System Parameter Uncertainties Research Articles

Polynomial Recurrent Neural Network-Based Adaptive PID Controller With Stable Learning Algorithm

This paper introduces a novel structure of a polynomial weighted output recurrent neural network (PWORNN) for designing an adaptive proportional—integral—derivative (PID) controller. The proposed adaptive PID controller structure based on a polynomial weighted output recurrent neural network (APID-PWORNN) is introduced. In this structure, the number of tunable parameters for the PWORNN only depends on the number of hidden neurons and it is independent of the number of external inputs. The proposed structure of the PWORNN aims to reduce the number of tunable parameters, which reflects on the reduction of the computation time of the proposed algorithm. To guarantee the stability, the optimization, and speed up the convergence of the tunable parameters, i.e., output weights, the proposed network is trained using Lyapunov stability criterion based on an adaptive learning rate. Moreover, by applying the proposed scheme to a nonlinear mathematical system and the heat exchanger system, the robustness of the proposed APID-PWORNN controller has been investigated in this paper and proven its superiority to deal with the nonlinear dynamical systems considering the system parameters uncertainties, disturbances, set-point change, and sensor measurement uncertainty.

Adaptive Line-of-Sight Tracking Control for a Tractor-Trailer Vehicle System With Multiple Constraints

In this paper, for the line-of-sight (LOS) tracking problem of a tractor-trailer vehicle system, we propose a novel adaptive constrained tracking control algorithm for the trailer to track a desired trajectory, while satisfying multiple <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">performance</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">feasibility</i> constraint requirements during the operation. To deal with these constraint requirements, both a universal barrier function approach and a novel state transformation scheme are incorporated to deal with constraints of different nature. An adaptive control structure is introduced to deal with system parameter uncertainties and external disturbances. We show that for the LOS distance and angle tracking errors, exponential convergence into small neighbourhoods of equilibrium can be guaranteed, with the convergence rate depending on the control input and adaptive gains. In the end, a simulation example and an experimental study further demonstrate the efficacy of the proposed algorithm.

Precision of attenuation coefficient measurements by optical coherence tomography.

.Significance: Optical coherence tomography (OCT) is an interferometric imaging modality, which provides tomographic information on the microscopic scale. Furthermore, OCT signal analysis facilitates quantification of tissue optical properties (e.g., the attenuation coefficient), which provides information regarding the structure and organization of tissue. However, a rigorous and standardized measure of the precision of the OCT-derived optical properties, to date, is missing.Aim: We present a robust theoretical framework, which provides the Cramér –Rao lower bound for the precision of OCT-derived optical attenuation coefficients.Approach: Using a maximum likelihood approach and Fisher information, we derive an analytical solution for when the position and depth of focus are known. We validate this solution, using simulated OCT signals, for which attenuation coefficients are extracted using a least-squares fitting procedure.Results: Our analytical solution is in perfect agreement with simulated data without shot noise. When shot noise is present, we show that the analytical solution still holds for signal-to-noise ratios (SNRs) in the fitting window being above 20 dB. For other cases (, focus position not precisely known), we show that the numerical calculation of the precision agrees with the derived from simulated signals.Conclusions: Our analytical solution provides a fast, rigorous, and easy-to-use measure for OCT-derived attenuation coefficients for signals above 20 dB. The effect of uncertainties in the focal point position on the precision in the attenuation coefficient, the second assumption underlying our analytical solution, is also investigated by numerical calculation of the lower bounds. This method can be straightforwardly extended to uncertainty in other system parameters.

