Design Of Robust Control Laws Research Articles

Large-Signal Stability of the Quadratic Boost Converter Using a Disturbance Observer-Based Sliding-Mode Control

The quadratic boost (QB) converter is a fourth-order system with a dc gain that is higher than the traditional second-order step-up configuration. The modern controllers that control these high-order dc–dc converters often only guarantee local stability around a steady-state equilibrium point, which is one of their primary drawbacks. In this article, a non-linear robust control law design to attain large-signal stability in this single switch QB converter is presented. In the presence of an unpredictable load, the control objective is to maintain the regulation of an output voltage. The Brunovsky canonical model of the converter was derived first, and the non-linear disturbance observer-based sliding-mode (SM) control law is designed based on it. An observer variable precisely estimates the output disturbances. The detailed process for deriving the control signal is described in this paper and the large-signal stability of the closed-loop converter system is ensured via the Lyapunov function. Finally, some simulation results are shown to validate the usefulness of the given controller.

Controller design on a new 2DOF PID structure for different processes having integrating nature for both the step and ramp type of signals

Chemical reactors, heat exchangers, level-loops, and distillation columns are commonly encountered in the chemical process industry, and these are having a significant role in the functioning of any chemical process. For the smooth and efficient functioning of any such process, a robust control law design is an important work to be considered. In this paper, a modified 2DOF robust PID control law has been developed to ensure satisfactory performance in both the step and ramp type references and disturbances. Controller parameters are derived with Maximum sensitivity, Gain, and Phase margin specifications. Case studies with different chemical processes like CSTR, distillation column, heat exchangers, and boiler drum level-loop are included for both the nominal and perturbed cases. Lastly, a performance comparison of ISE (Integral of square error), ITAE (Integral time absolute error), IAE (Integral absolute error), and Total variation (TV) of the control signal is also included.

Design of a backstepping technique-based robust state feedback optimal control law for autonomous underwater vehicle in depth plane using semi-definite programming

Design of a backstepping technique-based robust state feedback optimal control law for autonomous underwater vehicle in depth plane using semi-definite programming

Gain-Scheduled Control of LPV Systems with Structural Constraints

In large-scale dynamic systems, consisting of the interconnection of several subsystems, the control law must obey a certain distributed structure defined by the information exchange pattern on a communication network. In case the system exhibits parameters which vary over time, the Linear Parameter Varying (LPV) paradigm provides a control-oriented framework for the design of robust or gain-scheduled control laws. Since each subsystem has only access to a partial knowledge of the overall set of parameters, due to the constraint imposed by the communication network, the controller gain must satisfy some structural constraints which increase the complexity of the design problem. This paper proposes a novel approach based on Linear Matrix Inequalities (LMIs) to deal with the distributed control of large-scale systems described by a LPV dynamics. LMI conditions are established for the design of a gain-scheduled controller ensuring exponential stability of the overall system with a prescribed decay rate, while satisfying the structural constraints imposed by the communication network. A simulation case study is presented to show the effectiveness of the proposed approach.

Adaptive neural control for nonlinear switched systems with improved MDADT and its applications

In this paper, a new framework of the robust adaptive neural control for nonlinear switched stochastic systems is established in the presence of external disturbances and system uncertainties. In the existing works, the design of robust adaptive control laws for nonlinear switched systems mainly relies on the average dwell time method, while the design and analysis based on the model-dependent average dwell time (MDADT) method remains a challenge. An improved MDADT method is developed for the first time, which greatly relaxes the requirements of Lyapunov functions of any two subsystems. Benefiting from the improved MDADT, a switched disturbance observer for discontinuous disturbances is proposed, which realizes the real-time gain adjustment. For known and unknown piecewise continuous nonlinear functions, a processing method based on the tracking differentiator and the neural network is proposed, which skillfully guarantees the continuity of the control law. The theoretical proof shows that the semiglobal uniform ultimate boundedness of all closed-loop signals can be guaranteed under switching signals with MDADT property, and simulation results of the longitudinal maneuvering control at high angle of attack are given to further illustrate the effectiveness of the proposed framework.

