Uncertain Plant Research Articles

Static output feedback control for positive 2D discrete systems in Roesser model

Abstract This paper investigates the output stabilization problem for multi-input multi-output positive 2D systems described by a linear discrete-time Roesser system. This kind of systems have the property that the horizontal and vertical states take non-negative values whenever the initial boundaries are non-negative. Conditions for the existence of desired static output feedback controllers guaranteeing the resultant closed-loop system to be positive and asymptotically stable are obtained. Also, the synthesis of static output feedback controllers, including the requirement of positivity of the controllers, is solved. These results are then extended to the case of uncertain plants. All of the proposed conditions are expressed in terms of Linear Programming, which can be easily verified by using standard numerical software. Finally, several numerical examples are included to illustrate the validity and the effectiveness of the developed results.

Direct Synthesis of Reduced-Order Controllers With Integrating Action for a Class of Norm-Bounded Uncertain Plants

Direct Synthesis of Reduced-Order Controllers With Integrating Action for a Class of Norm-Bounded Uncertain Plants

An artificial bee colony optimization algorithms for solving fuzzy capacitated logistic distribution center problem

This paper presents a methodological approach to solving the fuzzy capacitated logistic distribution center problem, with a focus on the optimal selection of distribution centers to meet the demands of multiple plants. The distribution centers are characterized by fixed costs and capacities, while plant demands are modeled using fuzzy triangular membership functions. The problem is mathematically formulated by converting fuzzy demands into crisp values, providing a structured framework for addressing uncertainty in logistic planning. To support future research and facilitate comparative analysis, 20 benchmark problems were generated, filling a gap in the existing literature. Three distinct artificial bee colony algorithm variants were hybridized with a heuristic: one using the best solution per iteration, another incorporating chaotic mapping and adaptive procedures, and the third employing convergence and diversity archives. An experimental design based on Taguchi's orthogonal arrays was employed for optimizing the algorithm parameters, ensuring systematic exploration of the solution space. The developed methods offer a comprehensive toolkit for addressing complex, uncertain demands in logistic distribution, with code provided for reproducibility.Key contributions include:•Development of a fuzzy model for the selection of distribution centers with fixed costs and capacities under uncertain plant demands.•Generation of 20 benchmark problems to advance research in the fuzzy capacitated logistic distribution center problem domain.•Integration of a heuristic approach with three distinct ABC algorithm variants, each contributing unique methodological insights.

Load frequency control of uncertain power systems via a novel worst-case GADRC scheme

This article proposes a worst-case generalized active disturbance rejection control (WGADRC) technique for power systems with parametric uncertainties. The proposed scheme is based on the worst-case plant selection strategy. Firstly, a worst-case model of the plant is identified out of the various possible models of an uncertain system, and afterward, the GADRC scheme is employed to design a controller. The best feature of the proposed scheme is that the designed controller ensures superior performance under nominal as well as uncertain plant conditions than other control schemes in the existing literature. To authenticate the supremacy of the proposed methodology, the load frequency control (LFC) issues associated with numerous power systems such as single-area thermal power system, IEEE 39 bus 10 machine test power system, and higher order hydro-thermal power system involving unmodeled parametric uncertainties, unexpected nonlinearities, and physical discrepancies are considered.

Dissipative imitation learning for discrete dynamic output feedback control with sparse data sets

AbstractImitation learning enables synthesis of controllers for systems with complex objectives and uncertain plant models. However, ensuring an imitation learned controller is stable requires copious amounts of data and/or a known plant model. In this paper, we explore an input–output (IO) stability approach to imitation learning, which achieves stability with sparse data sets while only requiring coarse knowledge of the energy characteristics of the plant. A constrained optimization problem is developed, in which the controller learns to mimic expert data while maintaining stabilizing energy characteristics induced by the plant. While the learning objective is nonconvex, iterative convex overbounding (ICO) and projected gradient descent (PGD) are explored as methods to learn the controller. In numerical examples, it is shown that with little knowledge of the plant model and a small data set, the dissipativity constrained learned controller achieves closed loop stability and successfully mimics the behavior of the expert controller, while other methods often fail to maintain stability and achieve good performance.

