Controller Design For Systems Research Articles

Kernel-Based Models for System Analysis

This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized by suitable input-output properties required for system analysis and control design. This biased identification problem is shown to admit the tractable solution of a regularized least squares problem when formulated in a suitable reproducing kernel Hilbert space. The kernel-based framework is a departure from the prevailing state-space framework. It is motivated by fundamental limitations of nonlinear state-space models at combining the fitting requirements of data-based modeling with the input-output requirements of system analysis and physical modeling.

Robust control design for suspension system in LIGO

In this article, we present a relatively new state-space methodology, called synthesis, to design a robust controller for a subsystem of the Laser Interferometer Gravitational Wave Observatory. In particular, we examine the quadruple pendulum subsystem, which is simplified for the purpose of the study to a two wire simple pendulum system. Structured and unstructured uncertainties are considered in the modelling, though the structured ones are incorporated in the unstructured framework based on a design philosophy presented in the literature. Incorporating weighting functions that emphasize the spectral band of the uncertainties as well as the band in which disturbances are to be attenuated, we design a robust control law using the coprime factorization technique of the paradigm.

Anti-windup Controller Design for State-Delayed Discrete-Time Systems with Missing Measurements

Anti-windup Controller Design for State-Delayed Discrete-Time Systems with Missing Measurements

Sliding mode control design using generalized relative degree approach: Aerospace application

Relative degree (RD) approach is a powerful tool for obtaining system's input-output dynamics used for output tracking controller designs of minimum phase systems. Designs using the RD alone can fail due both to insufficient control authority in minimum phase systems, and instability of internal/zero dynamics attributed to nonminimum phase systems. A novel definition and a concept of Practical Generalized RD (PGRD) are proposed in this paper and are used in concert with Sliding Mode Control (SMC) to compensate for system perturbations in minimum phase systems. The use of known Generalized Relative Degree (GRD) in nonminimum phase systems allows for the elimination of internal dynamics. However, instability that emerges in the corresponding control dynamic extension is defeating any output tracking controller design. A novel methodology of using GRD for designing continuous SMC in nonminimum phase systems is presented. An algorithm for generating a bounded solution of the unstable dynamic extension is proposed and used in concert with SMC, allowing robust control design for nonminimum phase systems. The efficacy of the proposed GRD-based approaches is demonstrated on a minimum and nonminimum phase rocket attitude control problem both analytically and via simulation.

On a neural network approach for solving potential control problem of the semiclassical Schrödinger equation

Robust control design for quantum systems is a challenging and key task for practical technology. In this work, we apply neural networks to learn the control problem for the semiclassical Schrödinger equation, where the control variable is the potential given by an external field that may contain uncertainties. Inspired by a relevant work Li et al., 2021 [1], we incorporate the sampling-based learning process into the training of networks, while combining with the fast time-splitting spectral method for the Schrödinger equation in the semi-classical regime. The numerical results have shown the efficiency and accuracy of our proposed deep learning approach.

Hybrid whale optimization algorithm with simulated annealing for load frequency controller design of hybrid power system

Hybrid whale optimization algorithm with simulated annealing for load frequency controller design of hybrid power system

Systematic Analysis and Design of Control Systems Based on Lyapunov’s Direct Method

This paper deals with systematic approaches for the analysis of stability properties and controller design for nonlinear dynamical systems. Numerical methods based on sum-of-squares decomposition or algebraic methods based on quantifier elimination are used. Starting from Lyapunov’s direct method, these methods can be used to derive conditions for the automatic verification of Lyapunov functions as well as for the structural determination of control laws. This contribution describes methods for the automatic verification of (control) Lyapunov functions as well as for the constructive determination of control laws.

Event-triggered $$\mathcal {H}_{\infty }$$ controller design for Lurie systems with switching exponential time-varying gains

Event-triggered $$\mathcal {H}_{\infty }$$ controller design for Lurie systems with switching exponential time-varying gains

Nonlinear control design for walking assistance training robotic systems

AbstractIn this paper, the control problem for a novel walking assistance training robot is considered where the main objective is utilizing the robot to control the tilt angle and the position of a user. First, the novel walking assistance training robot together with a user is modeled as a nonlinear dynamical system in state space form with control input where the control input includes two elements standing for pulling forces on two straps which attach to the chest and back, respectively, of the user. Then, based on the nonlinear dynamical system and some results proposed in this paper, a feedback control system is developed, and a nonlinear state feedback control algorithm is designed where the control input includes two parts, namely, a dynamical part and a constant part. By doing this, it is ensured that the feedback control system is stable, and achieves the main objective under some limits for the control input. A simulation example is given to illustrate the effectiveness and performance of the proposed nonlinear state feedback control algorithm.