Adaptive active fault-tolerant MPPT control of variable-speed wind turbine considering generator actuator failure

In order to ensure that the wind power system (WPS) can realize maximum power point tracking (MPPT) under generator side fault, an MPPT control system with adaptive active fault tolerance capability is proposed in this paper. The basic idea of the proposed control strategy is that a perturbation term containing model uncertainties, system nonlinearities and unknown disturbances (generator actuator failure and disturbance torque) is estimated in real-time by a designed observer. The estimated perturbation is used for the compensation of actual perturbation. Then, an adaptive feedback linearizing control of variable-speed wind turbine (VSWT) system can be realized. Therefore, the control strategy neither requires detailed system model and full state measurements, nor relies on fault detection, diagnosis and isolation techniques when the generator actuator fails. Simulation results show that the proposed control scheme has smaller tracking error and better dynamic performance than the traditional PI control and MPPT control, and higher robustness against system parameter uncertainties, disturbance torque and generator actuator failure than the nonlinear static state feedback based MPPT (NSSF-MPPT) control, traditional PI control and MPPT control.

An Adaptive Sliding-Mode Controller With a Modified Reduced-Order Proportional Integral Observer for Speed Regulation of a Permanent Magnet Synchronous Motor

This article proposes an adaptive sliding-mode control (ASMC) with a modified reduced-order proportional integral observer (MROPIO) to provide speed control for a permanent magnet synchronous motor against unknown disturbances, such as system parameter uncertainties and external load torque variation. The ASMC method, based on a new sliding-mode reaching law, improves chattering in the control signal and reduces the time required for the system trajectory to reach the sliding-mode surface. The MROPIO estimates unknown disturbances and provides feed-forward compensation for the ASMC, thus overcoming incorrect estimations of unknown disturbances during speed jumps can cause overshoots in the speed response. All the proposed methods were implemented on an industrial motor drive. The experimental results confirm the validity of the proposed method for practical applications.

Distributed aggregative games for Euler–Lagrange systems with system parameter uncertainties

AbstractIn this paper, an aggregative game of Euler–Lagrange (EL) systems is studied, where the parameters of the EL systems are not available. To seek the Nash equilibrium of the game, a novel distributed Nash equilibrium seeking algorithm is proposed, where the system parameters are not used in the feedback control. Moreover, a Lyapunov function is constructed such that EL players are proved to exponentially converge to the Nash equilibrium of the game. Finally, an example in the electricity market is provided to illustrate our result.

Designing an oil supply chain network considering sustainable development paradigm and uncertainty

This study proposes a multi-objective mathematical programming model to design an oil supply chain network at three levels: upstream, midstream and downstream. It includes oil wells, gas injection wells, production units, refineries, gas injection centers, distribution centers, export and import terminals. The proposed model optimizes all three economic, social and environmental goals at the same time. Drilling injection and production wells, transportation costs, production costs, gas injection center costs, as well as fixed and annual costs of refineries and distribution centers are all minimized in the economic dimension. The environmental dimension of sustainability reduces greenhouse gas emissions, while the social dimension of sustainability increases job opportunities. The optimization of associated petroleum gas injection operations into the reservoir is also taken into account in this study. The proposed model considers the uncertainty of critical parameters and employs a robust possibilistic hybrid approach to deal with it, as well as an interactive fuzzy approach to solve it. A case study in Iran is used to evaluate the suggested model's performance. In comparison to the single-objective economic model, the results of solving the model show that taking sustainability into account has reduced greenhouse gas emissions and increased job opportunities. The crude oil extraction potential increases in each period when gas injection optimization and reservoir pressure are taken into account. Furthermore, the cost of the supply chain grows as the amount of uncertainty in the suggested model rises. As a result, the uncertainty of system parameters must be considered.