μ-Analysis and μ-Synthesis Control Methods in Smart Structure Disturbance Suppression with Reduced Order Control

In this study, we created an accurate model for a homogenous smart structure. After modeling multiplicative uncertainty, an ideal robust controller was designed using μ-synthesis and a reduced-order H-infinity Feedback Optimal Output (Hifoo) controller, leading to the creation of an improved uncertain plant. A powerful controller was built using a larger plant that included the nominal model and corresponding uncertainty. The designed controllers demonstrated robust and nominal performance when handling agitated plants. A comparison of the results was conducted. As an example of a general smart structure, the vibration of a collocated piezoelectric actuator and sensor was controlled using two different approaches with strong controller designs. This study presents a comprehensive simulation of the oscillation suppression problem for smart beams. They provide an analytical demonstration of how uncertainty is introduced into the model. The desired outcomes were achieved by utilizing Simulink and MATLAB (v. 8.0) programming tools.

Nonlinear Filtering and Reinforcement Learning Based Consensus Achievement of Uncertain Multi-Agent Systems

Abstract This paper introduces a novel approach for designing estimators to achieve consensus in uncertain multi-agent systems (MAS), even when various fault conditions are present and communication is assumed to be undirected and connected. The method includes an adaptive fault detection technique to detect faults and a unique adaptation in the unscented Kalman filter (UKF) to adjust noise covariance matrices and reconstruct uncertain states in the multi-agent system is proposed in the framework of Q-learning. Additionally, it involves training neural network internal parameters using previous measurements. A Chebyshev neural network (CNN) is employed to model the uncertain plant, and a hyperbolic tangent-based robust control term is used to mitigate neural network approximation errors. This novel approach is known as reinforced UKF (RUKF). The paper also discusses the asymptotic stability of the proposed method and presents numerical simulations to demonstrate its effectiveness with reduced computational load.

Multivariable robust tube-based nonlinear model predictive control of mammalian cell cultures

In this paper, the application of a robust nonlinear model predictive control (NMPC) framework to mammalian cell cultures is proposed, dealing with possible large kinetic parameter uncertainties. Industrial constraints formulated in view of good manufacturing practice and quality-by-design approach are also considered, namely the assurance that all state trajectories are contained within a corridor defined by lower and upper safety bounds. The latter are assimilated to the well-known tube-based paradigm which is used to formulate the corresponding robust NMPC problem. Both classical and tube-based NMPC performances are assessed in numerical simulations where specific key-species are regulated while dealing with an uncertain plant model. The capability of the tube-based method to reduce the impact of the parameter variations on the state trajectories and the violation of the constraints is highlighted, suggesting the transfer of the method on a real pharmaceutical process.

Robust State-Estimator-Based Control of Uncertain Semi-Markovian Jump Systems Subject to Actuator Failures and Time-Varying Delay

This note presents a reformed state-estimator-based adaptive control strategy for uncertain delayed semi-Markovian jump systems (DSMJS) via sliding mode technique. In comparison to most literature results requiring exact prior knowledge of system time-delay, a linear state estimator not linking any control inputs is developed to cope with the case with unknown state delays. By virtue of the acquired state estimation, the establishment of both a new switching surface of linear-type and the involved adaptive controller is provided, and the devised controller could not only admit the assigned SSL's reachability in limited time but also operate on the DSMJS as desired despite the hidden actuator failures and unknowable time-delays. Also, a new sufficient stochastic stability criterion serving as a crucial solution to the control parameters of the resultant plant is inferred. The method also holds in a similar fashion for uncertain plants with no time-delays and/or no switching case. Eventually, the raised method is verified by numerical examples.

