Control system design for a pressure-tube-type supercritical water-cooled nuclear reactor via a higher order sliding mode method

Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor(SCWR)is a fourth-generation conceptual reactor.In an SCWR,the non-linear dynamics of the reactor require a controller capable of control-ling the nonlinearities.In this study,a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding mode,and the reactor outgoing steam temperature and pressure were controlled simultaneously.In an SCWR,the temperature,pressure,and power must be maintained at a setpoint(desired value)during power maneuvering.Reactor point kinetics equations with three groups of delayed neutrons were used in the simulation.Higher-order and classic sliding mode controllers were separately manufactured to control the plant and were compared with the PI controllers speci-fied in previous studies.The controlled parameters were reactor power,steam temperature,and pressure.Notably,for these parameters,the PI controller had certain instabilities in the presence of disturbances.The classic sliding mode controller had a higher accuracy and stability;however its main drawback was the chattering phenomenon.HOSMC was highly accurate and stable and had a small computational cost.In reality,it followed the desired values without oscillations and chattering.

Generalized projective synchronization of the fractional-order chaotic system using adaptive fuzzy sliding mode control

An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractional- order chaotic system, where the slave system is not necessarily known in advance. Based on the designed adaptive update laws and the linear feedback method, the adaptive fuzzy sliding controllers are proposed via the fuzzy design, and the strength of the designed controllers can he adaptively adjusted according to the external disturbances. Based on the Lya- punov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Numerical simu- lations further support the theoretical results of the paper and demonstrate the efficiency of the proposed method. Moreover, it is revealed that the proposed method allows us to manipulate arbitrarily the response dynamics of the slave system by adjusting the desired scaling factor λi and the desired translating factor ηi, which may be used in a channel-independent chaotic secure communication.

The stability control of fractional order unified chaotic system with sliding mode control theory

This paper studies the stability of the fractional order unified chaotic system with sliding mode control theory. The sliding manifold is constructed by the definition of fractional order derivative and integral for the fractional order unified chaotic system. By the existing proof of sliding manifold, the sliding mode controller is designed. To improve the convergence rate, the equivalent controller includes two parts： the continuous part and switching part. With Gronwall＇s inequality and the boundness of chaotic attractor, the finite stabilization of the fractional order unified chaotic system is proved, and the controlling parameters can be obtained. Simulation results are made to verify the effectiveness of this method.

Synchronization of uncertain fractional-order chaotic systems with disturbance based on a fractional terminal sliding mode controller

This paper provides a novel method to synchronize uncertain fractional-order chaotic systems with external disturbance via fractional terminal sliding mode control. Based on Lyapunov stability theory, a new fractional-order switching manifold is proposed, and in order to ensure the occurrence of sliding motion in finite time, a corresponding sliding mode control law is designed. The proposed control scheme is applied to synchronize the fractional-order Lorenz chaotic system and fractional-order Chen chaotic system with uncertainty and external disturbance parameters. The simulation results show the applicability and efficiency of the proposed scheme.

Fuzzy Fractional-Order Fast Terminal Sliding Mode Control for Some Chaotic Microcomponents

In this paper,we propose a novel fractionalorder fast terminal sliding mode control method,based on an integer-order scheme,to stabilize the chaotic motion of two typical microcomponents.We apply the fractional Lyapunov stability theorem to analytically guarantee the asymptotic stability of a system characterized by uncertainties and external disturbances.To reduce chattering,we design a fuzzy logic algorithm to replace the traditional signum function in the switching law.Lastly,we perform numerical simulations with both the fractional-order and integer-order control laws.Results show that the proposed control law is effective in suppressing chaos.

Stabilization of Uncertain Fractional Memristor Chaotic Time⁃Delay System Based on Fractional Order Sliding Mode Control

Based on Lyapunov theorem and sliding mode control scheme,the chaos control of fractional memristor chaotic time⁃delay system was studied.In order to stabilize the system,a fractional sliding mode control method for fractional time⁃delay system was proposed.In addition,Lyapunov stability theorem was used to analyze the control scheme theoretically,which guaranteed the stability of commensurate and non⁃commensurate order systems with or without uncertainties and disturbances.Furthermore,to illustrate the feasibility of controller,the conditions for designing the controller parameters were derived.Finally,the simulation results presented the effectiveness of the designed strategy.

