System Parameter Uncertainties Research Articles

Robustness of energy landscape controllers for spin rings under coherent excitation transport

Abstract The design and analysis of controllers to regulate excitation transport in quantum spin rings presents challenges in the application of classical feedback control techniques to synthesize effective control and generates results in contradiction to the expectations of classical control theory. This paper examines the robustness of controllers designed to optimize the fidelity of an excitation transfer to uncertainty in system and control parameters. We use the logarithmic sensitivity of the fidelity error as the robustness measure, drawing on the classical control analog of the sensitivity of the tracking error. Our analysis shows that quantum systems optimized for coherent transport demonstrate significantly different correlation between error and the log-sensitivity depending on whether the controller is optimized for readout at an exact time T or over a time-window T ± Δ/2.

Optimized Load Frequency Controller Performances With a Reduced Number of Decision Variables: A Gravitational Search Algorithm-Based Method

Ensuring stability and maintaining performances of the load frequency controller (LFC) are stimulating tasks. A state feedback controller (SFC) with a generalized range of operation satisfying the necessary and sufficient conditions for system stability along with optimized performances through the gravitational search algorithm (GSA) are proposed. The proposed range is dependent on the system parameters. The agent-based systems in the literature consider the dimension of an agent as per the number of decision variables of the problem. The proposed method reduces the number of decision variables to obtain the controller gains and to use in the optimization process. The proposed method is validated through extensive results for different objective functions, contemplating both the steady state and the transient requirements as well as a consideration of different perturbed system parameters and variations in the input disturbances. Results and comparative studies with popular control techniques and optimization algorithms testify that the proposed method maintains system stability and improves the system performances while considering different system parameters, parametric uncertainties, and variations in input disturbances.

Finite-time tracking control with fast reaching condition for disturbed more electric aircraft direct current microgrid with constant power loads

Future more electric aircraft (MEA) can be seen as a direct current microgrid (DC MG). While DC MG can generally achieve safe, efficient and reliable operation of the system, constant power loads (CPLs), unknown resistive loads, DC source voltage variations, and disturbance inputs might degrade the overall stability and performance if they are not compensated in the control design procedure. In this paper, a fast-reaching condition-based sliding mode control (SMC) is proposed for the DC MG. The fast-reaching law contains two terms that improve the transient performance by forcing the system states to reach a sliding surface with two different rates. This attribute enhances the speed of convergence of the states to the sliding surface compared to conventional SMC. Additionally, the suggested method is resilient to system parameter uncertainties, which is indispensable in practice. The proposed controller is implemented to a DC MG that is supplied by an uncertain DC source and feeds CPLs and resistive load with time-varying power and resistance. OPAL RT results illustrate the robustness and fast convergence of the planned SMC controller.

Design of Robust Control for Vehicle Steer-by-Wire System

This study presented the design of a robust controller based on Integral Sliding Mode Control (ISMC) for controlling the Vehicle Steer-by-Wire (VSbW) system. The dynamic model of the VSbW system is first developed and then the design of ISMC has been conducted via the states of the system. The VSbW system has been described by two terms; one term represents the nominal model, which is free from nonlinearities, and the other term lumps the uncertainties in system parameters. The integral sliding mode controller has been designed for controlling the VSbW system. The control design consists of two parts. The first control part has addressed the nominal term of the system, while the second control part tackles and eliminates the effects of uncertainties and perturbation due to the uncertain term of the system. The numerical simulation has been conducted to show the robustness of ISMC and its capability to reduce the chattering effect in the control signal. In addition, a comparison study in performance has been conducted between the proposed controller and other controllers in the literature. We also carry out bibliometric analysis to see research trends. Based on our analysis, the number of publications regarding the keywords "controller", "steer", and "wire system" changes every year (25 (2018), 56 (2019), 51 (2020), 71 (2021), and 61 (2022)).