Two-stage multirate state feedback control designs for systems with slow and fast eigenvalue modes

Design of feedback control, for a system with slow and fast eigenvalue modes, using single sampling rate results in either information loss (for a larger sampling period) or increased computations (for a smaller sampling period). This paper contributes to designing multirate state feedback controllers for such systems. In this, it is shown that the feedback control for a linear time-invariant system, having slow and fast eigenvalue modes, can be successfully designed by multirate sampling of states in two stages. Multirate sampling refers to sampling slow- and fast-varying states at different rates, that is sampling slow states at a lower rate than the fast states. Here, two approaches for multirate sampling of states are presented, depending on the sampling sequence. In the first approach, fast subsystem states are sampled initially, and then, slow subsystem states are sampled, whereas in the second approach, slow subsystem states are sampled before sampling the fast subsystem states. As far as the two-stage design is concerned, the first stage of the design of feedback control is initiated just after sampling the first subsystem. Then, the left subsystem is sampled, and the second stage of the design of feedback control is accomplished. It is proved that the feedback controls derived with the multirate sampling of states stabilize the full-order system in both approaches. The design and implementation aspects of both approaches are compared. Finally, the applicability of the proposed control is demonstrated by simulating two examples. Simulations are also compared with other methods proposed in the literature.

Receding Horizon Actor–Critic Learning Control for Nonlinear Time-Delay Systems With Unknown Dynamics

With the development of modern mechatronics and networked systems, the controller design of time-delay systems has received notable attention. Time delays can greatly influence the stability and performance of the systems, especially for optimal control design. In this article, we propose a receding horizon actor–critic learning control approach for near-optimal control of nonlinear time-delay systems (RACL-TD) with unknown dynamics. In the proposed approach, a data-driven predictor for nonlinear time-delay systems is first learned based on the Koopman theory using precollected samples. Then, a receding horizon actor–critic architecture is designed to learn a near-optimal control policy. In RACL-TD, the terminal cost is determined by using the Lyapunov–Krasovskii approach so that the influences of the delayed states and control inputs can be well addressed. Furthermore, a relaxed terminal condition is present to reduce the computational cost. The convergence and optimality of RACL-TD in each prediction interval as well as the closed-loop property of the system are discussed and analyzed. Simulation results on a two-stage time-delayed chemical reactor illustrate that RACL-TD can achieve better control performance than nonlinear model predictive control (MPC) and infinite-horizon adaptive dynamic programming. Moreover, RACL-TD can have less computational cost than nonlinear MPC.

Adaptive fuzzy control design for nonlinear systems with actuation and state constraints: An approach with no feasibility condition

In this article, an adaptive fuzzy tracking control scheme is developed for a class of pure-feedback uncertain nonlinear systems in the presence of time-varying full-state constraints (TFSCs), actuators’ nonlinearities and external disturbances. Fuzzy logic systems (FLSs) are employed as universal approximators to online estimate unknown nonlinear functions A barrier Lyapunov function (BLF) is used to deal with the state constraint problem. In contrast to numerous adjacent studies, this research diligently tackles the open problem relating to the virtual control laws (VCLs) feasibility in the BLF-based backstepping control design. The resolution to this problem involves formulating VCLs with predefined bounds. The utilization of disturbance observers within a backstepping framework allows for effective compensation of estimation errors arising from the implementation of a predefined bounded VCL. This approach also helps prevent the occurrence of the ”complexity explosion”, making it a practical solution. The control strategy being proposed guarantees that the output tracking error will effectively approach a small region near the origin. Additionally, all signals of the closed-loop system will remain uniformly ultimately bounded (UUB), and there will be adherence to all state-constraints, ensuring no violations occur. Ultimately, an illustrative simulation example is provided to demonstrate the efficacy of the theoretical findings.

Fixed-Time Control for a Class of Nonlinear PH-DAE Systems

The globally fixed-time stabilization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> control for the port-Hamiltonian differential algebraic equation (PH-DAE) is addressed by applying the structural properties of the port-Hamiltonian (PH) systems, and the interconnection and damping assignment passivity-based control (IDA-PBC) technique. For fixed-time control design of the differential algebraic equation systems, the main obstacle lies that the algebraic variables are hidden in the system and their dynamics are ambiguous. We propose an available and effective approach to overcome this obstacle. The system variables are decomposed into differential component and the algebraic component, and the explicit representation of the dynamics of algebraic component is obtained. Fist, we investigate the locally fixed-time stabilization control as well as globally attractive for PH-DAE. Second, we focus on solving the globally fixed-time stabilization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> control problems by jointly taking advantage of the locally fixed-time stabilization control for the origin and the globally fixed-time attractivity control for a predeterminate region. Finally, in order to address fixed-time stabilization control and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> control for PH-DAE, new controllers are designed. Moreover, the convergence time of systems can be easily estimated after external disturbance vanishes. The efficiency of the theoretical results acquired in present article is verified via two examples with numerical simulation.

Adaptive Tracking Control of State-Constrained Strict-Feedback Nonlinear Systems Using Direct Method

In this article, we focus on adaptive tracking control design for strict-feedback nonlinear systems with full state constraints. Unlike the barrier Lyapunov function method, all theoretical results are derived by direct method instead of introducing nonlinear state-dependent transformations, which reduces the calculated amount and the high sensitivity of control signals, and provides a new perspective to solve state-constrained problems. Then, by using the backstepping technique, the proposed adaptive controller maintains that the output closely tracks the desired trajectory, all signals in the closed-loop systems are bounded and the time-varying state constraints are not violated. Finally, two numerical simulations are provided to exhibit the effectiveness and superiority of the proposed adaptive tracking controller.