No-chattering sliding mode control in a class of fractional-order chaotic systems

A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.

Fractional order nonsingular terminal sliding mode control for flexible spacecraft attitude tracking

This paper investigates a fractional terminal sliding mode control for flexible spacecraft attitude tracking in the presence of inertia uncertainties and external disturbances. The controller is based on the fractional calculus and nonsingular terminal sliding mode control technique,and it guarantees the convergence of attitude tracking error in finite time rather than in the asymptotic sense. With respect to the controller,a fractional order sliding surface is given,the corresponding control scheme is proposed based on Lyapunov stability theory to guarantee the sliding condition,and the finite time stability of the whole close loop system is also proven. Finally,numerical simulations are presented to illustrate the performance of the proposed scheme.

Constrained sliding mode control of nonlinear fractional order input affine systems

Asymptotic stability of nonlinear fractional order affine systems with bounded inputs is dealt.The main contribution is to design a new bounded fractional order chattering free sliding mode controller in which the system states converge to the sliding surface at a determined finite time.To eliminate the chattering in the sliding mode and make the input controller bounded,hyperbolic tangent is used for designing the proposed fractional order sliding surface.Finally,the stability of the closed loop system using this bounded sliding mode controller is guaranteed by Lyapunov theory.A comparison with the integer order case is then presented and fractional order nonlinear polynomial systems are also studied as the special case.Finally,simulation results are provided to show the effectiveness of the designed controller.

Dynamic analysis and fractional-order adaptive sliding mode control for a novel fractional-order ferroresonance system

Ferroresonance is a complex nonlinear electrotechnical phenomenon, which can result in thermal and electrical stresses on the electric power system equipments due to the over voltages and over currents it generates. The prediction or determination of ferroresonance depends mainly on the accuracy of the model used. Fractional-order models are more accurate than the integer-order models. In this paper, a fractional-order ferroresonance model is proposed. The influence of the order on the dynamic behaviors of this fractional-order system under different parameters n and F is investigated. Compared with the integral-order ferroresonance system, small change of the order not only affects the dynamic behavior of the system, but also significantly affects the harmonic components of the system. Then the fractional-order ferroresonance system is implemented by nonlinear circuit emulator. Finally, a fractional-order adaptive sliding mode control （FASMC） method is used to eliminate the abnormal operation state of power system. Since the introduction of the fractional-order sliding mode surface and the adaptive factor, the robustness and disturbance rejection of the controlled system are en- hanced. Numerical simulation results demonstrate that the proposed FASMC controller works well for suppression of ferroresonance over voltage.

Finite-time robust control of uncertain fractional-order Hopfield neural networks via sliding mode control

The finite-time control of uncertain fractional-order Hopfield neural networks is investigated in this paper. A switched terminal sliding surface is proposed for a class of uncertain fractional-order Hopfield neural networks. Then a robust control law is designed to ensure the occurrence of the sliding motion for stabilization of the fractional-order Hopfield neural networks. Besides, for the unknown parameters of the fractional-order Hopfield neural networks, some estimations are made. Based on the fractional-order Lyapunov theory, the finite-time stability of the sliding surface to origin is proved well. Finally, a typical example of three-dimensional uncertain fractional-order Hopfield neural networks is employed to demonstrate the validity of the proposed method.

Comparison between two different sliding mode controllers for a fractional-order unified chaotic system

Two different sliding mode controllers for a fractional order unified chaotic system are presented. The controller for an integer-order unified chaotic system is substituted directly into the fractional-order counterpart system, and the fractional-order system can be made asymptotically stable by this controller. By proving the existence of a sliding manifold containing fractional integral, the controller for a fractional-order system is obtained, which can stabilize it. A comparison between these different methods shows that the performance of a sliding mode controller with a fractional integral is more robust than the other for controlling a fractional order unified chaotic system.

Robust sliding mode control for fractional-order chaotic economical system with parameter uncertainty and external disturbance

This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractional-order integral, the effective sliding mode controller is designed to realize the asymptotical stability of fractional-order chaotic economical systems. Comparing with the existing results, the main results in this paper are more practical and rigorous. Simulation results show the effectiveness and feasibility of the proposed sliding mode control method.

