Systems In Presence Of Uncertainties Research Articles

Optimization of a fractional-order interval type-2 fuzzy PID controller based on BBO for real-time applications

This paper addresses the development of a robust controller for a nonlinear system to minimize the tracking errors and reduce the effects of external noise and disturbances. To achieve this, the biogeography-based optimization (BBO) algorithm is utilized for an optimally robust interval type 2 fractional-order fuzzy proportional integral derivative controller (BB0-IT2FO-FPID) is proposed. The proposed method offers several advantages. Firstly, the proposed controller is optimized to achieve robustness and minimize tracking errors. Secondly, it effectively handles external noise and disturbances, making it suitable for real-world applications. Thirdly, the use of the BBO algorithm enhances the controller's performance by dynamically adjusting its parameters based on system requirements. The performance of the proposed controller is validated by applying it to control a robotic manipulator, which presents challenges due to its nonlinear characteristics and interacting multi-input multi-output (MIMO) dynamics. Additionally, a real-time evaluation of the proposed controller is conducted by applying it to the speed control of a direct current (DC) machine. The effectiveness of the proposed controller is verified through simulation and practical experiments and comparisons with other optimized controllers, namely FO fuzzy type 1 PID (T1FO-FPID) and FOPID. The simulation and practical results demonstrate the superior performance of the BBO-IT2FO-FPID controller in the presence of system uncertainties and different types of disturbances.

Insights of using control theory for minimizing induced seismicity in underground reservoirs

Deep Geothermal Energy, Carbon Capture, and Storage and Hydrogen Storage have significant potential to meet the large-scale needs of the energy sector and reduce the CO2 emissions. However, the injection of fluids into the earth’s crust, upon which these activities rely, can lead to the formation of new seismogenic faults or the reactivation of existing ones, thereby causing earthquakes. In this study, we propose a novel approach based on control theory to address this issue. First, we obtain a simplified model of induced seismicity due to fluid injections in an underground reservoir using a diffusion equation in three dimensions. Then, we design a robust tracking control approach to force the seismicity rate to follow desired references. In this way, the induced seismicity is minimized while ensuring fluid circulation for the needs of renewable energy production and storage. The designed control guarantees the achievement of the control objectives even in the presence of system uncertainties and unknown dynamics. Finally, we present simulations of a simplified geothermal reservoir under different scenarios of energy demand to show the reliability and performance of the control approach, opening new perspectives for field experiments based on real-time regulators.

L1 adaptive controller design for a tail fin controlled fixed wing unmanned aerial vehicle

The aim of this study is to design L1 adaptive controller, which is one of the robust control methods that can overcome model uncertainties, disturbances and noises, for a fixed-wing unmanned aerial vehicle (UAV) with tail fin controlled. In this context, first of all, the decoupled equations of motion of the six-degrees-of-freedom system are derived for the roll, pitch and yaw channels of the UAV. Then, the performance of the controller is demonstrated by simulation results for linearized system representation. By adding parameter errors to the system in question, the feature of tracking the given angle commands are analyzed. It has been observed that the L1 adaptive control structure exhibits rapid adaptation even in presence of system uncertainties. Finally, the controller is applied to the nonlinear system and operated throughout the entire flight envelope.

Stages and main tasks of the century-long control theory and system identification development. Part IV. Methods and problems of designing robust control systems

The article provides a review of the most important methods and problems in the design of robust discrete control systems. In this case, the main attention was focused on the problems of suppressing limited external disturbances, information about which is presented only in the form of a limitation on their maximum value. The use of invariant ellipsoids is considered as the first mathematical apparatus for describing the characteristics of the influence of external disturbances on the trajectory of motion of dynamic systems. Theorems on the representation of invariant ellipsoids in the form of linear matrix inequalities (LMI) are formulated, which are further used to synthesize discrete state controllers that suppress external disturbances. The solution to a more general problem of robust suppression of limited disturbances based on the use of LMI in the presence of system uncertainties in the parameters of the mathematical model of the control object is considered. The use of H∞-control theory is considered as a second mathematical apparatus for suppressing external l2-limited external disturbances. In this case, the optimality criterion consists in minimizing the maximum ratio of the l2-norm of the vector of output stabilized coordinates to the l2-norm of the vector of input disturbances. The problem is solved by reducing it to the problem of robust control of a discrete dynamic system in space H∞ based on the Two-Ricatti approach. The standard H∞-optimization problem is also considered.