Decentralized control design and implementation for magnetic levitation systems with extended state observer

Decentralized control design and implementation for magnetic levitation systems with extended state observer

Adaptive Fuzzy Decentralized Control for Stochastic Nonlinear Interconnected System With Nontriangular Structural Dynamic Uncertainties

This paper constructs an adaptive fuzzy decentralized fault tolerant control strategy for stochastic nonlinear interconnected system with non-triangular structural uncertainties, unmodeled dynamics and actuator faults. During the controller design process, the difficultly of system controller design caused by non-triangular structural uncertainties that mixed unmodeled dynamics are handled by utilizing the variable separation technique and fuzzy logic system (FLS). Then, based on the adaptive compensation technique, a fault tolerant controller is designed to solve the influence of actuator faults for system stability. Finally, the stability of stochastic nonlinear interconnected system can be ensured by stochastic Lyapunov stability theory. In addition, numerical and practical simulations also illustrate the effectiveness of the proposed control strategy.

System-level modeling, analysis and coordinated control design for the pressurized water reactor nuclear power system

A flexible operation of the nuclear power system (NPS) over a large operating range is emphasized when it is used as marine power. The current study exposes two bottlenecks in this field: (1) lack of the system-level high-quality dynamic model whose structure is simple enough for control design limits the implementation of the model-based controller; (2) nonlinearity problem due to the large load variation poses challenges for NPS to maintain its performance over a wide operating range. For these reasons, a first-hand simplified nonlinear model is developed and validated for the pressurized water reactor nuclear power system (PWRNPS) through mixed modeling methods of mechanism analysis and data identification. An optimal 50% full-power compromise steady-state operation scheme is first proposed for PWRNPS to balance its primary coolant temperature and secondary steam pressure. Using the simplified nonlinear model as the predictive model, a novel nonlinear model predictive controller (NMPC) is designed to realize the wide-range flexible operation of PWRNPS. Especially, an integrating tracking error is innovatively added to the cost function of NMPC to achieve offset-free control. Two groups of simulations on a complex PWRNPS process developed on the MATLAB/SIMULINK platform demonstrate the effectiveness of the proposed methods.

The Robust Model Predictive Control Design for Linear Interconnected Systems

In this paper, we discuss the design of robust model predictive control for linear interconnected systems by several constraints. Linear interconnected system is a complex systems which consist of several subsystems and the dynamic of subsystem is influenced by the states or outputs of the other subsystems. The systems are controlled by formulating and applying the model predictive control on each subsystems. We formulate the optimization problem that minimize the cost function for each subsystems. The optimization problem is solved by gradient method to get the minimum cost function. Numerical simulation was conducted to show the effectiveness and performance of robust model predictive control. Based on the results of the numerical simulation and test the robustness, it can be shown that the robust model predictive control is effective to control the linear interconnected systems.

Data-driven [formula omitted] vibration control design and verification for an active suspension system with unknown pseudo-drift dynamics

This paper presents a data-based vibration control algorithm that can realize the vibration suppression of a laboratory suspension facility without knowing its drift dynamics. The vibration controller consists of two sub-controllers, a prestable controller that assists in generating higher quality operational data and a data-driven H∞ vibration controller that realizes vibration suppression. The proposed control algorithm only needs to know partial knowledge of the system dynamics without any information about the so-called pseudo-drift dynamics. We analyse and evaluate the control approach through simulation and experimentation based on a laboratory suspension platform. The comparison results shows that the data-based H∞ vibration control is quite promising. In addition, the influences of two critical parameters on the data-based controller are quantitatively studied, which can be used to optimize the control structure better and improve control performance.

Backstepping Based Grey Wolf and DPC for Power Quality Improvement and Active Power Injection in PV Grid-connected System Based on Interleaved Boost Converter

This research offers the backstepping based grey wolf control design for a multifunctional PV grid-connected system (MPGC) based on four phases interleaved boost converter. This work proposes a solution to the issues of harmonic mitigation, reactive power compensation, and PV-generated power injection into the grid-based MPGC. The interleaved boost converter (IBC), controlled using maximum power point tracking (MPPT), is utilized to harvest the photovoltaic (PV) system's peak power and overcome the conventional topology's drawbacks. Direct power control (DPC) based on space-vector pulse width modulation (SVPWM) is used to control the instantaneous power of the MPGC, and the backstepping control (BSC) is applied to the whole system to maintain the robustness and stability of the suggested method. The Grey Wolf Optimizer (GWO) optimized the system's dynamic response by adjusting the BSC parameters. The results were obtained using MATLAB/Simulink software. The suggested work shows excellent performance based on the obtained results, achieving the sinusoidal waveform of the currents and a unity power factor. Total harmonic distortion (THD) has been decreased below 5% in accordance with IEEE 519-2014 standard.