When artificial parameter evolution gets real: particle filtering for time-varying parameter estimation in deterministic dynamical systems

Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of these problems includes time-varying parameters with unknown evolution models that often cannot be directly observed. This work develops a systematic particle filtering approach that reframes the idea behind artificial parameter evolution to estimate time-varying parameters in nonstationary inverse problems arising from deterministic dynamical systems. Focusing on systems modeled by ordinary differential equations, we present two particle filter algorithms for time-varying parameter estimation: one that relies on a fixed value for the noise variance of a parameter random walk; another that employs online estimation of the parameter evolution noise variance along with the time-varying parameter of interest. Several computed examples demonstrate the capability of the proposed algorithms in estimating time-varying parameters with different underlying functional forms and different relationships with the system states (i.e. additive vs. multiplicative).

Adaptive Deformation Control of a Flexible Variable-Length Rotary Crane Arm With Asymmetric Input-Output Constraints.

This article constructs two adaptive control laws to achieve deformation reduction and attitude tracking for a rotary variable-length crane arm with system parameter uncertainties and asymmetric input-output constraints. Two auxiliary systems are given to deal with the input constraints, an asymmetric-logarithm-barrier Lyapunov function is established for achieving the asymmetric output constrains, and five adaptive laws are constructed to handle system parameter uncertainties. Besides, the control design is based on a partial differential equation model, and the S-curve acceleration and deceleration method is used for regulating the arm extension speed. Both the system stability and uniform ultimate boundedness of the controlled crane arm are analyzed. Simulation results validate the effectiveness of our established control laws.

Set‐theoretic localization for mobile robots with infrastructure‐based sensing

AbstractIn this article, we propose a set‐membership based localization approach for mobile robots using infrastructure‐based sensing. Under an assumption of known uncertainties bounds of the noise in the sensor measurement and robot motion models, the proposed method computes uncertainty sets that over‐bound the robot 2D body and orientation via set‐valued motion propagation and subsequent measurement update from infrastructure‐based sensing. We establish theoretical properties and computational approaches for this set‐theoretic localization method and illustrate its application to an automated valet parking example in simulations, and to omnidirectional robot localization problems in real‐world experiments. With deteriorating uncertainties in system parameters and initialization parameters, we conduct sensitivity analysis and demonstrate that the proposed method, in comparison to the FastSLAM, has a milder performance degradation, thus is more robust against the changes in the parameters. Meanwhile, the proposed method can provide estimates with smaller standard deviation values.

Adaptive Neural Network Control of a Flexible Spacecraft Subject to Input Nonlinearity and Asymmetric Output Constraint.

This article focuses on the vibration reducing and angle tracking problems of a flexible unmanned spacecraft system subject to input nonlinearity, asymmetric output constraint, and system parameter uncertainties. Using the backstepping technique, a boundary control scheme is designed to suppress the vibration and regulate the angle of the spacecraft. A modified asymmetric barrier Lyapunov function is utilized to ensure that the output constraint is never transgressed. Considering the system robustness, neural networks are used to handle the system parameter uncertainties and compensate for the effect of input nonlinearity. With the proposed adaptive neural network control law, the stability of the closed-loop system is proved based on the Lyapunov analysis, and numerical simulations are carried out to show the validity of the developed control scheme.

Advances in fine line-of-sight control for large space flexible structures

The increased need in pointing performance for Earth observation and science Space missions together with the use of lighter and flexible structures directly come with the need of a robust pointing performance budget from the very beginning of the mission design. An extensive understanding of the system physics and its uncertainties is then necessary in order to push control design to the limits of performance and constrains the choice of the set of sensors and actuators. A multi-body framework, the Two Input Two Output Ports approach, is used to build all the elementary flexible bodies and mechanisms involved in a fine pointing mission. This framework allows the authors to easily include all system dynamics with an analytical dependency on varying and uncertain mechanical parameters in a unique Linear Fractional Transformation (LFT) model. This approach opens the doors to modern robust control techniques that robustly guarantee the expected fine pointing requirements. In particular, a novel control architecture is proposed to reduce the microvibrations induced both by reaction wheel imbalances and Solar Array Drive Mechanism driving signal, by letting them work during the imaging phase. Thanks to a set of accelerometers placed at the isolated base of the payload and in correspondence of the mirrors with the largest size in a Space telescope (typically the primary and secondary ones), it is possible to estimate the line-of-sight error at the payload level by hybridizing them with the low-frequency measurements of the camera. While a classical Fast Steering Mirror in front of the camera can compensate for a large amount of microvibration, an innovative architecture with a set of six Proof-Mass Actuators installed at the payload isolator level can further improve the pointing performance. In particular, it is shown how the proposed architecture is able to robustly guarantee an absolute performance error of 10 arcsec in face of system parametric uncertainties at low frequency (≈ 1rad/s) with a progressive reduction of the jitter down to 40 marcsec for higher frequencies where micro-vibration sources act.