Design of robust pre‐compensators for decoupling polytopic linear systems

SummaryThis work proposes a new approach for designing dynamic pre‐compensators to reduce interactions of multivariable uncertain square systems. The proposed method is based on the minimization of the norm of the difference between the compensated system and a diagonal reference model. The main appeal of the technique is to propose a systematic procedure to obtain the reference model dynamics, in contrast to methods that use the identity matrix as a reference, and to obtain diagonal dominance in a frequency range of interest employing the generalized Kalman‐Yakubovich‐Popov (KYP) Lemma. The design conditions are expressed as linear matrix inequalities (LMI) thanks to a new general parametrization on the decision variables in bilinear products to reduce the conservatism of the solutions compared to standard approaches from the literature. Numerical examples verify the robustness of the proposed method, showing significant decoupling of the uncertain plant.

Multicriteria Parametric Optimization of Nonlinear Robust Control with Two Degrees of Freedom by a Discrete-Continuous Plant

A multicriteria parametric optimization of nonlinear robust control with two degrees of freedom by a discrete-continuous plant has been developed to increase accuracy and reduce sensitivity to uncertain plant parameters. Such plants are mounted on a moving base, on which sensors for angles, angular velocities and angular accelerations are installed. To increase the accuracy of control, systems with two degrees of freedom, which include control with feedback and a closed-loop, and with direct connections and open-loop control of the setting and disturbing effects, are used. The multicriteria optimization of nonlinear robust control with two degrees of freedom by a discrete-continuous plant is reduced to the solution of the Hamilton-Jacobi-Isaacs equations. The robust control target vector is calculated as a solution of a zero-sum antagonistic vector game. The vector payoffs of this game are direct indexes performance vector presented in the system in different modes of its operation. The calculation of the vector payoffs of this game is related to the simulation of the synthesized nonlinear system for different operating modes of the system, input signals and values of the plant parameters. The solutions of this vector game are calculated on the basis of the system of Pareto-optimal solutions, taking into account the binary relations of preferences, on the basis of the stochastic metaheuristic of Archimedes optimization algorithm by several swarms. Thanks to the synthesis of nonlinear robust control with two degrees of freedom by a discrete-continuous object, it is shown that the use of synthesized controllers made it possible to increase the accuracy of control of an electromechanical system with distributed parameters of the mechanical part to reduce the time of transient processes by 1.5–2 times, reduce dispersion of errors by 1.3 times and reduce the sensitivity of the system to changes in the plant parameters in comparison with typical controllers used in existing systems. Further improvement of control accuracy is restrained by energy limitations of executive mechanisms and information limitations of measuring devices.

Reinforced unscented Kalman filter for consensus achievement of uncertain multi‐agent systems subject to actuator faults

AbstractIn this paper, actuator fault detection and reconstruction in consensus tracking of uncertain multi‐agent systems (MAS) is addressed. The communication is assumed to be connected undirected. An adaptive fault detection method is developed to detect actuator faults. A novel‐reinforced unscented Kalman filter (RUKF) is employed to reconstruct the faults by adjusting the noise covariance matrices of unscented Kalman filter (UKF) as well as to train neural network internal parameters by providing a set of previous measurements. A Chebyshev neural network (CNN) is incorporated to learn the uncertain plant. To prevent the neural network approximation errors a hyperbolic tangent function‐based robust control term is applied. The Lyapunov stability approach guarantees the stability of the proposed RUKF, which runs in conjunction with robust control method. Lastly, numerical simulations are presented to show the effectiveness of the proposed RUKF under actuator abrupt, intermittent, and transient fault conditions.

