Linear Control Research Articles

LMI feasibility analysis of 2DOF NATA model

AbstractPresent paper shows the different types of tensor product model based linear matrix inequality controller design and feasibility analysis of two degrees of freedom aeroelastic wing section model. The tensor product models are based on reducing or removing the nonlinear behavior of the system and weighting functions. The linear matrix inequality based method results globally asymptotically stable system. The goal of the paper is to examine that selecting and varying the transformation space influences the feasibility of the linear matrix inequality based controller. The paper gives a comparison between the different tensor product models in terms of controller performance. The linear matrix inequality gives feasible solution for the controller design if the transformation space is selected adequately.

Tunable linear feedback control of urban drainage systems using models defined purely from data.

Real-time and model-predictive control promises to make urban drainage systems (UDS) adaptive, coordinated, and dynamically optimal. Though early implementations are promising, existing control algorithms have drawbacks in computational expense, trust, system-level coordination, and labor cost. Linear feedback control has distinct advantages in computational expense, interpretation, and coordination. However, current methods for building linear feedback controllers require calibrated software models. Here we present an automated method for generating tunable linear feedback controllers that require only system response data. The controller design consists of three main steps: (1) estimating the network connectivity using tools for causal inference, (2) identifying a linear, time-invariant (LTI) dynamical system which approximates the network, and (3) designing and tuning a feedback controller based on the LTI urban drainage system approximation. The flooding safety, erosion prevention, and water treatment performance of the method are evaluated across 190 design storms on a separated sewer model. Strong results suggest that the system knowledge required for generating effective, safe, and tunable controllers for UDS is surprisingly basic. This method allows near-turnkey synthesis of controllers solely from sensor data or reduction of process-based models.

Infinite Horizon Mean-Field Linear Quadratic Optimal Control Problems with Jumps and the Related Hamiltonian Systems

Infinite Horizon Mean-Field Linear Quadratic Optimal Control Problems with Jumps and the Related Hamiltonian Systems

On the simplification of the internal nonlinear robot models for the MPC-based visual servoing

AbstractVisual servoing enables tracking and grasping of static and moving objects and locating regions of interest. Its implementation requires the coordination of low-level control tasks with high-level supervision and planning. The use of the PID-based manipulation control addresses only the dynamical response and requires the use of optimization-based techniques at the supervisory level. On the contrary, model predictive control (MPC) simplifies the design as it combines both tasks within a single algorithm. However, successful MPC implementation depends on the quality of the internal model utilized by the algorithm. Robots are intrinsically and significantly nonlinear control objects, so their models are inherently complex. This leads to computational problems. Standard solutions are to shorten the MPC horizons or to parallelize calculations. The approach suggested here returns to the problem roots, i.e. to the model. This study proposes simplified models that allow the use of the MPC. General Hammerstein–Wiener-like model is applied to an arm, which is further simplified into the linear dynamics used as the predictive supervisory control over the torque control. The head uses linear dynamics used by the supervisory MPC working with the base servomotors. It is shown that they are computationally efficient and sufficiently accurate. It is shown that the linear MPC controllers, which use the suggested simplified dynamic robot models, can successfully support visual servoing with accurate control. They are compared with standard PID-based structures and show their superiority. The proposed approach is successfully validated using Matlab and Gazebo robot simulator and is ultimately confirmed by experiments on a real robot.

Linear quadratic optimal control problems of infinite‐dimensional mean‐field type with jumps

AbstractIn this paper, we formulate and investigate a framework for the theory of the linear quadratic optimal control problem (LQ problem) for infinite‐dimensional mean‐field stochastic evolution systems with jumps. We ensure the well‐posedness of the investigated problems by establishing the existence, uniqueness, and a priori estimates for mild solutions to general infinite‐dimensional mean‐field forward stochastic evolution equations (MF‐SEE) and mean‐field backward stochastic evolution equations (MF‐BSEE) with jumps. Leveraging the Yosida approximation theory, we establish a dual theory between MF‐SEE and MF‐BSEE with jumps, overcoming the challenge posed by the inapplicability of Itô's formula in the context of mild solutions. Our main results regarding the existence and uniqueness of the optimal control, along with corresponding dual characterizations and state feedback representations, are obtained through convex analysis techniques, our established dual theory, and decoupling methods.