Special issue on PID control in the information age: Theoretical advances and applications

Special issue on PID control in the information age: Theoretical advances and applications

Adaptive time-varying constraint control for uncertain flexible beam systems

In this paper, the vibration control design of the Euler–Bernoulli beam with time-varying constraints is studied when the mass, bending stiffness and tension of the system parameters are known or unknown. For satisfying the time-varying constraints, the controller is designed and the system stability is analysed based on the tangent barrier Lyapunov function (TAN-BLF). Among them, the uncertainty of system parameters is dealt with by the adaptive method. In both cases, the vibration of the Euler–Bernoulli beam can be well restrained without violating the constraint conditions, and all signals in the system are bounded. Finally, the effectiveness of the proposed method is illustrated by a simulation example.

H ∞ Robust Frequency Control of Wind Turbine Generators and Electric Vehicles in Isolated grid

Wind turbine generators (WTGs) occupy an increasingly larger share in power system. WTGs in isolated grid lead to fluctuation in power and decrease system inertia. To reduce frequency deviation due to power fluctuation or wind speed change, model of WTGs is established based on deloading control. Considering that WTGs will have institutional wear because of frequent frequency regulation, which would short the life of WTGs, a robust frequency control strategy is proposed. WTGs and electric vehicles (EVs) are used in this control strategy. To suppress disturbances due to wind speed and uncertainty of system parameters, a H ∞ robust controller is solved using linear matrix inequality (LMI) methodology. Time-domain simulation results shows that the adopted control methodology can decrease frequency deviation during power fluctuations and wind speed changes.

Parameter-Variation-Tolerant Robust Current Sensorless Control of a Single-Phase Boost PFC

With the objective to eliminate the input current sensor in a totem-pole boost power factor corrector (PFC) for its low-cost design, a novel discretized sampling-based robust control scheme is proposed in this work. The proposed control methodology proves to be beneficial due to its ease of implementation and its ability to support high-frequency operation, while being able to eliminate one sensor and, thus, enhancing reliability and cost-effectiveness. In addition, detailed closed-loop stability analysis is carried out for the controller in discrete domain to ascertain brisk dynamic operation when subjected to sudden load fluctuations. To establish the robustness of the proposed control scheme, a detailed sensitivity analysis of the closed-loop performance metrics with respect to undesired changes and inherent uncertainty in system parameters is presented in this article. A comparison with the state-of-the-art (SOA) methods is provided, and conclusive results in terms of better dynamic performance are also established. To verify and elaborate on the specifics of the proposed scheme, a detailed simulation study is conducted, and the results show 25% reduction in response time as compared to SOA approaches. A 500-W boost PFC prototype is developed and tested with the proposed control scheme to evaluate and benchmark the system steady-state and dynamic performance. A total harmonic distortion of 1.68% is obtained at the rated load with a resultant power factor of 0.998 (lag), which proves the effectiveness and superiority of the proposed control scheme.

