Lyapunov-based Adaptation Law Research Articles

Coordinate Control for an SMIB Power System with an SVC

To improve power quality in power systems vulnerable to current disturbances and unbalanced loads, a hybrid control scheme is proposed in the present paper. A hybrid adaptive robust control strategy is devised for an SMIB power system equipped with a static VAR compensator to ensure robust transient stability and voltage regulation (SVC). High-order sliding mode control is combined with a dynamic adaptive backstepping algorithm to form the basis of this technique. To create controllers amenable to practical implementation, this method uses a high-order SMIB-SVC model and introduces dynamic constraints, in contrast to prior approaches. Improved transient and steady-state performances of the turbine steam-valve system are the goals of the dynamic backstepping controller. A Lyapunov-based adaptation law is developed to address the ubiquitous occurrence of parametric and nonparametric uncertainty in electrical power transmission systems due to the damping coefficient, unmodeled dynamics, and external disturbance. High-order sliding mode (HOSM) control is used for generator excitation and SVC devices to construct finite-time controllers. The necessary derivatives for HOSM control are calculated using high-order numerical differentiators to prevent simulation instability and convergence issues. Simulations demonstrate that the suggested method outperforms conventionally coordinated and hybrid adaptive control schemes regarding actuation efficiency and stability.

Online System Identification of a Fuel Cell Stack With Guaranteed Stability for Energy Management Applications

Designing an accurate model for a proton exchange membrane fuel cell (PEMFC) is very difficult owing to its multivariate nature. Hence, PEMFC online system identification (OSI), which serves as a basis for its application in energy management of hybrid fuel cell vehicles, is considerably important to cope with the performance drifts. In this paper, an OSI method is proposed for estimating the time-varying parameters of a well-known PEMFC semi-empirical model in the literature. Unlike the other similar approaches, the proposed technique in this manuscript suggests a Lyapunov-based adaptation law with guaranteed stability to estimate online the fuel cell parameters. To highlight the effectiveness of the suggested approach, it is used to estimate the characteristics of a 500-W Horizon PEMFC and its performance is compared with Kalman filter which is perceived as a reliable linear estimator. Experimental results along with the comparative study prove the successful performance of the suggested technique.

Real-Time Parameter Estimation of a Fuel Cell for Remaining Useful Life Assessment

This article presents a real-time parameter estimation of a proton exchange membrane fuel cell (PEMFC). The proposed strategy estimates online the PEMFC's resistance, since it is directly correlated to its remaining useful life assessment. The estimation of the PEMFC's parameters is a difficult task to undertake due to various uncertainties, like temperature and aging, that lead to a drift in parameters and limit the performance of the overall energy system. Therefore, online system identification is essential to track online the PEMFC's time-varying parameters. Unlike other identification techniques, the proposed strategy is based on a simple yet accurate PEMFC's model and adjusts its parameters in real-time using a Lyapunov-based adaptation law, which yields guaranteed stability. Experiments are conducted on a 500-W Horizon PEMFC and results along with a comparison against the well-known Kalman filter highlight the effectiveness of the proposed approach, which is instrumental for its numerous applications, such as the energy management of hybrid fuel cell vehicles.

Adaptive Control of a 3-DOF Helicopter Under Structured and Unstructured Uncertainties

In this paper, an adaptive control strategy is presented for a three-degree-of-freedom helicopter under both structured and unstructured uncertainties. The adaptive control scheme learns online the helicopter’s inverse model with a Lyapunov-based adaptation law to estimate the system’s parameters. Moreover, a reference model is introduced to stabilize the helicopter at start-up and cope with unstructured uncertainties such as external disturbance. Therefore, the controller achieves accurate motion tracking in the presence of both structured uncertainties (parameters variation) and unstructured uncertainties (unknown disturbance). Unlike many controllers, the proposed adaptive control scheme’s stability is guaranteed by Lyapunov direct method. The proposed controller’s performance in coping with various uncertainties is highlighted in different operating conditions.

Lyapunov-based state of charge diagnosis and health prognosis for lithium-ion batteries

Tracking the state-of-charge and state-of-health presently attracts much attention as they are important evaluation indexes for energy storage systems diagnosis and prognosis in electric vehicles and smart grids. This paper presents a hybrid state-of-charge and state-of-health estimation technique according to adaptation of parameters in an equivalent circuit model and a Lyapunov-based adaptation law. The online adaptation of the equivalent circuit model is employed to maintain accurate estimations by capturing battery age-dependent dynamics. The Lyapunov-based adaptation law is employed to enable the production of internal battery state and age-dependent parameters estimations using only battery terminal voltage and noisy current measurements. Though parameters vary with aging, temperature or other factors, accurate estimations are still achieved without prior knowledge of battery parameters. Besides, the stability of the proposed observer can also be guaranteed by Lyapunov direct method. The proposed method is verified using data collected over randomized discharge profiles. Experimental results highlight the high estimation accuracy and robustness of the proposed model and technique.

