Boundary Disturbance Research Articles

Finite-Time Bounded Control for Coupled Parabolic PDE-ODE Systems Subject to Boundary Disturbances

In this paper, the finite-time bounded control problem for coupled parabolic PDE-ODE systems subject to time-varying boundary disturbances and to time-invariant boundary disturbances is considered. First, the concept of finite-time boundedness is extended to coupled parabolic PDE-ODE systems. A Neumann boundary feedback controller is then designed in terms of the state variables. By applying the Lyapunov-like functional method, sufficient conditions which ensure the finite-time boundedness of closed-loop systems in the presence of time-varying boundary disturbances and time-invariant boundary disturbances are provided, respectively. Finally, the issues regarding the finite-time boundedness of coupled parabolic PDE-ODE systems are converted into the feasibility of linear matrix inequalities (LMIs), and the effectiveness of the proposed results is validated with two numerical simulations.

Input-to-State Stability of Non-uniform Linear Hyperbolic Systems of Balance Laws via Boundary Feedback Control

In this paper, a linear hyperbolic system of balance laws with boundary disturbances in one dimension is considered. An explicit candidate Input-to-State Stability (ISS)-Lyapunov function in $$L^2-$$ norm is considered and discretised to investigate conditions for ISS of the discrete system as well. Finally, experimental results on test examples including the Saint-Venant equations with boundary disturbances are presented. The numerical results demonstrate the expected theoretical decay of the Lyapunov function.

Spatial sampled-data control for stochastic reaction-diffusion systems

This paper considers the control problems for stochastic reaction-diffusion systems (SRDSs) with a spatial sampled-data (SSD) controller. The SSD controller engenders spatial discrete term such that the SRDS with SSD controller is a hybrid system. The coexistence of stochastic disturbance, spatial diffusion and discrete term brings out new challenges for the analysis of system properties. Utilizing the Lyapunov functional and inequality techniques, we establish several criteria on mean square exponential stabilization and robust mean square finite-time stabilization of SRDSs. Moreover, we consider the H∞ control problem when there exist external disturbances. Both system disturbances and boundary disturbances are included in our model. Sufficient conditions are obtained to ensure the mean square H∞ performance. The effects of the length of sampled-data interval and the diffusion term on the stability are reflected in all obtained criteria. Numerical simulations verify our theoretical results.

Robust Boundary Vibration Control of Uncertain Flexible Robot Manipulator with Spatiotemporally-varying Disturbance and Boundary Disturbance

In this paper the vibration control problem is addressed for the Euler-Bernoulli beam with system parameters uncertainties, spatiotemporally-varying disturbance, and boundary disturbance. By using global sliding-mode boundary control (GSMBC) through method of lines (MOL), a robust boundary control design is suggested to diminish the perturbations of uncertain Euler-Bernoulli beam and to compensate the influence of the spatiotemporally-varying disturbance and boundary disturbance. Dynamics of the Euler-Bernoulli beam are described by non-homogenous hyperbolic partial differential equation (PDE) and ordinary differential equations (ODEs). MOL is employed to acquire the beam dynamics represented by ODE system in lieu of PDE system, therefore a precise solution is obtained by solving the resulting ODE system. Then, GSMBC is established for mitigating the vibrations of the beam affected by system parameters uncertainties, spatiotemporally-varying disturbance, and boundary disturbance. Chattering phenomena is avoided by using exponential reaching law supported by a relay function. Exponential convergence and stability robustness of the closed-loop system are assured by Lyapunov direct approach. In the end, simulation outcomes show that the GSMBC-based MOL scheme is valid for vanishing the vibrations of the uncertain Euler-Bernoulli beam efficiently.

Error-based output tracking for a one-dimensional wave equation with harmonic type disturbance

Abstract In this paper, we consider output tracking for a one-dimensional wave equation, where the boundary disturbances are either collocated or non-collocated with control. The regulated output and the control are supposed to be non-collocated with control, which represents a difficult case for output tracking of PDEs. We apply the trajectory planning approach to design an observer, in terms of tracking error only, to estimate both states of the system and the exosystem from which the disturbances are produced. An error-based feedback control is proposed by solving a standard regulator equation. It is shown that (a) the closed-loop system is uniformly bounded whenever the exosystem is bounded; (b) when the disturbance is zero, the closed-loop is asymptotically stable; and (c) the tracking error converges to zero asymptotically as time goes to infinity. Numerical simulations are performed to validate the effectiveness of the proposed control.