Synchronization between a novel class of fractional-order and integer-order chaotic systems via a sliding mode controller

In order to figure out the dynamical behaviour of a fractional-order chaotic system and its relation to an integer- order chaotic system, in this paper we investigate the synchronization between a class of fractional-order chaotic systems and integer-order chaotic systems via sliding mode control method. Stability analysis is performed for the proposed method based on stability theorems in the fractional calculus. Moreover, three typical examples are carried out to show that the synchronization between fractional-order chaotic systems and integer-orders chaotic systems can be achieved. Our theoretical findings are supported by numerical simulation results. Finally, results from numerical computations and theoretical analysis are demonstrated to be a perfect bridge between fractional-order chaotic systems and integer-order chaotic systems.

Sliding Mode Control of Fractional-Order Memristive System

A sliding mode controller for a fractional-order memristor-based chaotic system is designed to address its problem in stabilization control.Firstly,aphysically realizable fractional-order memristive chaotic system was introduced,which can generate a complex dynamic behavior.Secondly,a sliding mode controller based on sliding mode theory along with Lyapunov stability theory was designed to guarantee the occurrence of the sliding motion.Furthermore,in order to demonstrate the feasibility of the controller,a condition was derived with the designed controller＇s parameters,and the stability analysis of the controlled system was tested.A theoretical analysis shows that,under suitable condition,the fractional-order memristive system with a sliding mode controller comes to a steady state.Finally,numerical simulations are shown to verify the theoretical analysis.It is shown that the proposed sliding mode method exhibits a considerable improvement in its applications in a fractional-order memristive system.

A Novel ANFIS Based SMC with Fractional Order PID Controller

Interacting The highest storage capacity of a circular tank makes it pop-ular in process industries.Because of the varying surface area of the cross-sec-tions of the tank,this two-tank level system has nonlinear characteristics.Controlling theflow rate of liquid is one of the most difficult challenges in the production process.This proposed effort is critical in preventing time delays and errors by managing thefluid level.Several scholars have explored and explored ways to reduce the problem of nonlinearity,but their techniques have not yielded better results.Different types of controllers with various techniques are implemented by the proposed system.Sliding Mode Controller(SMC)with Fractional Order PID Controller based on Intelligent Adaptive Neuro-Fuzzy Infer-ence System(ANFIS)is a novel technique for liquid level regulation in an inter-connected spherical tank system to avoid interferences and achieve better performance in comparison of rise time,settling time,and overshoot decrease.Evaluating the simulated results acquired by the controller yields the efficiency of the proposed system.The simulated results were produced using MATLAB 2018 and the FOMCON toolbox.Finally,the performance of the conventional controller(FOPID,PID-SMC)and proposed ANFIS based SMC-FOPID control-lers are compared and analyzed the performance indices.

Flight control for a flexible air-breathing hypersonic vehicle based on quasi-continuous high-order sliding mode

The focus of this paper is on control design and simulation for the longitudinal model of a flexible air-breathing hypersonic vehicle（FAHV）.The model of interest includes flexibility effects and intricate couplings between the engine dynamics and flight dynamics.To overcome the analytical intractability of this model,a nominal control-oriented model is constructed for the purpose of feedback control design in the first place.Secondly,the multi-input multi-output（MIMO） quasi-continuous high-order sliding mode（HOSM） controller is proposed to track step changes in velocity and altitude,which is based on full state feedback.The simulation results are presented to verify the effectiveness of the proposed control strategy.

Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

Sliding Mode Control for Fractional Differential Systems with State-delay

The problem of sliding mode control for fractional differential systems with statedelay is considered.A novel sliding surface is proposed and a controller is designed correspondingly,such that the state starting from any initial value will move toward the switching surface and reach the sliding surface in finite time and the state variables on the sliding surface will converge to equilibrium point.And the stability of the proposed control design is discussed.

Sliding Mode Control Design via Reduced Order Model Approach

This paper presents a design of continuous-time sliding mode control for the higher order systems via reduced order model. It is shown that a continuous-time sliding mode control designed for the reduced order model gives similar performance for thc higher order system. The method is illustrated by numerical examples. The paper also introduces a technique for design of a sliding surface such that the system satisfies a cost-optimality condition when on the sliding surface.