ADAPTIVE CONTROL OF A SUBMARINE FOR VARIOUS DIVING DEPTHS USING AN EXPONENTIAL

Due to the progress of deep submergence capabilities, a submarine is extensively employed on many sides of marine science. For that reason, it has become necessary to design an effective submarine position controller while achieving a fast and stable mission. An adaptive analytical scheme for the underwater submarine was developed. The main purpose of the adaptive analytical scheme is to provide a powerful analytical controller that can successfully steer the submarine from the current state under the water to the surface of water in a short time. To achieve that, a seventh-term exponential function was proposed to reshape the reference diving depth while maintaining the control variable limitation and satisfying initial and final boundary conditions. The direct search method with two cascade loops was employed to achieve a minimum cost function by determining an appropriate constant of the function and minimum final time. However, using the direct search method can be time-consuming since a number of algebraic operations are executed inside these two loops. Therefore, the curve fitting method was used to fit the set of direct search method data using power functions. Then, at a certain diving depth, the function coefficients were computed based on the final settling time and function constant using the Gaussian elimination method. A nominal numerical simulation of the submarine’s model was implemented using both adaptive analytical and linear controllers.

Improved Linear Active Disturbance Rejection Control With Dynamic Event-Triggered Mechanism for Hybrid Energy Storage System

Improved Linear Active Disturbance Rejection Control With Dynamic Event-Triggered Mechanism for Hybrid Energy Storage System

Neural network optimizer of proportional-integral-differential controller parameters

Wide application of proportional-integral-differential (PID)-regulator in industry requires constant improvement of methods of its parameters adjustment. The paper deals with the issues of optimization of PID-regulator parameters with the use of neural network technology methods. A methodology for choosing the architecture (structure) of neural network optimizer is proposed, which consists in determining the number of layers, the number of neurons in each layer, as well as the form and type of activation function. Algorithms of neural network training based on the application of the method of minimizing the mismatch between the regulated value and the target value are developed. The method of back propagation of gradients is proposed to select the optimal training rate of neurons of the neural network. The neural network optimizer, which is a superstructure of the linear PID controller, allows increasing the regulation accuracy from 0.23 to 0.09, thus reducing the power consumption from 65% to 53%. The results of the conducted experiments allow us to conclude that the created neural superstructure may well become a prototype of an automatic voltage regulator (AVR)-type industrial controller for tuning the parameters of the PID controller.

Neural network predictive controller based on the improved TPA-LSTM model for ultra-supercritical units

To mitigate the impact of large-scale renewable energy power on the national grid in China, it is imperative to enhance the flexible peaking capability of coal-fired thermal power units. The coordinated control system, central to the load control of coal-fired units, faces challenges such as multivariable coupling, sluggish response, and uncertain coal quality parameters. This paper introduces a neural network predictive controller based on the improved TPA-LSTM model, aimed at addressing these issues. Initially, a data-driven control model is established to break through the limitations of traditional linear predictive control and effectively handle disturbance uncertainties. Then, a multivariable coordinated control strategy based on the neural network controller is designed, achieving effective decoupling of multiple parameters and ensuring high adaptability across all load conditions. Additionally, by integrating an automatic model updating mechanism, the system can recalibrate in real-time when model mismatches occur due to equipment aging, maintenance, or changes in coal quality, thereby enhancing overall control performance. Simulation results demonstrate that this strategy has excellent control effectiveness, meeting the flexible peaking demands of 1000 MW ultra-supercritical units. The calibration feature of the data-driven model significantly improves control performance following model mismatches.

Trajectory compensation based adaptive control (TCAC) for high-precision piezoelectric actuators