Stabilization for a Hybrid System of Elasticity with Boundary Disturbances

The paper deals with a boundary feedback stabilization problem of a hybrid system with disturbances, which is clamped at one end and linked to a rigid body at the other end. The active disturbance rejection control approach is adopted in investigation. State observers are first designed to estimate disturbances, and then boundary feedback controllers are proposed to cancel the disturbances. Moreover, under different assumptions of time varying high gain functions, the asymptotical stability and the exponential stability of the closed-loop system are proved by the Lyapunov function approach. Finally, numerical simulations are presented to validate the theoretical conclusions.

Exponential stabilisation and dissipativity analysis of semilinear parabolic systems

In this paper, exponential stabilisation and dissipativity analysis for the scalar distributed parameter system governed by semilinear partial differential equations (PDE) are investigated. The PDE under consideration is the parabolic type with unstable dynamics and assumed to have an external disturbance and mixed boundary conditions. First, the existence and uniqueness results for the PDE are discussed using semigroup theory. Then the sufficient conditions to guarantee the exponential stability and dissipativity are obtained using the Lyapunov stability theory. Finally, the results are verified through numerical examples.

Leader-Follower Synchronization and ISS Analysis for a Network of Boundary-Controlled Wave PDEs

A network of agents, modeled by a class of wave PDEs, is under investigation. One agent in the network plays the role of a leader, and all the remaining “follower” agents are required to asymptotically track the state of the leader. Only boundary sensing of the agent's state is assumed, and each agent is controlled through the boundary by Neumann-type actuation. A linear interaction protocol is proposed and analyzed by means of a Lyapunov-based approach. A simple set of tuning rules, guaranteeing the exponential achievement of synchronization, is obtained. In addition, an exponential ISS relation, characterizing the effects on the tracking accuracy of boundary and in-domain disturbances, is derived for the closed loop system.

Telehealth Therapy for Therapists: Barriers and Benefits

Personal therapy for therapists is described as a means for advancing personal and professional growth. Therapist problems contribute to boundary disturbance, ethical violation, and incompetence. Benefits of therapy include enhanced counselor reflection and therapeutic alliance. Telehealth therapy overcomes barriers and represents an innovation in self-care and career development.

Stabilization for Euler–Bernoulli Beam Equation with Boundary Moment Control and Disturbance via a New Disturbance Estimator

We address the output feedback stabilization for a Euler–Bernoulli beam equation with boundary moment control and disturbance. The stabilization of this system has been studied in Guo et al. (J Dyn Control Syst. 2014;20:539–58), where the controller is based on full state feedback. In order to derive the output feedback controller, we design a new disturbance estimator to estimate the total disturbance in the sense that the estimation error signal belongs $L^{2}(0,\infty )$ , and it decays exponentially if the initial state is smooth. Using the estimated total disturbance, we propose a control law to stabilize the system. Using admissibility theory, we show that the closed-loop system is exponentially stable and the signals in the disturbance estimator in the closed-loop are proved to be bounded.

A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances

In this paper, we introduce a weak maximum principle-based approach to input-to-state stability (ISS) analysis for certain nonlinear partial differential equations (PDEs) with boundary disturbances. Based on the weak maximum principle, a classical result on the maximum estimate of solutions to linear parabolic PDEs has been extended, which enables the ISS analysis for certain {}{nonlinear} parabolic PDEs with boundary disturbances. To illustrate the application of this method, we establish ISS estimates for a linear reaction-diffusion PDE and a generalized Ginzburg-Landau equation with {}{mixed} boundary disturbances. Compared to some existing methods, the scheme proposed in this paper involves less intensive computations and can be applied to the ISS analysis for a {wide} class of nonlinear PDEs with boundary disturbances.

Output feedback stabilization for 1-D unstable wave equations with boundary control matched disturbance and van der Pol nonlinear boundary

In this paper we study the output feedback stabilization of a plant described by a one-dimensional wave equation with a van der Pol type nonlinear boundary condition, an unknown internal nonlinear uncertainty and an external disturbance acting at the control end (boundary). The simultaneous occurrence of nonlinear internal uncertainty, external disturbance, and van der Pol type nonlinear boundary term in the plant leads to the system is more complicated. First, we show that the open-loop system is well-posed and we design an infinite-dimensional estimator to estimate the disturbance. It is shown that the disturbance estimator can successfully estimate the total disturbance, in the sense that the estimation error signal is in L2(0,∞). Using the estimated disturbance, we propose an asymptotic state observer, and then we design an observer-based output feedback stabilizing controller. The closed-loop system is shown to be asymptotically stable. Finally, a numerical simulation is carried out to illustrate the theoretical results and effectiveness of the proposed control law.