Fuzzy Logic dalam Pengontrolan Nilai Intensitas Cahaya LED pada Mini Plant Factory Budidaya Tanaman Pak Choy (Brassica Chinensis L.) Hidroponik

Ideally, the Pak Choy plant (Brassica Chinensis L) is cultivated with microenvironmental conditions of temperature 150C- 320C, humidity 60% - 80% and the same intensity of sunlight as other vegetable plants, namely in a vegetative vase of 300-400 micromols/m2/second and a period of generative 500-1000 micromols/m2/sec . The challenge of agriculture today is to meet the increasing need for food with limited land and uncertain plant microenvironmental conditions, one solution to this problem is planting using a plant factory system. Fuzzy logic has an effective method for controlling plant factory control systems, due to its flexibility and simple calculations. The purpose of this research is to find the PWM value in the plant factory control system that suits the optimal needs of pak choy vegetable cultivation. There are 4 stages in the research, namely the primary data input of the LED plant factory, Fuzzyfication, Fuzzy Interface System and Defuzzification. Data was taken using a lux meter and there were a total of 56 fuzzy rules and 4 fuzzy rules that did not have a value of 0. The lighting level/light intensity control system based on fuzzy logic was obtained with a PWM (Pulse Width Modulation) value of 872.1662 for a light intensity set point of 8000 Lux.

Robust QFT control design for a multivariable torsion/bending of rotational nanoscanner

This paper proposes a reasonable, practical, and novel method for designing a robust controller for two degrees of freedom nano-electromechanical scanners based on the combination of quantitative feedback theory (QFT) and the Taguchi method. Although the main primary of this paper devotes to rotational control, an investigation of two-degree freedom (rotational/bending) is studied by employing the Taguchi method. A moveable main plate suspended by two nano-beams over a fixed substrate electrode is used to represent the scanner. The nanoscanner is thoroughly analyzed using the most comprehensive modeling design, considering the elastic, electrical, Casimir force and moment, and squeezes film damping. The nanoscanner’s governing equations are initially derived by considering both rotation and deformation. In addition, because the size dependency of materials is significant in ultra-small structures, we developed the constitutive equations within the context of the modified couple stress theory to integrate the effect of scale dependency. Next, system uncertainties have been wholly addressed to achieve an accurate model. As a result, using robust control methods such as quantitative feedback theory to precisely control nano-scanners in the presence of uncertainties is inevitable. The quantitative feedback approach transforms the nonlinear plant into a family of linear uncertain plants in the first part. This is accomplished using a fixed-point theorem, after which appropriate disturbance rejection boundaries are discovered. In this problem, quantitative feedback controllers and checking the system’s stability at any frequency and time are intended to solve the tracking problem and the disturbance rejection issue. Due to the uncertainty associated with the system model’s complexity and accuracy, we employ a QFT controller to control the system. Moreover, because this system has only one input and two outputs, and changing the controller’s gain is complicated, the Taguchi method has been employed to enhance better performance. Nonlinear simulations of the tracking issue are carried out, and the results demonstrate the effectiveness of the developed controllers and prefilters. The findings show that using the suggested approach effectively overcomes the challenges to robust control of a nonlinear rotational nanoscanner, and also the system achieves the best angle and deflection adjustment accuracy.

Robust adaptive control design of nonlinear systems with input delay

AbstractIn this paper a robust adaptive controller for a class of uncertain nonlinear systems is developed with additive disturbance and unknown time‐varying input delay. The control law is composed of a Desired Compensation Adaptation Law (DCAL) based feedforward term for the adaptation of uncertain plant parameters and two robust feedback terms based on the integral of the past control to compensate the input delay. The sufficient conditions on controller gains and limit on delay bound are derived through stability analysis by choosing suitable Lyapunov‐Krasovskii functionals which gives a globally uniformly ultimately bounded (GUUB) tracking. The performance of the controller is evaluated by performing simulation on a two link robot manipulator system for different values of the input delay.