Improving Performance of Flight Control System in Presence of Uncertainties and Extreme Changes in Parameters using Multiple Model Adaptive Control

Improving Performance of Flight Control System in Presence of Uncertainties and Extreme Changes in Parameters using Multiple Model Adaptive Control

A generalization of the maximum likelihood expectation maximization (MLEM) method: Masked-MLEM

Objective. In our previous work on image reconstruction for single-layer collimatorless scintigraphy, we developed the min–min weighted robust least squares (WRLS) optimization algorithm to address the challenge of reconstructing images when both the system matrix and the projection data are uncertain. Whereas the WRLS algorithm has been successful in two-dimensional (2D) reconstruction, expanding it to three-dimensional (3D) reconstruction is difficult since the WRLS optimization problem is neither smooth nor strongly-convex. To overcome these difficulties and achieve robust image reconstruction in the presence of system uncertainties and projection noise, we propose a generalized iterative method based on the maximum likelihood expectation maximization (MLEM) algorithm, hereinafter referred to as the Masked-MLEM algorithm. Approach. In the Masked-MLEM algorithm, only selected subsets (‘masks’) from the system matrix and the projection contribute to the image update to satisfy the constraints imposed by the system uncertainties. We validate the Masked-MLEM algorithm and compare it to the standard MLEM algorithm using experimental data obtained from both collimated and uncollimated imaging instruments, including parallel-hole collimated SPECT, 2D collimatorless scintigraphy, and 3D collimatorless tomography. Additionally, we conduct comprehensive Monte Carlo simulations for 3D collimatorless tomography to further validate the effectiveness of the Masked-MLEM algorithm in handling different levels of system uncertainties. Main results. The Masked-MLEM and standard MLEM reconstructions are similar in cases with negligible system uncertainties, whereas the Masked-MLEM algorithm outperforms the standard MLEM algorithm when the system matrix is an approximation. Importantly, the Masked-MLEM algorithm ensures reliable image reconstruction across varying levels of system uncertainties. Significance. With a good choice of system uncertainty and without requiring accurate knowledge of the actual system matrix, the Masked-MLEM algorithm yields more robust image reconstruction than the standard MLEM algorithm, effectively reducing the likelihood of erroneously reconstructing higher activities in regions without radioactive sources.

Adaptive and intelligent control of a dual-arm space robot for target manipulation during the post-capture phase

Dual-arm space robots provide a promising solution for efficiently and flexibly completing complex on-orbit servicing tasks. However, their effectiveness is often hindered by strong dynamic coupling between the robotic arms and the satellite base in the microgravity environment. In this paper, both robotic arms are used as task arms, and a system model that considers the closed-loop constraint formed after a dual-arm space robot captures a target is established. On this basis, two types of control strategies, namely self-tuning control strategy (STC) and radial basis function neural network control strategy (RBF) are proposed for trajectory tracking of the target transferred or detumbled by the robot arms in the presence of system uncertainty or external disturbances. The control methods are verified and compared against the traditional computed torque control strategy (CTC) in terms of control accuracy and system robustness through simulation. The results demonstrate the excellent robustness of both RBF and STC strategies. RBF outperforms the other strategies in terms of control accuracy, while STC proves to be the most energy-efficient.

Fractional order sliding mode control for an omni-directional mobile robot based on self-organizing interval type-2 fuzzy neural network

Four-wheeled omnidirectional mobile robots (FM-OMR) are widely used in various fields due to their excellent steering ability and adaptability. As application scenarios expand, higher requirements are placed on their trajectory tracking capabilities. FM-OMR is highly complex and difficult to model accurately, and the system contains uncertainties. Therefore, achieving accurate trajectory tracking in the presence of system uncertainty is a pressing problem. Traditional control methods struggle to accurately estimate uncertainty, and existing controllers often rely on model parameters, resulting in poor transferability. To address this issue, this paper proposes a new control method based on an online self-organizing interval type II fuzzy neural network (SOIT2FNNFSMC). This method employs an online self-organizing algorithm to dynamically compensate for uncertainty, providing greater flexibility and accuracy compared to traditional approximation networks in terms of network construction and approximation performance. A new combined reaching law is proposed based on the characteristics of traditional reaching laws, resulting in improved chattering reduction. Additionally, fractional calculus is introduced to enhance the dynamic characteristics of the controller. Simulation and experimental results demonstrate the effectiveness of this method in achieving precise trajectory tracking while handling uncertainty and not relying on model parameter features. The self-organizing algorithm proposed in this method also provides a reference for the application of SOIT2FNN in FM-OMR.

