example.

An Enhanced Strategy for Adaptive Output-Feedback Control of Uncertain Nonlinear Systems

We are concerned with global practical tracking for uncertain nonlinear systems with intrinsic dependence on unmeasured states. Typically, we aim to remove the polynomial restrictions on system growth rates in relevant works, admitting the rates to be of arbitrary function-of-output type. Note that such highly nonlinear rates could alter so drastically in magnitude that no polynomial can upper bound them on any unbounded region, and would undermine the design rationale and the analysis route that are followed in polynomial rate scenarios. This entails refining/integrating state-of-the-art techniques and developing new ones, from design to analysis. Concretely, to circumvent the need for knowledge on polynomials, dual dynamic high gains are devised ingeniously which particularly incorporate certain highly nonlinear components to counteract the arbitrary function-of-output rates and other inherent nonlinearities and uncertainties. But unfavorable impacts of the components would also arise putting the effectiveness of the high gains at risk, which necessitates noticeable changes in the choice of vital variables/functions. In addition, to provide tractable observer error dynamics for control design and analysis, a nonlinear high-gain observer is pursued, which is filter based and of reduced order, following the design methodologies in relevant works. In terms of performance analysis, practical tracking suffers extra time variants and additive uncertainties which together with the highly nonlinear rates would carry over to stability analysis inevitably and in turn ruin the existing analysis routes. Hence, a new analysis route is paved to verify the anticipated performance. Notably, by unfolding an important implication, the performance verification boils down largely to the boundedness of the high gains. This makes plain and intelligible the verification, although sophisticated integration of multiple composite Lyapunov functions is still required. An exception, i.e., asymptotic stabilization, is presented to demonstrate its close connection with practical tracking.

Sliding Mode Control of Grid-Connected Neutral-Point-Clamped Converters Via High-Gain Observer

In this article, a nonlinear high-gain observer (NHGO)-based second-order sliding mode (SOSM) control strategy is proposed for the three-phase three-level neutral-point-clamped (NPC) converter. This controller applies the advanced SOSM algorithm both in the voltage regulation loop and in the power tracking loop, which provides a fast dynamic for the dc-link voltage, and also assures a good steady-state behavior for the NPC converter. Additionally, an NHGO technique is implemented in the voltage regulator combining with the SOSM algorithm. The conventional observer-based controllers suffer from the destructive effects of measurement noise, and it can only be addressed by diminishing the observer gain, which sacrifices the observer property. The NHGO technique adopts a time varying gain, that is, high gain in transient while low gain in steady state, which minimizes the adverse influence of measurement noise. The tuning method of the proposed NHGO-based SOSM controller is given to simplify the implementation process. Finally, the simulation and experimental results of the proposed control scheme for the NPC converter are given and compared with the conventional PI controller as well as the well-known linear extended state observer-based control method, which validates the feasibility and superiority of the proposed controller.

A turbidity sensor development based on NL-PI observers: Experimental application to the control of a Sinaloa’s River Spirulina maxima cultivation

AbstractThis article addresses the problem of controlling the growth of microalgae originating in Mexican rivers, especially in the state of Sinaloa, Culiacan River. For this purpose, a robust, high-gain nonlinear observer is proposed to estimate the unknown disturbance in the cultivation of mixotrophic microalgae with the presence of organic nutrients. Once a perturbation function related to the change of ambient light is estimated, an output feedback control for the photobioreactor is proposed, in which through Lyapunov’s convergence functions, the final boundary stability conditions are obtained. Thus, a turbidity sensor was designed for Spirulina platensis, a native microalgae of Culiacan River, which is presented using the MATLAB-Arduino programming environment. This sensor is calibrated using biomass culture and is a low-cost device. Through the numerical study, the feasibility and performance of the control and the observer are evaluated. Finally, real-time experimental evaluations are made based on the literature, studying the use of robust controllers in a photobioreactor with a mixed culture, in the presence of environmental changes in lighting.

A Fractional High-Gain Nonlinear Observer Design—Application for Rivers Environmental Monitoring Model

The deterioration of current environmental water sources has led to the need to find ways to monitor water quality conditions. In this paper, we propose the use of Streeter–Phelps contaminant distribution models and state estimation techniques (observer) to be able to estimate variables that are very difficult to measure in rivers with online sensors, such as Biochemical Oxygen Demand (BOD). We propose the design of a novel Fractional Order High Gain Observer (FOHO) and consider the use of Lyapunov convergence functions to demonstrate stability, as it is compared to classical extended Luenberger Observer published in the literature, to study the convergence in BOD estimation in rivers. The proposed methodology was used to estimated Dissolved oxygen (DO) and BOD monitoring of River Culiacan, Sinaloa, Mexico. The use of fractional order in high-gain observers has a very effective effect on BOD estimation performance, as shown by our numerical studies. The theoretical results have shown that robust observer design can help solve problems in estimating complex variables.

Adaptive non-linear high gain observer based sensorless speed estimation of an induction motor

An efficient sensor-less speed estimator, based on an adaptive non-linear high gain observer (HGO) which uses only the measured stator currents and control voltages in the presence of measurement noise, is proposed to estimate the speed of an induction motor. The proposed observer is an improved version of the common HGOs proposed in the literature. The observer gain, involving the use of a scalar time-varying design parameter governed by the Riccati differential equation, guarantees the best compromise between the fast convergence of the states and noise rejection with such adaptation of gains that the internal states of the observer exert low influence during the transient period and thus prevent system peaking. The design methodology of the proposed observer is given and its stability is studied. Results of simulation studies demonstrate that robustness and efficiency of the proposed observer are maintained under critical operating conditions, even where the efficiency of the fixed gain observer is decreased.