Piezoelectric actuator (PEA) has been widely used in micro-systems, due to the advantages of nano-scale precision, rapid response speed, high stiffness, etc. Nevertheless, the intrinsic nonlinearities of PEA, particularly hysteresis, severely deteriorate its positioning and tracking control accuracy. In most existing control algorithms of PEA, the approximate inverse model of hysteresis is developed to compensate for motion error, which requires high modeling accuracy. To avoid the influence of complex modeling procedures and modeling errors on tracking precision, a trajectory compensation-based adaptive control method has been proposed in this paper. Firstly, a simple linear controller is used to establish the closed-loop feedback system and to guarantee the basic tracking performance of the PEA system. And then, the trajectory compensation is designed according to the frequency analysis of the closed-loop control system. Finally, nonlinear adaptive compensation is used to eliminate the residual errors of the above linear frequency domain model. Different from conventional controllers, the proposed method can achieve excellent tracking control performance without any hysteresis model of PEA. The stability and convergence of the proposed method have been theoretically proved. In addition to theoretical guarantees, the proposed method is validated experimentally and demonstrated to achieve the root-mean-square and maximum value of tracking errors to less than 8 nm and 25 nm, respectively, which has a clear accuracy advantage over other methods.

Exact Controllability for Mean-Field Type Linear Game-Based Control Systems

Exact Controllability for Mean-Field Type Linear Game-Based Control Systems

Steering control for handling and stability and wear resistance of multi-axle vehicles

The steering performance of a vehicle directly affects its handling and stability, and tire wear during steering. For multi-axle vehicles equipped with a mechanical hydraulic steering system (MHS), this paper describes a steering-by-wire hydraulic system (SHS) for a third axle that can reduce the steering wear of third-axle tires while improving the handling and stability. A hydraulic steering system based on a reliable self-locking alignment cylinder was designed in this study, and a nonlinear dynamics model of a multi-axle vehicle was developed. In terms of the control strategy, the upper controller was a decision selector with a lateral acceleration threshold of 0.3 g , at which point the system entered the nonlinear kinematic state as a criterion for decision-making. The suboptimal linear time-varying model predictive control (S-LTV-MPC) method or Ackermann steering theory was used to calculate the target steering angle of the third axle. The lower controller was a fuzzy proportional–integral–derivative controller for tracking the steering angle of the third axle. The simulation and test results showed that the S-LTV-MPC method can meet the requirements of real-time control and accuracy. The designed SHS exhibited good handling and stability, and anti-wear properties during steering.

An optimal regulation of grid-connected doubly-fed induction generator angular speed and the DC-link voltage

In this work, a linear quadratic regulator controller is utilized to optimize the gains of the machine-side converter and grid-side converter controllers. The DC-link voltage and the rotational speed of the doubly-fed induction generator are optimally regulated by these controls. Additionally, the small-signal stability of the proposed system has been evaluated using the linearized model of the system. The small-signal stability analysis of the designed system has been accomplished through the application of the eigenvalues and participation factors technique. The suggested controller has been tested in a variety of operating conditions under small disturbances. MATLAB/SIMULINK simulation simulations have been used to evaluate the efficacy of the suggested optimal control system. Additionally, the generator-angular speed and DC-link voltage dynamic performances demonstrate the efficacy of the proposed controller. Finally, the robustness of the proposed controller has also been tested and validated using OPAL-RT technology under large perturbations at stator terminal voltage.

Robust control strategies applicable to DC–DC converter with reliability assessment: A review

AbstractThis paper provides an overview of various control strategies for DC–DC converters along with a brief discussion on various performance indices for evaluating the reliability of designed controller. DC–DC converters are emerging as the fastest‐growing interfacing devices in the world because of their emergent applications in almost all domains of engineering. Notably, the non‐linear behavior of DC–DC converters offers a perplexing problem in designing a robust controller. A robust controller must ensure proper closed‐loop stability with desired performance and reliable control for output voltage regulation in the event of various possible perturbations. This creates the requirement for practically implementable non‐linear controllers that can effectively overlook the drawbacks of linear controllers. The prominence of this composition is based on the expansion in tuning techniques of proportional‐integral‐derivative controller gain parameters using linear strategies and heading towards non‐linear strategies by reviewing 196 research papers. The modification in non‐linear control strategies in terms of their fundamental features associated with key benefits and limitations are comprehensively reviewed. This study mostly revolves around non‐linear internal model control (IMC) strategies for parameter tuning of IMC‐based controllers for various order of plants with an improved degree of freedom.