Entropy generation versus transition time of heat exchanger during transient processes

The flexibility of thermal power plants plays a critical role to accommodate high penetration of fluctuant renewable energy. Heat exchanger is the key device restricting the flexibility and energy efficiency of thermal power plants owing to its large thermal inertia. Therefore, evaluation of the additional entropy generation and transition time for the heat exchanger during transient processes is important, which are quantitative measures of the efficiency and flexibility. Consequently, dynamic models of a heat exchanger are developed. The dynamic behaviors of the heat exchanger are analyzed using numerical simulation and entropy generation analyses. The relationship between additional entropy generation and transition time is determined. Results show that: when flow rate decreases and temperature increases, this relationship is synergetic for hot fluid, metal wall and heat exchanger. The opposite correlation occurs when flow rate increases and temperature decreases. However, the cold fluid has the contrary tendency. The augmentation in heat transfer resistance reduces the additional entropy generation and transition time, whereas the effect of increasing the range of the boundary disturbances, such as temperature and flow rate, is on the contrary. For a heat exchanger, the additional entropy generation versus the transition time can be described by an exponential function.

Constructive and destructive interparental conflict, problematic parenting practices, and children's symptoms of psychopathology.

According to spillover theory (Engfer, 1988), disruptions in one relationship (e.g., interparental) may lead to perturbations in another (e.g., parent-child), and these boundary disturbances have been linked to child psychopathology. Yet few studies have explored spillover from both constructive and destructive interparental conflict in relation to children's symptoms of psychopathology, and fewer have differentiated mothers' and fathers' parenting in these investigations. Thus, the purpose of the current study was to explore mothers' and fathers' problematic parenting practices-specifically, their inconsistent discipline, unsupportive reactions, and control through guilt-as indirect pathways between constructive and destructive interparental conflict and children's internalizing and externalizing symptoms. Two sequential mediation models were constructed-one for destructive interparental conflict and another for constructive interparental conflict-using 3 waves of data collected annually beginning when children (N = 235) were approximately 6 years old. Direct effects of the 2 models showed that constructive conflict was associated with lower levels of problematic parenting practices, whereas destructive conflict was associated with higher levels. Indirect effects findings showed that mothers' control through guilt was an explanatory mechanism between constructive and destructive interparental conflict and children's externalizing symptoms, whereas mothers' unsupportive reactions were a significant intermediary process between constructive interparental conflict and children's internalizing symptoms. Therefore, results of the current study support the spillover hypothesis and suggest that differentiating mothers' and fathers' problematic parenting practices-as well as distinguishing between constructive and destructive interparental conflict-remain important, as each can have distinct relations to child adjustment. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

HGO-based adaptive super-twisting sliding mode power level control with prescribed performance for modular high-temperature gas-cooled reactors

This paper proposes a high-gain observer-based adaptive super-twisting sliding mode control strategy with prescribed performance (HGO-ASTSMCS-PP) for the power level of a modular high-temperature gas-cooled reactor (MHTGR). The dynamic model of the MHTGR is firstly described. By using this established model, a high-gain observer is constructed to recover the unmeasured states including relative density of delayed neutron precursor and reactor core temperature in real time. On the basis of the recovering values from the HGO, an adaptive super-twisting sliding mode control method with prescribed performance is designed. The super-twisting sliding mode control approach is adopted to improve control performance of power level for a MHTGR and suppress high-frequency chattering effects simultaneously. An adaptive mechanism is introduced to tune the control gains online so as to overcome the overestimation of the unknown disturbance boundary. In addition, by error transformation and introduction of performance function, the prescribed control performance of power level is guaranteed, which implies that the desirable convergence rate, steady power error, and maximum overshoot can be prescribed in advance. It is verified through Lyapunov stability theory that the overall closed-loop control system is globally uniformly ultimately bounded (GUUB). Finally, simulation and comparison results are presented to reveal the effectiveness of the proposed control scheme in terms of the steady and dynamic performance.