High-Gain Observer Design for Nonlinear Systems with Delayed Outputs

This paper deals with high-gain nonlinear observer design for a class of triangular systems with delayed output measurements. Based on a recent high-gain like observer design method, called HG/LMI observer, a larger bound of the time-delay is allowed compared to that obtained by using the standard high-gain methodology. Such a HG/LMI observer leads to a significantly lower tuning parameter, which reduces the values of the observer gains and increases the maximum bound of the delay allowed to ensure exponential convergence. Indeed, an explicit relation between the maximum bound of the delay and the observer tuning parameter is inferred by using a Lyapunov-Krasovskii functional jointly with the Halanay inequality. Such a relation shows clearly the superiority of the use of the HG/LMI observer design methodology.

Robust bang-bang control of disturbed nonlinear systems based on nonlinear observers

This paper proposes a robust bang-bang controller (RBC) based on the high-gain nonlinear observer for a nonlinear system with intermittent disturbances. The intermittent disturbances are able to model the system faults and sudden changes of operating conditions of practical nonlinear systems. A bang-bang constant funnel controller (BCFC) is employed, and the largest control capabilities of the control system is explored to stabilize the nonlinear system against the disturbances. The BCFC functions with the estimates of tracking error of control target and its derivatives estimated with a high-gain state observer, which eliminates the requirement on the derivative calculations of the system output tracking error. The error convergence of the observer is verified. The closed-loop stability of the RBC is proved in a bounded-input bounded-state sense. Simulation studies are undertaken with a single-machine infinite-bus (SMIB) power system to test the performance of the RBC.

Semiglobal Asymptotic Stabilization of Lower Triangular Systems by Digital Output Feedback

Digital control of nonlinear systems is studied by output feedback. It is proved that for nonlinear systems with a lower triangular structure, semiglobal asymptotic stabilization is still possible via discretized output feedback as long as a sampling time is small. The establishment of semiglobal asymptotic stabilizability needs no restrictive condition on the nonlinearities and/or unmeasurable states of the system, such as a linear growth condition or an output-dependent growth condition as commonly required in the case of global output feedback stabilization. It involves, however, tedious but subtle stability analysis due to the hybrid nature of the closed-loop system. A design method through “sample and hold” is developed to construct a semiglobally asymptotically stabilizing, digital output feedback compensator that consists of a high-gain nonlinear observer and controller, both with saturated states.

Simultaneous Observation of the Wheel Torque and Tire Force as well as the Vehicle Speeds

Individual torques at each vehicle wheel are important intermediate variables for the design of Advanced Driver Assistance Systems, and their knowledge stays an interesting research problem. In this study, a nonlinear high-gain unknown inputs state observer is designed to compute simultaneously longitudinal and transversal tire forces, resultant torques applied to wheels and the vehicle speeds. The necessary measurements are the usual rotation speed. Having validated the model of knowledge using a realistic vehicle simulator, the observer is tested under the same conditions and shows good performances for the vehicle state, tire forces and the unknown torques reconstruction.

Nonlinear High-Gain Observer-Based Diagnosis and Compensation for Actuator and Sensor Faults in a Quadrotor Unmanned Aerial Vehicle

This paper studies the diagnosis and compensation for sensor and actuator faults in a quadrotor unmanned aerial vehicle. Without adding sensors or actuators for increased hardware redundancy, an observer-based adaptive controller is proposed to estimate and compensate for the faults. First, using a feedback linearization technique, an inner controller is designed to transform the form of the considered quadrotor unmanned aerial vehicle with faults into a nonlinear system with Lipschitz-like nonlinearities and parametric faulty models. Second, the estimations for unmeasurable state and actuator faults are performed in an output-feedback outer controller to compensate for the actuator faults. Third, a nonlinear high-gain observer is designed to provide the information of the state and faults to the outer controller, with the compensations for sensor faults. A Lyapunov-based analysis shows that appropriate choices of the controller parameters can guarantee the exponential convergence of errors in estimation and trajectory tracking under uncertainties and faults. The robustness to the external disturbances is also discussed. Simulations are given to verify the effectiveness of the proposed scheme. The proposed approach is also implemented on a quadrotor unmanned aerial vehicle to show its feasibility in real-time applications.

Nonlinear interconnected high gain observer for series-parallel resonant DC/DC converter

We are considering the problem of state observation in series-parallel resonant converters (LCC). This is a crucial issue in (LCC) output voltage control as the control model is nonlinear and involves non-physical state variables, namely real and imaginary parts of complex electrical variables. An interconnected high gain observer is designed to get online estimates of these states. The observer is shown to be globally asymptotically stable. The global stability of the observer is analytically treated using the Lyapunov theory; finally we present numerical simulation to illustrate the performance of the suggested approach.

Nonlinear interconnected high gain observer for series-parallel resonant DC/DC converter

Nonlinear interconnected high gain observer for series-parallel resonant DC/DC converter

An approximate high gain observer for speed-sensorless estimation of induction motors

Rotor speed estimation for induction motors is a key problem in speed-sensorless motor drives. This paper performs nonlinear high gain observer design based on the full-order model of the induction motor. Such an effort appears non-trivial due to the fact that the full-model at best admits locally a non-triangular observable form &#x0028 NTOF &#x0029, and its analytical representation in the NTOF can not be obtained. This paper proposes an approximate high gain estimation algorithm, which enjoys a constructive design, ease of tuning, and improved speed estimation and tracking performance. Experiments demonstrate the effectiveness of the proposed algorithm.