Observer Synthesis for Uncertain Linear Systems under Multiple Sampled Outputs: Application to a Building-Like Structure

In this work a full-state observer is presented for MIMO linear systems in presence of uncertainties and multiple sampled outputs. The observer is capable to reconstruct the state vector in a continuous form even if it recieves the output in a sampled form. Then, it is possible to establish that the observation error will converge to a bounded value depending on the magnitude of the maximum sampling interval and uncertainties. In the case when there is no uncertainties, the observation error converges to zero. The proposed observer is tested to estimate the state vector in a building structure in which the seismic signal is treated as uncertainty.

Novel Single Bounded Input Control Synchronization Criterion for a Category of Hyperchaotic and Chaotic Systems in Presence of Uncertainties

Abstract Dynamical systems that have a chaotic underlying structure have a sensitive dependency on the initial conditions and the values of their parameters. In this piece of work, a straightforward method for solving the synchronization issue in master–slave arrangement for a category of chaotic or hyperchaotic systems, in which perturbations are present in the parameters of the response system, is discussed. The desired control signal is bounded by the initial state when the controller is activated. There is just one control input that is used, and it is derived from Lyapunov's concept of stability. In general, it is tricky to synchronize hyperchaotic or chaotic systems with single controller, and the work turns out to be significantly more complex when the parameters of the slave system are perturbed. The feedback controller using single input that has been constructed makes certain that the state variables of the response system are in synchronization with the state variables that correspond to them in the drive system. In order to attain the desired level of synchronization, the required conditions that must be satisfied to do so have been identified utilizing Lyapunov's stability analysis in a simple manner. In addition, numerical illustrations have been provided in order to support and confirm the theoretical findings of the paper.

Safety-enhanced observer-based adaptive fuzzy synchronization control framework for teleoperation systems

Due to the lake of enough information about the remote environment, safety and performance play critical role in the teleoperation systems. However, some applications such as tele-robotic surgery require high performances and the outcomes of delayed leader-follower communication and external forces measurement can be catastrophic in such area. In hence, to guarantee the predefined performances for the synchronization error and enhance the safeness of operation in the presence of system uncertainties, external disturbances and time-varying delay, the error constrained control is employed to the proposed controller design mechanism by the Barrier Lyapunov function (BLF). The key idea of this paper is to develop a new adaptive fuzzy torque observer and relax the system from the practical limitations of force sensors. Moreover, the main contribution of this paper is to deal with time-delay’s derivative of communication channels and lessen the computational complexity in the backstepping-based adaptive controller by means of the dynamic surface control and the BLF strategy is embedded to enforce bounds on the leader-follower position synchronization errors. In addition, the stability analysis of the observer and controller together is studied via the BLF in a unified farmwork. Finally, the evaluation of performance of the proposed observer-based adaptive fuzzy synchronization controller, is investigated by the help of various scenarios and comparison.

Robust Approach for Global Stabilization of a Class of Underactuated Mechanical Systems in Presence of Uncertainties

Underactuated mechanical systems offer complex dynamic behavior and poses control challenges, especially in the presence of uncertainties in the system. To cope with such systems, control mechanisms are required, which needs to be robust. In this research, an algorithm based on sliding mode control (SMC) is presented. The algorithm design offer a methodical way to handle underactuation, while the robustness properties of SMC suppresses the effect of norm bounded uncertainties and external disturbances. To proceed with the design, an underactuated system is converted into cascaded subsystems, a linear one and reduced-order nonlinear subsystem. The proposed SMC design is backed by rigorous mathematical presentation and based on Lyapunov theory, so that the global stabilization of overall system is ensured. Numerical simulations are performed, on the laboratory test bench underactuated systems (Inertial Wheel, Furuta Pendulum, TORA, and an Overhead Crane), to validate the efficacy of the proposed design. In addition, a novel sliding surface is presented for Inertial Wheel and Furuta Pendulum to achieve swingup control and global stabilization subjected to uncertainties.