Satellite Dynamics Toolbox Library: a tool to model multi-body space systems for robust control synthesis and analysis

The level of maturity reached by robust control theory techniques nowadays contributes to a considerable minimization of the development time of an end-to-end control design of a spacecraft system. The advantage offered by this framework is twofold: all system uncertainties can be included from the very beginning of the design process; the validation and Verification (V&V) process is improved by fast detection of worst-case configurations that could escape to a classical sample-based Monte Carlo simulation campaign. Before proceeding to the control synthesis and analysis, a proper uncertain plant model has to be available in order to push these techniques to their limits of performance. In this spirit, the Satellite Dynamics Toolbox Library (SDTlib) offers many features to model a spacecraft system in a multi-body fashion on SIMULINK. Parametric models can be easily built in a Linear Fractional Transformation (LFT) form by including uncertainties and varying parameters with minimal number of repetitions. Uncertain Linear Time Invariant (LTI) and uncertain Linear Parameter-Varying (LPV) controllers can then be synthesized and analyzed in a straightforward way. The authors present in this article a tutorial, that can be downloaded at https://nextcloud.isae. fr/index.php/s/XDfRfHntejHTmmp, to show how to deal with an end-to-end robust design of a spacecraft mission and to provide to researchers a benchmark to test their own algorithms.

On Self-Learning Mechanism for the Output Regulation of Second-Order Affine Nonlinear Systems

This article studies global robust output regulation of second-order nonlinear systems with input disturbances that encompass the fully-actuated Euler–Lagrange systems. We assume the availability of relative output (w.r.t. a family of reference signals) and output derivative measurements. Based on a specific separation principle and self-learning mechanism, we develop an internal model-based controller that does not require <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of reference and disturbance signals and it only assumes that the kernels of these signals are a family of exosystems with unknown parameters (e.g., amplitudes, frequencies, or time periods). The proposed control framework has a self-learning mechanism that extricates itself from requiring absolute position measurement nor precise knowledge of the feedforward kernel signals. By requiring the high-level task/trajectory planner to use the same class of kernels in constraining the trajectories, the proposed low-level controller is able to learn the desired trajectories, to suppress the disturbance signals, and to adapt itself to the uncertain plant parameters. The framework enables a plug-and-play control mechanism in both levels of control.

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

Active vibration control of smart beam by μ -synthesis technology: modeling via finite element method based on FSDT

This article proposes an efficient strategy for the active vibration control of smart beam that combines the Finite Element Method (FEM) and advanced robust control to suppress vibration. The piezoelectric actuator and sensor are coupled as part of the smart structure by using the 2D First-order Shear Deformation (FSDT) plate theory. The accurate modeling of the mechanical displacement field and electric potential field is achieved by approximating the sub-layered coupling of the piezoelectric potential field in the z-axis direction. In practice, most active controls of smart structures do not take into account the influence of the piezoelectric itself and the piezoelectric effect on the natural frequency of the smart structures, and they do not emphasize the internal stability and stability margin of the control system. Regarding the above questions, a modeling method of a generalized uncertain plant for the piezoelectric smart beam is proposed in this article. Fully considering the uncertainty of the system model caused by parameter perturbation and modeling error, a dynamic controller is designed with the μ-Synthesis technology. The proposed approach is numerically verified to have good robust performance on piezoelectric smart beam, which can effectively enhance the performance of smart structure control in other scenarios.

Initial excitation based discrete-time multi-model adaptive online identification

This paper proposes a novel multi-model adaptive identification (MMAI) algorithm for discrete-time linear time invariant (LTI) uncertain systems with tunable performance. The uncertain plant parameter vector is assumed to belong to a known convex hull of a finite number of vertices; these vertices are considered as initial choice of vertices of an adaptive model parameter set. The estimated parameter, corresponding to the uncertain plant parameter, is computed at every instant as a convex combination of the model set vertices. To update the vertices of the adaptive model parameter set, a switched adaptive update law is proposed, along with a novel discrete-time initial excitation (IE) condition, which is imposed on the regressor signal. The proposed discrete-time IE condition is online verifiable and is milder than persistence of excitation (PE) condition, required for parameter convergence in classical adaptive estimation routines. The switched adaptive law guarantees exponential convergence of the vertices of the model set as well as the estimated parameter, to the true plant parameter, provided the regressor signal satisfies the IE condition. The properties of the designed MMAI strategy are validated through suitable simulation examples.