Koopman operator for time-dependent reliability analysis

Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work, we propose a Koopman operator based approach for time-dependent reliability analysis of nonlinear dynamical systems. Since the Koopman representations can transform any nonlinear dynamical system into a linear dynamical system, the time evolution of dynamical systems can be obtained by Koopman operators seamlessly regardless of the nonlinear or chaotic behavior. Despite the fact that the Koopman theory has been in vogue a long time back, identifying intrinsic coordinates is a challenging task; to address this, we propose an end-to-end deep learning architecture that learns the Koopman observables and then use it for time marching the dynamical response. Unlike purely data-driven approaches, the proposed approach is robust even in the presence of uncertainties; this renders the proposed approach suitable for time-dependent reliability analysis. We propose two architectures; one suitable for time-dependent reliability analysis when the system is subjected to random initial condition and the other suitable when the underlying system have uncertainties in system parameters. The proposed approach is robust and generalizes to unseen environment (out-of-distribution prediction). Efficacy of the proposed approached is illustrated using four numerical examples. Results obtained indicate supremacy of the proposed approach as compared to purely data-driven auto-regressive neural network, long short- term memory network, and DeepONet.

A Robust Fractional-Order Control Technique for Stable Performance of Multilevel Converter-Based Grid-Tied DG Units

In this article, we propose a sliding fractional-order (FO) control strategy to provide robustness feature for integrating a multilevel converter into the power grid under the system parameter uncertainties, nonlinear load alterations, and grid voltage sag. All dynamics achieved from the input capacitors and output inductances of the multilevel converter are utilized to design the proposed sliding fractional surfaces (SFSs) such that a robust operation of the grid-tied converter-based system is achieved. Then, an SFS-based Lyapunov function is built to assess the proposed controller stability. A thorough analysis of the Lyapunov function is carried out for distinguishing suitable boundaries of the controller coefficients when the error components of the system state variables are changed, accordingly. Using the derivative of Lyapunov function and SFS, a comprehensive evaluation is executed to detail the regulation procedure for the robustness and fractional PI controller coefficients. Finally, a closed-loop system using the converter current dynamics aims to discern the differences between different values of FO. Experimental tests using dSPACE-1202 along with MATLAB/Simulink simulations are employed to verify the effectiveness of the proposed control technique for providing proper harmonic compensation, enhanced power quality, unity power factor, voltage sag tolerance, and very low total harmonic distortion grid current.

Design of Active Disturbance Rejection Controller Variants for Solar Tracker System

In this paper, two controller design techniques such as linear active disturbance rejection control (LADRC) and generalized active disturbance rejection control (GADRC) are proposed for solar tracker system. The merit of the proposed method is that there is no need of tuning of proportional-integral-derivative (PID) parameters which is normally done in existing PID controller design techniques. As, the soft computing PID-based techniques involve very large iterations, so they consume much time. Also, these techniques are computationally inefficient. Therefore, to get rid of the conventional PID controller design topology, the LADRC scheme is proposed, which requires very few information of the system and even then the performance of the controller is impressive. The performance of the controller is further improved via GADRC scheme by including complete information of the system. Next, the robustness of proposed methods is investigated by the presence of system parametric uncertainty. Further, the performance of the proposed controllers is checked under time delays. Simulation results reveal that the proposed methods exhibit superb capability of disturbance rejection, high robustness and excellent transient performance in the presence of time delay in comparison to numerous existing PID-based control techniques.

Controlling mode-coupling instability in friction-induced vibration by acceleration feedback

Self-excited friction-induced oscillation, such as brake squeal, railway wheel squeal, chattering in machine tools, etc., is harmful in many mechanical systems. In the present study, the efficacy of acceleration feedback control with a second order filter is theoretically studied to mitigate friction-induced mode-coupling instability. Two different control strategies based on acceleration feedback are employed to control friction-induced mode-coupling instability of a two degrees-of-freedom linear system. Linear stability analysis near the equilibrium point of the system shows the efficacy of control laws to stabilize the system. The optimum filter parameters are determined by the pole crossover optimization method to attenuate the transient response as well as to achieve greater relative stability of the system. The Robustness study confirms the ability of the controller to stabilize the system in the presence of uncertainties in system parameters. Analytical results match closely with simulation results. Finally, nonlinearity in the form of stiffness is incorporated into the system for which the dynamics of the system show the presence of subcritical, supercritical Hopf bifurcation, and cyclic fold bifurcation. In the presence of nonlinearity, the feedback control is also able to reduce the range of instability of static equilibrium as well as the amplitude of the self-excited oscillation. The method of averaging is used to determine the stability and amplitude of the limit cycle. For the nonlinear system, the bifurcation diagram is constructed in AUTO and validated with results obtained from MATLAB SIMULINK and the method of averaging.