Active observer-based T-S fuzzy control scheme for maximum power point tracking in PV systems

This paper addresses the problem of maximum power point tracking of photovoltaic (PV) systems in the presence of model uncertainty as well as varying load and atmospheric conditions using techniques based on a Takagi–Sugeno fuzzy model. The proposed approach relies on the linear matrix inequality tool, Lambert W function, and the Newton–Raphson method. First, adopting a quadratic Lyapunov function, an active observer-based fuzzy non-parallel distributed compensation (non-PDC) controller is designed for asymptotic tracking of the desired reference input. Next, to subdue the impact of uncertainty on the PV system, the closed-loop nominal system is regarded as a reference model, and then the main control law is developed using an online lumped uncertainty estimator and keeping the nominal control law within the staple controller. This control law does not require that the bounds on uncertainties be known. The reference voltage is determined by a novel maximum power point-seeking algorithm that is organized based on the one-diode model of PV panel, Lambert W function, and Newton–Raphson method. Finally, simulations are performed for three scenarios to point out the merits and effectiveness of the proposed methodology in the presence of system uncertainties, environmental changes, and load variations.

Trajectory tracking control for unmanned helicopter based on RBFNN

This paper proposes a nonlinear adaptive radial basis function neural network (RBFNN) control method for Unmanned Helicopter. The control objective is to reduce the trajectory tracking error of the unmanned helicopter in the presence of system uncertainty and external disturbances. Based on the backstepping control technique, the controller of the unmanned helicopter are designed in order of position kinematics, position dynamics, attitude kinematics and attitude dynamics, and the block processing is used in the last three steps above.Then, RBFNN is added to compensate the error caused by external interference. Meanwhile, the derivatives of virtual controls are obtained by second-order command filter, and the stability of the system is analyzed by Lyapunov stability theorems. Finally, the simulation results verify the stability and robustness of the control method.

Robust Frequency Control of Microgrids: A Mixed H 2 / H ∞ Virtual Inertia Emulation

This article proposes a robust inertial controller for converter-based distributed generators employed in low-inertia power systems like microgrids. The increasing penetration level of renewable energy sources based on power electronics converters in modern power systems reduces the inertial features of the system. It also increases concerns associated with the system uncertainty and sensitivity against disturbances. To cope with these challenges, by employing the proposed linear matrix inequality (LMI)-based mixed H 2 / H ∞ robust method, an optimal robust controller aided for inertial support as well as fast frequency restoration is provided. Using the proposed solution not only presents a better inertial response but also proposes a faster frequency restoration, by which the system’s frequency can be restored immediately following any disturbance, even in the presence of system uncertainties. Through in-detailed frequency response analysis and time-domain simulations for different scenarios, it is illustrated that the proposed mechanism can be successfully employed to address the inertial requirements in power electronic-based power systems. In addition, the proposed LMI-based mixed H 2 / H ∞ control solution is compared with a number of other solutions to illustrate its better performance against disturbances. Simulation results validate the merits and effectiveness of the proposed controller.

Disturbance-Observer-Based Adaptive Fuzzy Tracking Control for Unmanned Autonomous Helicopter With Flight Boundary Constraints

In this article, a disturbance-observer-based adaptive fuzzy tracking control scheme is proposed for a medium-scale unmanned helicopter of six degrees of freedom in the presence of system uncertainties, flight boundary constraints, and external disturbances. A flight boundary protection algorithm is proposed to ensure its flight trajectory within the given safety range. A fuzzy logic system is utilized to estimate the system uncertainties and a nonlinear disturbance observer is adopted to handle the unknown compound terms of the external disturbances and the estimation errors resulting from the fuzzy logic system. An inverse optimal control approach is then used to avoid solving the Hamilton–Jacobi–Bellman equation in minimizing a cost function in the attitude loop. It is shown via the Lyapunov method that the desired safe tracking performance of the position loop and attitude loop of the controlled unmanned helicopter can be achieved. Simulations are provided to illustrate the effectiveness of the proposed control scheme.