Uncertainty Evaluation of Stochastic Structural Response with Correlated Random Variables

It has been realized that the influence of system parameter uncertainties may be very significant, even dominant, in stochastic response evaluation. Nevertheless, in reality, this evaluation process may be difficult to conduct due to these parameter variables (viz. structural property parameters, such as stiffness, damping, and strength, and excitation characteristics parameters, such as frequency content and duration) that are usually correlated with each other. Therefore, this study devotes to develop a method for evaluating stochastic response uncertainty involving correlated system parameter variables. In this method, the evaluation expression for the mean and standard deviation of the maximum response including uncertainty parameter variables are provided first; subsequently, a third-moment pseudo-correlation normal transformation is able to be performed for converting the correlated and non-normal system parameter variables with unknown joint probability density function (PDF) or marginal PDF into the mutually independent standard normal ones; ultimately, a point estimate procedure (PEP) based on univariate dimension reduction integration can be carried out for evaluating the structural stochastic response including uncertainty system parameters. Several numerical examples with an engineering background involving correlated system parameter variables are analyzed and discussed under stochastic excitation, and their results are compared with those yielded by Monte Carlo simulation (MCS) so as to demonstrate the effectiveness of the approach proposed. It indicated that the method proposed, in this study, provides an effective path to deal with uncertainty evaluation of stochastic structural response involving correlated random variables.

Adaptive fuzzy backstepping control of flexible marine riser with uncertain parameters and input saturation constraint

To suppress the vibration of a flexible riser system with input saturation and uncertain parameters under the influence of unknown external disturbances, an adaptive fuzzy backstepping boundary control algorithm was designed. First, the backstepping method and Lyapunov function are used to analyze the subsystem and design the virtual control law. On this basis, the adaptive fuzzy system was designed to approximate the unknown nonlinear term in the design process, and the smooth hyperbolic tangent function and the auxiliary system based on Nussbaum function were introduced to limit control input. The stability and uniform boundedness of the closed-loop control system are proved by the Lyapunov stability theory without simplifying or discretizing the infinite dimensional dynamic model. Finally, the effectiveness of the proposed control algorithm is verified by comparing the control effect with proportional–integral–derivative control and the previous adaptive backstepping control by MATLAB simulation. The simulation results show that the proposed control algorithm can overcome the uncertainty of system parameters and effectively suppress the riser vibration under input constraints, and its control effect is better than proportional–integral–derivative control and adaptive backstepping control.

Fuzzy-Sliding Mode Control for Humanoid Arm Robots Actuated by Pneumatic Artificial Muscles With Unidirectional Inputs, Saturations, and Dead Zones

Recently, the pneumatic artificial muscle (PAM) that can reproduce natural muscle functionalities has become one of the core actuator mechanisms of intelligent interactive soft robots. Unfortunately, some inherent defects (e.g., unignorable nonlinearities, hysteresis, low shrinkage frequencies, etc.) have limited the application progress of humanoid PAM arm robots. Additionally, the input constraints (e.g., saturations, dead zones, unidirectional inputs, etc.), unexpected external disturbances, unidentifiable system parameters, and inevitable unmodeled dynamics are usually complicated, which cannot be easily eliminated through existing adaptive control methods. This article proposes an adaptive fuzzy-sliding mode control method for humanoid PAM arm robots <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> any information of precise model structures and system parameters, which can suppress the unexpected effects of complicated unknown functions and achieve high performance tracking control, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simultaneously</i> . To the best of our knowledge, the proposed controller is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> method for the humanoid PAM arm robots that considers the nonlinear input constraints including unidirectional conditions, saturations, and dead zones, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simultaneously</i> . Next, all the input constraints, system parameter uncertainties, unmodeled dynamics, and external disturbances can be estimated adaptively by utilizing the proposed fuzzy update law. Particularly, a sliding mode control law is designed to compensate possible fuzzy approximation errors, and rigorous Lyapunov-based stability analysis is provided to ensure that the state errors can converge to zero within <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">finite</i> time. Hardware experiments are carried out later tovalidate the effectiveness and robustness of the proposed method.

Robust iterative learning control for linear discrete-time systems with initial state learning

This paper investigates a new sufficient robust convergence condition of iterative learning control with initial state learning in the presence of iteration-varying uncertainty for multivariable systems in the time domain. The uncertainty in system parameters may lead to divergence of the ILC algorithm. Moreover, in the basic ILC algorithm, the initial state is constant in each iteration and, consequently, always leads to a tracking error. Providing fixed learning gains over time and iteration is a significant achievement of this norm-based method. For this purpose, first, a new robust convergence condition is designed based on the iterative learning control with initial state learning algorithm, and in the next step, a semi-optimal solution is achieved for it by the imperialist competitive algorithm . Finally, the effectiveness of the proposed convergence scheme is evaluated through two numerical examples.