Observer-Based Robust Finite-Time Trajectory Tracking Control for a Stratospheric Satellite Subject to External Disturbance and Actuator Saturation

The stratospheric satellite is regarded as an ideal stratosphere flight platform and is able to accomplish various missions such as surveillance, earth observation, and remote sensing, which requires a robust and effective trajectory tracking control method to support these tasks. A novel observer-based robust finite-time control scheme is proposed to address the trajectory tracking control problem dedicated to a stratospheric satellite in the presence of external disturbance and actuator saturation. Firstly, an extended state observer (ESO) is adopted to observe the unavailable velocity states and unknown disturbances simultaneously, and the estimated data are utilized in the robust control law design. Then, an auxiliary system based on anti-windup compensator is developed to directly compensate for the actuator saturation difference. After that, a backstepping nonsingular fast terminal sliding mode control (BNFTSMC) strategy is designed to track the desired trajectory with high accuracy, fast convergence rate, and finite-time convergence. Then, a stability analysis using Lyapunov-based theory is performed, in which the stabilization of the stratospheric satellite system and finite-time convergence are proven. Furthermore, a number of simulations are conducted further to verify the excellent performance of the designed control strategy.

Forced sliding mode control for chaotic systems synchronization

Synchronization of chaotic systems is considered to be a common engineering problem. However, the proposed laws of synchronization control do not always provide robustness toward the parametric perturbations. The purpose of this article is to show the use of synergy-cybernetic approach for the construction of robust law for Arneodo chaotic systems synchronization. As the main method of design of robust control, the method of design of control with forced sliding mode of the synergetic control theory is considered. To illustrate the effectiveness of the proposed law, in this article it is compared with the classical sliding mode control and adaptive backstepping. The distinctive features of suggested robust control law are the more good compensation of parametric perturbations (better performance indexes—the root-mean-square error (RMSE), average absolute value (AVG) of error) without designing perturbation observers, the ability to exclude the chattering effect, less energy consuming and a simpler analysis of the stability of a closed-loop system. The study of the proposed control law and the change of its parameters and the place of parametric perturbation’s application is carried out. It is possible to significantly reduce the synchronization error and RMSE, as well as AVG of error by reducing some parameters, but that leads to an increase in control signal amplitude. The place of application of parametric disturbances (slave or master system) has no effect on the RMSE and AVG of error. Offered approach will allow a new consideration for the design of robust control laws for chaotic systems, taking into account the ideas of directed self-organization and robust control. It can be used for synchronization other chaotic systems.

Robust feedback feed-forward PD-type iterative learning control for uncertain discrete systems over finite frequency ranges

This paper proposes a robust feedback feed-forward proportional-derivative type (PD-type) iterative learning control (ILC) scheme for a class of linear discrete systems with polytopic uncertainty over finite frequency ranges. First, the ILC process is transformed into an equivalent discrete linear repetitive process. Then, with the help of the generalized Kalman–Yakubovich–Popov lemma, the issue of a robust control law design algorithm in the process model is converted into the problem of solutions to the corresponding linear matrix inequality conditions. This procedure not only meets the robust performance specifications along the trial, but also guarantees the monotonic converge of the trial-to-trial error dynamics over finite frequency ranges. Finally, the simulations for a direct current servo motor system are adopted to show the effectiveness and superiority of the proposed method. Compared with previously established works, the new algorithm is more effective in delivering higher performance and achieving better tracking effect.

Automatic weighting filter tuning for robust flight control law design

This article presents a practical framework for the co-design of weighting filter parameters and controller gains in the context of multi-objective/multi-model tuning of flight control laws. A non-smooth optimization-based procedure is proposed aiming to reduce the complexity of the control design process, evolving from a rather classical manual filter selection all the way to a fully automatic one. A normal acceleration Control Augmentation System (CAS), designed by making use of non-smooth optimization software, for the linearized dynamics of an agile autonomous aerospace vehicle is used as an illustrative example. Several performance indexes are compared in the context of the developed framework as well as against more classical tuning methods such as pole placement, demonstrating that the proposed approach may lead to improved results and potentially benefit the flight control engineer via an easier handling of conflicting design requirements, model uncertainty and application-tailored control structures.

Disturbance‐observer‐based adaptive neural control for switched nonlinear systems with average dwell time

AbstractIn this article, a robust control framework is developed for nonstrict‐feedback switched nonlinear systems in the presence of unknown time‐varying delays and external disturbances. Taking into account the differences in the disturbance of each subsystem, a novel disturbance observer (DO) based on the auxiliary system is proposed for the first time. The auxiliary system is designed with the same order as that of the studied switched system, whose state variables are used to adjust the parameters of the DO in real time. Furthermore, by improving the stability condition in the frame of average dwell time (ADT), a robust control law design method based on the DO is extended to the switched system. Based on the Lyapunov–Krasovskii function, an improved delay processing method is developed, which can eliminate the widely used growth assumptions of unknown functions. Based on the DO and neural network, a robust adaptive neural network controller is constructed, and the ADT approach is adopted to analyze the semiglobal uniform ultimate boundedness of all closed‐loop system signals. Finally, the effectiveness of the proposed control scheme is further verified through simulation studies of an electromechanical system.