Fuzzy logic control of five-DOF active magnetic bearing system based on sliding mode concept

In rotor dynamics, the deviation of the shaft is a common phenomenon. The main reasons for the deviation are non-linear attractive forces, harmonic disturbances, system parameter variations, etc. Active magnetic bearings (AMBs) are used to support the rotor inside the air gap in rotating machines, thus avoiding wear and tear and possible breakdowns. This paper proposes a fuzzy sliding mode-inspired control (FSMIC) technique for the five-degrees-of-freedom (DOF) AMB system in the presence of system uncertainties and measurement noises. The fuzzy logic is used to estimate the auxiliary control input of the sliding mode control (SMC) to attenuate the chattering. The variable gains are designed with the help of superintended fuzzy logic to bring more flexibility to the controller performance. The stability analysis is presented with the help of the Lyapunov function candidate. The simulation studies for the AMB system under distinct types of control techniques, i.e., PID, SMC, and FSMIC, illustrate the effectiveness of the proposed control strategy.

A global fast terminal sliding mode control for trajectory tracking of unmanned aerial manipulation

Unmanned Aerial Manipulation (UAM) is a novel type of Unmanned Aerial Vehicle (UAV) equipped with manipulators instead of manual operation in hazardous and unreachable environments. The combination of UAV and manipulator unavoidably causes a significant predicament due to the increase of nonlinearity and coupling of the UAM system. Consequently, the system’s robustness becomes more vulnerable in the presence of system uncertainty and external disturbance. In addition, as a real-time embedded system, rapid and precise tracking of the desired trajectory is an essential aspect of UAM performance. This study aims to establish the dynamic model of UAM and propose a global fast terminal sliding mode controller for trajectory tracking. The controller is derived from Lyapunov theory to ensure the stability of the closed-loop system. We propose a set of illustrative metrics to evaluate the performance of the designed controller and compare it with the other two controllers by simulation. The results show that the proposed controller can effectively reduce the convergence time of tracking error and has good robustness and mechanical properties. And experimental results also verified its effectiveness.

H∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for a class of nonlinear systems with parametric uncertainties and external disturbances. The primary goals of the proposed controller are to guarantee system stability and performance in the presence of system uncertainties and time-dependent disturbances. To meet the specified objectives, the LMI form is calculated as a hierarchical control structure. Using the Lyapunov stability function, the asymptotic stability of the nominal system obtained from the nonlinear state feedback is proven, and the LMI condition is attained. After applying the nonlinear state feedback controller, asymptotic stability conditions for the nominal system are constructed using the Lyapunov function, and the nonlinear state-feedback control mechanism is determined accordingly. Considering the external disturbance as input, the terms of the state matrices are substituted in the obtained LMI, and the LMI condition for a nominal system is achieved in the presence of disturbances. The asymptotic stability condition of the uncertain system in the presence of external disturbances is determined by adding uncertainties to the system. The proposed approach yields a simple control mechanism representing an independent of system order. The performance of the proposed approach was assessed using a simulation study of a ball and beam system.

Resilient Model Predictive Adaptive Control of Networked Z-Source Inverters Using GMDH

Power grids are increasingly evolving into more efficient smart grids thanks to advancements in information technology. However, these intelligent communication-dependant power systems are becoming more susceptible to cyberattacks than their traditional peers. Power inverters are one of the main network connected devices supporting grid stability, which can potentially be targets for cyber-threats. This article presents an attack-resilient model predictive adaptive controller for a class of inverters, called Z-source inverters, to protect them against deception attacks. The proposed control structure includes a model predictive controller equipped with an unknown input Kalman filter and an estimator for system perturbations. The group method of data handling technique is used to estimate system uncertainties and make the system robust against perturbations. The unknown input Kalman filter is also adopted to estimate the states and unknown inputs in the presence of noisy measurements and cyberattacks on the control signal. We mathematically prove that in the presence of noise and perturbations, the proposed controller guarantees the stability of the system under a deception attack, which causes a delay, less than a sampling time, in control signals. Simulation results reveal the effectiveness of the presented controller in protecting the system against pulse, scaling and random attacks in the presence of system uncertainties, source and load fluctuations and output noises.