Accurate demand response participation in regulating power system frequency by Modified Active Disturbance Rejection Control

One of the significant problems in demand response (DR) participation in the smart power system is calculating how much electrical power is required to extract from DR ( ) to keep the power system frequency in the allowable range. Calculating the precise amount of this value is impossible due to the random nature of load disturbance (LoD). In this paper, a new method is presented to control the DR participation in the load frequency control considering communication time delay. Extended State Observer is used to estimate the magnitude of the LoD, considering the structural uncertainty of the power system parameters. Then, the DR program is implemented in load frequency control to compensate the whole or part of LoD considering the available electrical power at the aggregators (PAV‐AGG) and communication time delay. Afterward, Active Disturbance Rejection Control is modified and adopted to control the uncompensated LoD. The salp swarm algorithm is employed to design the parameters of the proposed method, which is verified in comparison with the previous methods. The results demonstrate that the presented approach has potentially significant performance, assisting the power system frequency to be damped immediately with the small overshoot and undershoot.

Model Predictive Control Using Artificial Neural Network for Power Converters

There has been an increasing interest in using model predictive control (MPC) for power electronic applications. However, the exponential increase in computational complexity and demand of computing resources hinders the practical adoption of this highly promising control technique. In this article, a new MPC approach using an artificial neural network (termed ANN-MPC) is proposed to overcome these barriers. A power converter with a virtual MPC controller is first designed and operated under a circuit simulation or power hardware-in-the-loop simulation environment. An artificial neural network (ANN) is then trained offline with the input and output data of the virtual MPC controller. Next, an actual FPGA-based MPC controller is designed using the trained ANN instead of relying on heavy-duty mathematical computation to control the actual operation of the power converter in real time. The ANN-MPC approach can significantly reduce the computing need and allow the use of more accurate high-order system models due to the simple mathematical expression of ANN. Furthermore, the ANN-MPC approach can retain the robustness for system parameter uncertainties by flexibly setting the input elements. The basic concept, ANN structure, offline training method, and online operation of ANN-MPC are described in detail. The computing resource requirement of the ANN-MPC and conventional MPC are analyzed and compared. The ANN-MPC concept is validated by both simulation and experimental results on two kW-class flying capacitor multilevel converters. It is demonstrated that the FPGA-based ANN-MPC controller can significantly reduce the FPGA resource requirement (e.g., 2.11 times fewer slice LUTs and 2.06 times fewer DSPs) while offering a control performance same as the conventional MPC.

On the ergodicity assumption in Performance-Based engineering

In the Performance-Based Engineering (PBE) framework, uncertainties in system parameters, or modelling uncertainties, have been shown to have significant effects on capacity fragilities and annual collapse rates of buildings. Yet, since modelling uncertainties are non-ergodic variables, their consideration in failure rate calculations offends the Poisson assumption of independent crossings. This problem has been addressed in the literature, and errors found negligible for small annual collapse failure rates. However, the errors could be significant for serviceability limit states, and when failure rates are integrated in time, to provide lifetime failure probabilities. Herein, we present a novel formulation to fully avoid the error in integration of non-ergodic variables. The proposed product-of-lognormals formulation is fully compatible with popular fragility modelling approaches in PBE context. Moreover, we address collapse limit states of realistic reinforced concrete buildings, and find errors of the order of 5 to 8% for 50-year lifetimes, up to 14% for 100 years. Computation of accurate lifetime failure probabilities in a PBE context is clearly important, as it allows comparison with lifetime target reliability values for other structural analysis formulations.