Identification of Frequencies and Track Irregularities of Railway Bridges Using Vehicle Responses: A Recursive Bayesian Kalman Filter Algorithm

On-board monitoring of track irregularities and bridge dynamic characteristics based on vehicle vibration responses provides basic data for the condition assessment of high speed railway bridges. However, the identification process inevitably introduces estimation uncertainty because of measurement noise and system parameter uncertainty. Here, in a probability framework, we propose a recursive Bayesian Kalman filtering (RBKF) algorithm for quantifying the identification uncertainty of the track irregularities and bridge natural frequencies. A nonlinear state-space model with measurement noise and process noise was first established for vehicle-bridge (VB) systems. Then the RBKF algorithm was formulated using a nonlinear state-space model, and the identification uncertainty was quantified in terms of estimation variances. A numerical study of two high speed railway bridges validated the RBKF algorithm. This study may help develop new approaches for on-board monitoring and condition assessment of high speed railway bridges.

A novel analysis method for vibration systems under time-varying uncertainties based on interval process model

Non-probabilistic models can quantify the uncertainties of engineering systems with limited data, which is significantly convenient and economical for engineering applications. However, a key issue in the application of non-probabilistic methods to vibration problems is how to address the time-varying uncertainties, especially when the correlation is involved. In this study, a novel analysis method based on the interval process model is proposed to obtain the dynamic response bounds of vibration systems under time-varying uncertainties, where uncertainties inherently existed in external excitations and system parameters are considered. Firstly, the interval process model is utilized for describing the uncertain-but-bounded variables, and the correlation function quantifies the correlation between the variables at different times. By solving two optimization problems, the dynamic response bounds concerning uncertain system parameters are obtained. Based on the response bounds, the first-order Taylor expansion is used to handle the uncertainties of system parameters, and a homogenization treatment is proposed to suppress the interval expansion. Thus the upper and lower bounds of the dynamic response under time-varying uncertainties can be determined. To quantify the reliability of vibration systems under time-varying uncertainties, the time-varying reliability indexes related to the proposed method are constructed. Finally, the proposed method is validated by the corresponding Monte Carlo simulation method and further applied in lunar soil coring. The findings from this study can provide an important tool for uncertainty and reliability analysis of vibration systems in practical engineering.

Altitude control of a quadcopter using interval type-2 fuzzy controller with dynamic footprint of uncertainty

Footprint of uncertainty (FOU) characteristics of interval type-2 membership functions (IT2-MFs) play an important role in the performance and robustness of interval type-2 fuzzy controllers (IT2-FCs). In literature, fixed FOU structures are used in almost all IT2-FC designs. In this study, an IT2-FC with dynamic FOU is proposed to provide high performance and robustness in the altitude control of a quadcopter. A proportional–derivative (PD) type FC with Takagi–Sugeno rule structure is used in the design procedure of the proposed controller. Additionally, input variables (error and derivative of error) are defined by using triangular IT2-MFs. To provide a dynamic FOU structure, the height of the lower MF (LMF) of each interval type-2 fuzzy set is defined as a function of the system error. In this way, FOU levels of IT2-MFs are adjusted dynamically since the height value of the LMF directly determines the FOU level of the IT2-MF. To evaluate the effectiveness of the proposed controller, comparison studies are performed under different conditions, including unmodeled measurement noises, an external disturbance, and a system parameter uncertainty. A classical PD, a type-1 fuzzy PD, and an interval type-2 fuzzy PD with fixed FOU controllers are used in the comparisons. The comparison results demonstrate that the proposed interval type-2 fuzzy PD controller with dynamic FOU exhibits better performance and more robustness than the other controllers.