Adaptive Fuzzy Logic Control for a Class of Unknown Nonlinear Dynamic Systems with Guaranteed Stability

In this paper, a stability analysis is suggested for adaptive fuzzy logic systems (FLSs) without the requirement of states measurement or estimation. Fuzzy logic is viewed as a powerful tool in providing accurate approximation of systems with uncertainties. The proposed methodology exploits the power of adaptive control theory to find a Lyapunov-based adaptation law for FLSs. As such, both stability and tracking problems are addressed for a class of nonlinear dynamic systems. The proposed method yields reduced complexity with respect to many adaptive FLSs available in the literature. In addition, the use of an observer to estimate immeasurable states is not required as in other methods. First, a stability analysis is presented for adaptive control. Then, results are extended to adaptive FLSs with unknown dynamics. A numeric illustrative example highlights the implementation details and the performance of the suggested scheme.

Online Lifetime Estimation of Supercapacitors

This paper proposes an online lifetime estimation methodology for supercapacitors. The online technique uses a Lyapunov-based adaptation law to estimate online the supercapacitor's parameters. Unlike offline time- or frequency-domain characterization techniques that require discontinuation of the system's normal operation, the proposed approach is more suitable for real-time applications, such as electric/hybrid vehicles, as it provides online lifetime estimation. Furthermore, convergence and stability analysis is provided by Lyapunov's stability theory as opposed to many online estimators available in the literature. The effectiveness of the proposed strategy is validated through experiments along with comparison against two different methods.

Boundary Estimation of Boundary Parameters for Linear Hyperbolic PDEs

We propose an adaptive observer scheme to estimate boundary parameters in first-order hyperbolic systems of Partial Differential Equations (PDE). The considered systems feature an arbitrary number of states traveling in one direction and one counter-convecting state. Uncertainties in the boundary reflection coefficients and boundary additive errors are estimated relying on a pre-existing observer design and a novel Lyapunov-based adaptation law.

Online System Identification for Lifetime Diagnostic of Supercapacitors With Guaranteed Stability

In this paper, an online system identification method is introduced for lifetime diagnostic of supercapacitors. The online strategy uses a Lyapunov-based adaptation law to estimate online the supercapacitor’s parameters. Therefore, the adaptive observer’s stability is guaranteed by Lyapunov’s direct method. State-of-health (SoH) estimation is crucial since aging introduces degradation in supercapacitors’ performance, which might eventually lead to their failure. SoH is usually measured by offline time or frequency domain characterization techniques such as spectroscopy. However, these methods require interruption of the system’s operation, and hence, they are not suitable for real-time applications such as electric vehicles. Unlike other online estimation strategies, only voltage and current measurements are required. Simulation and experimental results along with comparison against two different methods highlight the effectiveness of the proposed approach in estimating the SoH.

Adaptive Control of Piezoelectric Actuators with Hysteresis and Disturbance Compensation

In this manuscript, an adaptive control strategy is presented for piezoactuators with hysteresis and disturbance estimation. The adaptive control scheme learns the piezoelectric actuator’s inverse model with a Lyapunov-based adaptation law. Then, an adaptive estimator is used in a feedback loop to estimate hysteresis and disturbance. Therefore, the controller achieves accurate displacement tracking with hysteresis/disturbance uncertainties. Unlike many controllers, the proposed adaptive control scheme’s stability is guaranteed by Lyapunov direct method. The proposed controller’s performance in coping with hysteresis and disturbance is highlighted in different operating conditions.

Lyapunov-Based Adaptive State of Charge and State of Health Estimation for Lithium-Ion Batteries

This paper presents an adaptive state of charge (SOC) and state of health (SOH) estimation technique for lithium-ion batteries. The adaptive strategy estimates online parameters of the battery model using a Lyapunov-based adaptation law. Therefore, the adaptive observer stability is guaranteed by Lyapunov's direct method. Since no a priori knowledge of battery parameters is required, accurate estimation is still achieved, although parameters change due to aging or other factors. Unlike other estimation strategies, only battery terminal voltage and current measurements are required. Simulation and experimental results highlight the high SOC and SOH accuracy estimation of the proposed technique.

Lyapunov-based Adaptive Regulation of Limit Cycle Oscillations in Aircraft Wings Using Synthetic Jet Actuators

In this paper, a SJA-based nonlinear adaptive controller is developed, which is capable of completely suppressing LCO in UAV systems with uncertain actuator dynamics. Specifically, the control law compensates for uncertainty in an input gain matrix, which results from the unknown airflow dynamics generated by the SJA. Challenges in the control design include compensation for input-multiplicative parametric uncertainty in the actuator dynamic model. This difficulty was handled via innovative algebraic manipulation in the error system development, along with a Lyapunov-based adaptive law. A rigorous Lyapunov-based stability analysis is utilized to prove asymptotic plunging regulation, considering a detailed dynamic model of the pitching and plunging dynamics; and numerical simulation results are provided to demonstrate that simultaneous pitching and plunging suppression is achieved using the proposed control law.