Integration of field-oriented and steady-state linear Kalman filter control in PMSG-based grid-connected system for improving voltage control and power balance operation

Integration of field-oriented and steady-state linear Kalman filter control in PMSG-based grid-connected system for improving voltage control and power balance operation

Feedback linearization control to avoid saturation of the high frequency transformer of a dual active bridge DC–DC converter for a DC microgrid

This paper introduces an innovative control strategy for a dual active bridges DC–DC converter employed to regulate voltage levels between two feeders in a DC microgrid. The controller is specifically designed to regulate the output voltage at a predetermined reference value and to ensure a zero mean value for both primary and secondary currents of the high-frequency transformer, regardless of any imbalance in one of the active bridges. This is particularly important in the face of potential imbalances in one of the active bridges resulting from construction disparities in converters or variations in conduction resistances in power transistors. Given the nonlinear nature of the converter, the controller is designed using feedback linearization. The output is selected with a relative degree equal to the system order, resulting in a stable controller exhibiting good dynamic performance under scenarios such as reference changes, linear load fluctuations, and the integration of constant power loads. The performance of the proposed control strategy is validated through both simulation and experimental results.

Bond graph realizations of state space linear time-invariant multivariable descriptions

Given a state space description of a linear time-invariant multivariable system, a similarity transformation is applied to get a controllability canonical form. This transformation assures a Bond Graph (BG) realization and avoids the use of active bonds. Active or signal bonds do not preserve the continuity of power flows and consequently, energy conservation properties are lost. The state matrix of the system in transformed coordinates contains an antisymmetric matrix associated with the storage field and the rest is associated with the dissipative field. Thus, in general, the dissipative field is implemented with a multiport element, and in order to give physical meaning, the storage field is implemented with one-port elements. The resulting BG model does not have zero-order causal paths, that is, algebraic loops between the dissipative elements. The results are applied to the BG realization of a linear robust multivariable controller that is designed for a two mass system modelled in BG.

Analysis and Synchronization of the Chen System with Fractional Derivative

In this paper, we study the dynamic behaviors and chaos synchronization of the Chen system described by Caputo–Hadamard fractional derivative. First, the existence and uniqueness of a solution to the Chen system with Caputo–Hadamard derivative are proved by qualitative analysis. Further, the stability of equilibria of the considered system is analyzed with the aid of Routh–Hurwitz criteria. Meanwhile, the bifurcation condition of the Caputo–Hadamard Chen system is compared with the integer-order Chen system, where the differences between the two systems are demonstrated numerically. In the study of chaos synchronization of the drive–response Chen systems with Caputo–Hadamard derivative, two control schemes are developed: three nonlinear controllers and single linear controller. The feasibility of two control schemes is verified, and the synchronization performances of these two schemes are compared by numerical simulations. Based on this, the influence of the fractional-order on chaos synchronization performance is illustrated as well.

Decentralized control of forward and backward stochastic difference system with nested asymmetric information

This paper is concerned with the linear quadratic decentralized control of forward and backward stochastic difference system (FBSDS) with multiplicative noises and nested asymmetric information. The main contribution is to give the equivalent condition for the solvability of the problem and the explicit decentralized optimal controllers in terms of Riccati equations. The key technology is solving the forward and backward stochastic difference equations with partial information derived from stochastic maximum principle.

Enhancing vehicular platoon stability in the presence of communication Cyberattacks: A reliable longitudinal cooperative control strategy

This study proposes a reliable longitudinal distributed control strategy for connected and automated vehicles (CAVs) in the presence of communication cyberattacks. The proposed strategy is designed to utilize dependable measurements from onboard sensors to evaluate the reliability of vehicle-to-vehicle (V2V) information and enhance the platoon string stability in an integrated manner. Specifically, this paper proposes a real-time reliability evaluation mechanism for the ego vehicle based on sensing and communication information from multiple predecessors, employing an upper-tailed chi-squared test. The mechanism is then incorporated into a distributed multi-predecessor linear feedback controller to adaptively weigh the preceding vehicles’ information, ensuring robustness against cyberattacks and maintaining the string stability of the vehicular platoon. To better understand the whole framework, sufficient conditions of true string stability and pseudo string stability are theoretically derived, unveiling the disturbance amplification jointly impacted by measurement accuracy of onboard sensors, cyberattack severity in V2V communication, and control parameters. Numerical experiments are conducted to validate the controller across various types of communication cyberattacks. The results suggest that the proposed control strategy can significantly alleviate the impact of cyberattacks and simultaneously dampen traffic oscillations effectively.