Adaptive State-Feedback Shared Control for Constrained Uncertain Mechanical Systems

This study develops two kinds of adaptive state feedback shared-control algorithms for a class of nonlinear mechanical systems in the presence of output constraints described by a set of linear inequalities. The parametric uncertainties and unknown external disturbances in the dynamical model are compensated by the proposed adaptive control laws for the feedback controller. In particular, an adaptive fixed-time state-feedback control law is also developed after the classical robust adaptive state-feedback control law design. The properties of the closed-loop shared-control systems are studied by using Lyapunov method. Simulation results demonstrate the effectiveness of the proposed approach.

Robust control of a DC-DC three-port isolated converter

This work presents the design of state-feedback robust control law for a DC-DC three-port isolated converter, which interfaces a photovoltaic panel, a rechargeable battery, and an isolated output DC bus. First, the converter is represented through a state-space model that considers disturbances in both the photovoltaic and bidirectional (battery) input ports. The system is linearized around an average operational point, such that robust control techniques can be applied. Due to varying solar irradiation, battery charge, and load levels, the converter is subjected to step-like disturbances. The proposed controller is designed to maintain stabilization and voltage tracking performance in the presence of these disturbances. This approach is different from multiport control strategies usually employed in the literature, which are based on decentralized controllers that require the use of decoupling techniques that can lead to control problems. To ensure robustness, stabilization, and voltage tracking, an [Formula: see text] approach with pole placement restrictions and based on linear matrix inequality (LMI) constraints is formulated and solved. Finally, the performance of the proposed controller has been verified via hardware-in-the-loop (HIL) experiments and compared with a decentralized control strategy.

Robust circumnavigation of a heterogeneous multi-agent system

This paper focuses on the design of robust control laws for a heterogeneous multi-agent system composed of omnidirectional and differential-drive mobile robots under the leader–follower scheme and considering the distance and orientation measurements. It is assume that the agent leader is an omnidirectional mobile robot moving freely in the plane while the rest of the agents are the followers. The control laws are designed by means of the Backstepping approach. It is proved that, although the control laws do not need information about the velocity of the leader, the followers will circumnavigate the leader. Numerical simulations and real-time experiments exhibit the performance of the proposed control strategy.

A delay‐independent output feedback law for discrete‐time linear systems with bounded unknown input delay

AbstractBounded input delay frequently arises in discrete‐time linear systems. The standard predictor feedback design requires the exact knowledge of the delay. Such a requirement on the availability of the delay knowledge poses challenges in the design of robust control laws when only the knowledge of an upper bound of the delay is known. We propose such a design in this article. Based on the delay‐independent truncated predictor state feedback design, an observer‐based output feedback law is constructed that does not contain any explicit information of the delay. For a general, possibly exponentially unstable, discrete‐time linear system, the proposed output feedback law stabilizes the system as long as the delay does not exceed a certain amount. For the special case of systems with all the open‐loop poles on or inside the unit circle, a low gain feedback design is presented. This low gain design allows us to establish that, when all the open‐loop poles of a system are at z = 1 or inside the unit circle, stabilization can be achieved for an arbitrarily large bounded delay as long as the value of the low gain parameter is chosen small enough.

Design and Experimental Validation of Robust Self-Scheduled Fault-Tolerant Control Laws for a Multicopter UAV

In recent years, multicopter unmanned aerial vehicles (UAV) have been widely used in many commercial and military applications. Due to the increasing requirement for high autonomy and safety, UAVs should possess a fault-tolerant ability to accommodate malfunctions during flight. This article presents two fault-tolerant control (FTC) designs for a multicopter UAV subject to actuator faults. The proposed FTC approach is based on gain-scheduling (GS) control in the framework of structured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> synthesis. The scheduled gains of the first controller are parameterized as polynomial functions of the loss of actuator effectiveness, given by an appropriate fault detection and diagnosis system. In order to facilitate the tuning process, the second controller uses the loss of virtual control effectiveness as the GS variable. Experimental results performed on an hexacopter UAV show the effectiveness and the robustness of these methods subject to multiple critical actuator faults.