Nonlinear disturbance observer-based direct joint control for manipulation of a flexible payload with output constraints

This paper discusses a nonlinear direct joint control scheme for manipulation of a flexible payload by a single-arm system with disturbances, parametric uncertainty and output constraints. The flexible payload can be considered as an Euler–Bernoulli beam. The equations of the coupled rigid-flexible motion are established on the basis of the ordinary differential equations (ODEs) and partial differential equation (PDE), which can avoid system spillover instability. A novel nonlinear disturbance observer-based control approach is proposed to enhance its disturbance attenuation ability. To handle the system parametric uncertainty, we apply adaptive direct joint control to approximate the unknown parameter, which does not require endpoint boundary control. Then a Barrier Lyapunov Function (BLF) is adopted to eliminate the impact of output restriction. The asymptotic stability of the closed-loop system is rigorously proven by semi-group theory and LaSalle's Invariance Principle extended to an infinite-dimensional system. Finally, the performance of the direct joint control is validated via numerical simulations.

Designing of a non‐fragile robust predictive controller for uncertain systems with time‐varying delay: A delay‐range‐dependent approach

This study addresses a new delay-dependent non-fragile robust model predictive controller for a class of uncertain continuous-time systems with time-varying delay subjected to constrained input and perturbed controller gain. The uncertainties in system parameters and controller gain are considered as general additive forms. The proposed controller can provide a suitable linear feedback control law depending on delay such that robust performance is achieved to the possible existence of uncertainties. To this end, an optimisation problem is formulated to minimise the upper-bound of the cost function involving some conditions in terms of linear matrix inequalities, utilising the information of lower-and upper-bounds of time-varying delay. By including information regarding the delay range in the quadratic function, the ability to have less conservative results compared to the related works in literature is provided. The effectiveness of the proposed technique is illustrated through a comparison with recent works.

Robust adaptive attitude control of flexible spacecraft using a sliding mode disturbance observer

A composite control scheme based on a disturbance observer is presented in this paper to deal with the attitude control problem of flexible spacecraft. Specifically, a sliding mode disturbance observer (SMDO) is developed to attenuate the unmodeled system dynamics, parameter uncertainties, and multiple external disturbances. The key feature of this approach is to relax the assumption imposed on disturbance to be constant or changing at a slow rate, which is a typical assumption in this class of problems involving a disturbance observer. Then, an exclusive adaptive integral sliding mode controller is combined with the SMDO to get the improved closed-loop control performance of the system. The underlying benefit of the proposed control scheme is improved robustness against time-dependent external disturbances and system model uncertainties. The stability analysis of the closed-loop system is provided using Lyapunov’s stability theory. Simulation results are provided to show the effectiveness of the proposed control scheme, especially in comparison with existing results.

Optimization-based clustering of random fields for computationally efficient and goal-oriented uncertainty quantification: Concept and demonstration for delineation of wellhead protection areas in transient aquifers

A general approach to deal with parameter uncertainty in natural systems is to use ensembles of many parameter realizations. However, this might result in extremely expensive computational time, especially when additional loops for transient simulation and for optimization are involved. One possibility to mitigate computing time is to use few but well-selected realizations that best represent the involved geological uncertainties, e.g., by clustering techniques.The goal of this paper is to address the search for representative realizations that best approximate the distribution and its tails of a model ensemble. In our test application, this ensemble is used to delineate wellhead protection areas (WHPAs) under transient flow conditions and subject to random heterogeneity of the aquifer. Our approach is based on clustering and proposes that the cluster medoids (representatives) should be optimized not for “statistical representation in the space of some selected proxy metrics”, but for “a minimum of decision-relevant errors”. And, if the underlying decision problem is multi-objective, then the clustering optimization can be made multi-objective, too. In this way, many subsequent analyses can be performed on the condensed set of representative scenarios that would be computationally too expensive otherwise, even if distribution tails and extreme realizations are relevant. We demonstrate the advantage of our clustering optimization methodology on a dynamic probabilistic WHPA delineation, and we compare its performance with a standard clustering analysis.Our results show that: (1) in probabilistic transient WHPA analysis, clustering is a suitable technique to account for geological uncertainty. (2) However, clustering analysis should be based on optimization concepts rather than on simple medoid concepts, and (3) of course, it should use problem-specific and decision-relevant metrics for cluster optimization. In our WHPA application, this leads to a more accurate representation of decision-relevant statistical extremes. (4) The additional extension to multi-objective cluster selection probes to be a valid approach in multi-objective WHPA delineation. (5) Using our framework, we reduce the computational cost of addressing highly expensive simulations.