An adaptive fuzzy controller based on harmony search and its application to power plant control

Considering the reliability and safety requirements of power stations, a novel adaptive fuzzy controller is presented to implement non-overshoot control in power plants in which the Lyapunov-based adaptive law is employed to guarantee the stability of the controller while a modified Adaptive Binary Harmony Search (ABHS) algorithm is utilized to search the optimal control parameters to improve the dynamic performance. Two strategies are analyzed and used with ABHS to guarantee the non-overshoot of control. Furthermore, a simple but efficient repair operation is developed to deal with the time-varying characteristic of the thermal process. Finally, the proposed ABHS-based Adaptive Fuzzy Control (ABHSAFC) method is applied to the bed temperature control of the Circulating Fluidized Bed Boiler (CFBB). The experimental results demonstrate that ABHSAFC can implement the expected non-overshoot control efficiently and outperforms the classical Lyapunov-based adaptive fuzzy control, ABHS-based fuzzy control and ABHS-based PID control. Considering the characteristics of the easy implementation, robustness and the guaranteed stability, ABHSAFC promises a favorable engineering application prospect.

A Lyapunov-based Adaptive Control Law for an Electromagnetic Actuator

Electromagnetic devices in industrial systems are utilised for problems of positioning and tracking control. A direct adaptive non-linear control framework for a non-linear electromagnetic actuator is presented in this paper. Starting from a Lyapunov approach a continuous control law is calculated for the actuator. After that, an approximated sampled final control law is proposed. The resulting control strategy is an adaptive one in which the main parameter depends on the variable inductance of the actuator itself. This aspect seems to be important to prevent saturation during the control phase.

Adaptive control of non-linearly parameterised pure-feedback systems

This study proposes an adaptive tracking control approach for non-linearly parameterised pure-feedback systems with completely non-affine property. Using the parameter separation technique, a state predictor is developed for deriving adaptive laws of non-linearly connected parameters. The proposed adaptive control system is designed by a combination of the backstepping and singular perturbation concept where the virtual controllers and the actual controller are defined as solutions of fast dynamic equations which accomplish the time-scale separation between the state predictor and controllers. The Lyapunov-based adaptive laws guarantee that the predictor states track the system states with bounded errors, and thus the tracking error between the system output and the desired signal is bounded. Finally, simulation results are provided to illustrate the effectiveness of the proposed control system.

Adaptive Dynamic Inversion via Time-Scale Separation

This paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input. Using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input, a state predictor is defined for derivation of the adaptive laws. The adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation, which achieves time-scale separation between the state predictor and the controller dynamics. Lyapunov-based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors. As a result, the system state tracks the desired reference model with bounded errors. Benefits of the proposed design method are demonstrated using Van der Pol dynamics with nonlinear control input.

Adaptive Control Design Methodology for Nonlinear-in-Control Systems in Aircraft Applications

An adaptive control design method for both short-period and lateral/directional control of a fighter aircraft is presented. The proposed method is directly applicable to flight control of vehicles with state-dependent and nonlinear-in-control uncertain dynamics. The developed design approach uses a specialized set of radial basis function approximators and Lyapunov-based adaptive laws to compensate for the unknown control-dependent nonlinearities. The adaptive controller is defined as a solution of fast dynamics, which verifies the assumptions of Tikhonov’s theorem from singular perturbations theory. Simulations illustrate the theoretical findings.

Combining Genetic Algorithms and Lyapunov-Based Adaptation for Online Design of Fuzzy Controllers

This paper proposes a hybrid approach for the design of adaptive fuzzy controllers (FCs) in which two learning algorithms with different characteristics are merged together to obtain an improved method. The approach combines a genetic algorithm (GA), devised to optimize all the configuration parameters of the FC, including the number of membership functions and rules, and a Lyapunov-based adaptation law performing a local tuning of the output singletons of the controller, and guaranteeing the stability of each new controller investigated by the GA. The effectiveness of the proposed method is confirmed using both numerical simulations on a known case study and experiments on a nonlinear hardware benchmark.

Robust contact force estimation for robot manipulators in three-dimensional space

Information on contact forces in robot manipulators is indispensable for fast and accurate force control. Instead of expensive force sensors, estimation algorithms for contact forces have been widely developed. However, it is not easy to obtain the accurate values due to uncertainties. In this article, a new robust estimator is proposed to estimate three-dimensional contact forces acting on a three-link robot manipulator. The estimator is based on the extended Kalman filter (EKF) structure combined with a Lyapunov-based adaptation law for estimating the contact force. In contrast to the conventional EKF the new estimator is designed such that it is robust to the deterministic uncertainties such as the modelling error and the sensing bias. The performance of the proposed estimator is evaluated through simulations of a robot manipulator and demonstrates robustness in estimating the contact force. The estimation results show that it can be potentially used to replace the expensive force sensors in robot applications.