Sliding Mode Control Laws Design by the ADAR Method with Subsequent Invariant Manifolds Aggregation

Sliding mode control (SMC) laws are commonly used in engineering to make a system robust to parameters change, external disturbances and control object unmodeled dynamics. State-of-the-art capabilities of the theory of adaptive and robust control, the theory of fuzzy systems, artificial neural networks, etc., which are combined with SMC, couldn’t resolve current issues of SMC design: vector design and stability analysis of a closed-loop system with SMC are involved with considerable complexity. Generally the classical problem of SMC design consists in solving subtasks for transit an object from an arbitrary initial position onto the sliding surface while providing conditions for existence of a sliding mode at any point of the sliding surface as well as ensuring stable movement to the desired state. As a general rule these subtasks are solved separately. This article presents a methodology for SMC design based on successive aggregation of invariant manifolds by the procedure of method of Analytical Design of Aggregated Regulators (ADAR) from the synergetic control theory. The methodology allows design of robust control laws and simultaneous solution of classical subtasks of SMC design for nonlinear objects. It also simplifies the procedure for closed-loop system stability analyze: the stability conditions are made up of stability criterions for ADAR method functional equations and the stability criterions for the final decomposed system which dimension is substantially less than dimension of the initial system. Despite our paper presents only the scalar SMC design procedure in details, the ideas are also valid for vector design procedure: the main difference is in the number of invariant manifolds introduced at the first and following stages of the design procedure. The methodology is illustrated with design procedure examples for nonlinear engineering systems demonstrating the achievement of control goals: hitting to target invariants, insensitivity to emerging parametric and external disturbances.

Embedded Robust Control of Multivariable Plants

The paper is devoted to the problems arising in the design and implementation of robust control laws for embedded multivariable control systems. Identifcation, derivation of uncertainty models of multivariable plants as well as problems associated with the determination of robust controllers on the basis of such models are discussed in some details. A methodology for building uncertainty models based on the identifcation results is presented. The problems arising on the diferent design stages are illustrated by a case study presenting embedded robust control of two-input two-output analog model. The plant is identifed by using black box and gray box identifcation methods which produce the necessary information to build the corresponding uncertainty models. Two discrete-time robust controllers are designed and embedded in the real system. Simulation results for the closed-loop system and experimental results obtained by using the robust controllers are given.

Nonlinear Control of Marine Surface Vessels

In the present study, a robust yaw control law design derived from nonlinear extended state observer (NESO) based nonlinear state error feedback controller (NSEFC) in conjunction with nonlinear tracking differentiator (NTD) for marine surface vessels is presented. As marine vessel operates in an environment where significant uncertainties and disturbances are present, an NESO is used to estimate the effect of the uncertainties and disturbances along with the plant states leading to a robust design through disturbance estimation and compensation. Convergence of NESO and NTD is demonstrated. The notable feature of the formulation is that to achieve robustness, accurate plant model or any characterization of the uncertainties and disturbances is not needed. Efficacy of the design is illustrated by simulation. Further, performance of the proposed design is compared with some existing controllers to showcase the effectiveness of the proposed design.

Direct discrete time design of robust state derivative feedback control laws

ABSTRACTThis paper is concerned with the problem of designing robust state derivative feedback control laws in discrete time. The main contribution consists of a method for recasting a continuous time state space model in the form of a discrete time model formulated in terms of the state derivative. Uncertain input delays and parametric uncertainties in polytopic form can be propagated from the original state space representation to the resulting state derivative model. Therefore, robust control techniques originally developed for discrete time state space models can be directly employed to design the state derivative feedback law. Three computational examples are presented for illustration. The first example highlights the importance of accounting for the effect of sampling in the design procedure. More specifically, a linear quadratic regulation problem involving the state derivative is addressed. The second example involves the design of a robust predictive controller in the presence of input constraints and uncertain time delay. Finally, the third example is concerned with robust pole placement in the presence of parametric uncertainty.

Dynamics Analysis and Robust Control for Electric Unicycles Under Constrained Control Force

This paper investigates the dynamics analysis and robust control law design for the proposed schematic design of electric unicycles. The schematic design of the proposed unicycle possesses a supportive seat for the rider and is also equipped with a handling rod for maneuvering, similar to a Segway device. First, this paper conducts an analysis and comparison of the dynamics properties and derivation of the nonlinear governing equation for the unicycle. Next, it emphasizes the development of an input-constrained robust controller design for the proposed configuration of the electric unicycle. The issues investigated in this paper include the dynamics property analysis and comparison, nonlinear dynamics derivation, robust control diagram formulation, controller synthesis regarding linear matrix inequalities (LMIs), and time response simulations and discussions. In this control law design via LMIs, the desired performances of: (1) relative stability or decay rate for command tracking capability; (2) disturbance attenuation for robustness against uncertainty parameters; and (3) an accommodation of control effort constraints under the regulation or command tracking of certain initial state condition are investigated and demonstrated using time response simulations of the controlled unicycle dynamics.