Numerical simulation of nonlinear interactions in a naturally transitional flat plate boundary layer

This paper presents numerical simulations of the natural laminar-turbulent transition in a flat plate boundary layer. Natural transition occurs in low disturbance environments and is triggered by the growth of boundary layer instabilities or disturbances. This contribution specifically aims at investigating the interaction of multiple disturbances and their effect on the transition mechanism. The numerical simulations employ a lattice Boltzmann method (LBM) in conjunction with a highly accurate cumulant collision operator and a shared memory multi-GPU framework. The numerical approach is validated by comparing the growth of single Tollmien-Schlichting (T-S) waves with results of the linear stability theory (LST) prior to transition. Moreover, a comprehensive comparison with available direct numerical simulation results (DNS) for the post transition and the fully turbulent regime confirms the validity of the employed numerical approach. Subsequently, the influence of disturbances on the transition process are investigated in detail and for different disturbance frequencies and amplitudes. Two types of natural transition scenarios (H- & K-type transition) are analyzed and the LBM results are compared to predictions of the classical eN-method. Both approaches are found to reproduce a similar frequency influence. Higher frequency T-S waves trigger an earlier transition until a critical frequency is reached, above which the boundary layer is stable. In addition, it is observed that in case of multiple interacting disturbances, the laminar-turbulent transition occurs earlier than predicted by simplified methods that ignore the nonlinear interactions between disturbances. A spectral analysis of the velocity field confirms that secondary disturbances are crucial for the resonance transition and can significantly accelerate the transition process. The paper offers a comparison of linear and nonlinear results using a classical LST map and furthermore the laminar-turbulent natural transition is comprehensively investigated using the LBM.

Boundary-to-Displacement asymptotic gains for wave systems with Kelvin–Voigt damping

We provide estimates for the asymptotic gains of the displacement of a vibrating string with endpoint forcing, modelled by the wave equation with Kelvin–Voigt and viscous damping and a boundary disturbance. Two asymptotic gains are studied: the gain in the spatial norm and the gain in the spatial sup norm. It is shown that the asymptotic gain property holds in the norm of the displacement without any assumption for the damping coefficients. The derivation of the upper bounds for the asymptotic gains is performed by either employing an eigenfunction expansion methodology or by means of a small-gain argument, whereas a novel frequency analysis methodology is employed for the derivation of the lower bounds for the asymptotic gains. The graphical illustration of the upper and lower bounds for the gains shows that the asymptotic gain in the norm is estimated much more accurately than the asymptotic gain in the sup norm.

Exponential input-to-state stabilization of a class of diagonal boundary control systems with delay boundary control

This paper deals with the exponential input-to-state stabilization with respect to boundary disturbances of a class of diagonal infinite-dimensional systems via delay boundary control. The considered input delays are uncertain and time-varying. The proposed control strategy consists of a constant-delay predictor feedback controller designed on a truncated finite-dimensional model capturing the unstable modes of the original infinite-dimensional system. We show that the resulting closed-loop system is exponentially input-to-state stable with fading memory of both additive boundary input perturbations and disturbances in the computation of the predictor feedback.

Tracking Control of a Flexible String System Based on Iterative Learning Control

This brief addresses a flexible string with disturbances and a tip payload which is described by a coupled partial differential equation (PDE)-ordinary differential equation (ODE) system. An exosystem under unknown initial condition is utilized to generate the disturbances and prescribed trajectory, both of which can be periodic or aperiodic with respect to iteration. An observer and adaption laws are designed to estimate the distributed and boundary disturbances. The reference system under the estimated distributed disturbance is defined and proved to be uniformly bounded, where the endpoint displacement is set as the known prescribed trajectory in order to address the tracking control problem. Iterative learning controller is then designed to guarantee the convergence of the tracking error and the uniform boundedness of the closed-loop system. A set of simulation examples are presented to describe the performance of a closed-loop system.

Input-to-State Stability of a Clamped-Free Damped String in the Presence of Distributed and Boundary Disturbances

This note establishes the Exponential Input-to-State Stability (EISS) property for a clamped-free damped string with respect to distributed and boundary disturbances. While efficient methods for establishing ISS properties for distributed parameter systems with respect to distributed disturbances have been developed during the last decades, establishing ISS properties with respect to boundary disturbances remains challenging. One of the well-known methods for well-posedness analysis of systems with boundary inputs is the use of a lifting operator for transferring the boundary disturbance to a distributed one. However, the resulting distributed disturbance involves time derivatives of the boundary perturbation. Thus, the subsequent ISS estimate depends on its amplitude, and may not be expressed in the strict form of ISS properties. To solve this problem, we show for a clamped-free damped string equation that the projection of the original system trajectories in an adequate Riesz basis can be used to establish the desired EISS property.