Robust Speed Tracking Control for Future Electric Vehicles under Network-Induced Delay and Road Slope Variation.

Integrated motor-transmission (IMT) powertrain systems are widely used in future electric vehicles due to the advantages of their simple structure configuration and high controllability. In electric vehicles, precise speed tracking control is critical to ensure good gear shifting quality of an IMT powertrain system. However, the speed tracking control design becomes challenging due to the inevitable time delay of signal transmission introduced by the in-vehicle network and unknown road slope variation. Moreover, the system parameter uncertainties and signal measurement noise also increase the difficulty for the control algorithm. To address these issues, in this paper a robust speed tracking control strategy for electric vehicles with an IMT powertrain system is proposed. A disturbance observer and low-pass filter are developed to decrease the side effect from the unknown road slope variation and measurement noise and reduce the estimation error of the external load torque. Then, the network-induced delay speed tracking model is developed and is upgraded considering the damping coefficient uncertainties of the IMT powertrain system, which can be described through the norm-bounded uncertainty reduction method. To handle the network-induced delay and parameter uncertainties, a novel and less-conservative Lyapunov function is proposed to design the robust speed tracking controller by the linear matrix inequality (LMI) algorithm. Meanwhile, the estimation error and measurement noise are considered as the external disturbances in the controller design to promote robustness. Finally, the results demonstrate that the proposed controller has the advantages of strong robustness, excellent speed tracking performance, and ride comfort over the current existing controllers.

Robust Errorless-Control-Targeted Technique Based on MPC for Microgrid with Uncertain Electric Vehicle Energy Storage Systems

Regarding the microgrid with large-scale electric vehicle (EV) energy storage systems working at the vehicle-to-grid (V2G) mode, uncertain factors (e.g., the number of EVs feeding the microgrid shifts frequently) make the system unfixed, leading to the fact that it is difficult to precisely determine the real-time droop coefficients of the system, thereby degrading the performance of the traditional inverter control strategies that rely on the droop coefficients. To solve the problem, this paper proposes an errorless-control-targeted double control loop (DCL) technique based on robust MPC to control the microgrid with EV energy storage systems without using droop coefficients. Firstly, the structure of the DCL method is developed, with each component in the structure detailed. Compared to the traditional control strategies, the novel one regards the frequency, voltage, and currents as the control objectives instead of active/inactive power. It deserves to be mentioned that the frequency and voltage are regulated by proportional-integral controllers, while the currents are regulated by the finite control set model predictive control (FCS-MPC) method. Secondly, the impacts of system parameter uncertainties on the prediction accuracy of the FCS-MPC controller are analyzed clearly, illustrating that it is necessary to develop effective techniques to enhance the robustness of the controller. Thirdly, sliding mode observers (SMO) based on a novel hyperbolic function are constructed to detect the real-time disturbances, which can be used to generate voltage compensations by using automatic disturbance regulators. Then, the voltage compensations are adopted to establish a modified predicting plant model (PPM) used for the FCS-MPC controller. By using the proposed SMO-based disturbance detection and compensation techniques, the MPC controller gains a strong robustness against parameter uncertainties. Finally, a simulation is conducted on a microgrid system to verify the effectiveness of the proposed techniques, and the obtained results are compared with the traditional virtual synchronous machine (VSG) strategy relying on droop coefficients.