Boundary Control Scheme Research Articles

Adaptive boundary control of a flexible manipulator with input saturation

ABSTRACTIn this study, we consider the anti-windup design as one of the approaches for the boundary control problem of a flexible manipulator in the presence of system parametric uncertainties, external disturbances and bounded inputs. The dynamics of the system are represented by partial differential equations (PDEs). Using the singular perturbation approach, the PDE model is divided into two simpler subsystems. With the Lyapunov's direct method, an adaptive boundary control scheme is developed to regulate the angular position and suppress the elastic vibration simultaneously and the adaptive laws are designed to compensate for the system parametric uncertainties and the disturbances. The proposed control scheme allows the application of smooth hyperbolic functions, which satisfy physical conditions and input restrictions, be easily realised. Numerical simulations demonstrate the effectiveness of the proposed scheme.

Boundary control for a flexible manipulator based on infinite dimensional disturbance observer

This paper focuses on disturbance observer and boundary control design for the flexible manipulator in presence of both boundary disturbance and spatially distributed disturbance. Taking the infinite-dimensionality of the flexural dynamics into account, this study proposes a partial differential equation (PDE) model. Since the spatially distributed disturbance is infinite dimensional, it cannot be compensated by the typical disturbance observer, which is designed by finite dimensional approach. To estimate the spatially distributed disturbance, we propose a novel infinite dimensional disturbance observer (IDDO). Applying the IDDO as a feedforward compensator, a boundary control scheme is designed to regulate the joint position and eliminate the elastic vibration simultaneously. Theoretical analysis validates the stability of both the proposed disturbance observer and the boundary controller. The performance of the closed-loop system is demonstrated by numerical simulations.

A Novel Boundary Control Solution for Unstable Heat Conduction Systems Based on Active Disturbance Rejection Control

AbstractIn this study, a new boundary control scheme is proposed for a class of unstable heat conduction systems based on active disturbance rejection control and frequency domain analysis methods. The unstable heat conduction systems studied here corresponds to a thin rod with surface heat loss and internal heat generation. An active disturbance rejection boundary controller is designed to stabilize the unstable heat conduction systems. Using the frequency domain analysis method, the Nyquist stability criterion for distributed parameter systems, the relative stability indices (gain margin, phase margin, and exponential stability speed) can be obtained for performance evaluation, and a constructive parameter‐tuning method for controller is proposed. Finally, it is proved that an active disturbance rejection boundary controller can stabilize the unstable heat conduction systems with one unstable pole, and the simulation results demonstrate that the temperature profile of the whole rod has good convergence properties under both Dirichlet and Neumann boundary control.

Boundary control of dual‐output boost converter using state‐energy plane

A boundary control scheme for dual-output boost converter (DBC) with enhanced performance using second-order switching surface is presented in this study. The derivation of the switching surface is performed in state-energy plane rather than the state-plane to obtain a general geometrical representation that provides a good dynamic response during start-up and sudden load changes, achieving steady state in two switching actions. To illustrate the control characteristic and performance, a detailed mathematical analysis is fully developed and compared with other control methods for the DBC. The proposed control was simulated, implemented in a digital signal processor TMS320F2812, and tested using prototype hardware. The results obtained for the DBC show good performance in terms of fast transient response under 50% load change and respectable output DC-bus balancing.

Fast Transient Boundary Control and Steady-State Operation of the Dual Active Bridge Converter Using the Natural Switching Surface

This paper presents a boundary control scheme for dual active bridge (DAB) converters using the natural switching surface (NSS). The implementation of a curved switching surface for DAB converters is a new area of research undertaken in this paper. The proposed technique brings the benefit of unprecedented dynamic performance, already developed for nonisolated topologies (e.g., buck and boost), to this more complex isolated topology. The analysis provides insight into the natural trajectories of the DAB converters and creates an accurate framework in the normalized geometrical domain. As a result, the physical limits of the converter under study become evident. Those physical limits are exploited by employing the NSS to obtain fast transient response under start-up, sudden load transients, and reference change. In addition, fixed-frequency operation is one of the key features of the proposed control scheme, which allows optimizing the design of the high-frequency transformer. Experimental results are presented to validate the NSS for DAB converters and illustrate the benefits of the normalization technique.

Adaptive boundary control for flexible two‐link manipulator based on partial differential equation dynamic model

In this studies, adaptive boundary control for a flexible two-link manipulator with a changeable payload at the free-end. Taking into account the infinite-dimensionality of the flexural dynamics, this study proposes a partial differential equation (PDE) model, so that the problem of possible spillover instability caused by the neglect of flexible modes can be avoided. Based on the PDE model, an adaptive boundary control scheme is designed to regulate joint position and suppress elastic vibration while compensating for parametric uncertainties. The asymptotic stability of the closed-loop system is validated theoretically. The effectiveness of the control scheme is also verified by the numerical simulations.

End-Point Regulation of a Flexible Robotic Manipulator under the Unknown Spatiotemporally Varying Disturbance

Abstract In this paper, the end-point regulation problem is investigated for a flexible robotic manipulator under the spatiotemporally varying disturbance. By using the Hamilton's principle, the dynamics of the flexible robotic manipulator are represented by one partial differential equation (PDE) and five ordinary differential equations (ODEs). Boundary control is developed to drive the manipulator to the desired set-point and simultaneously suppress the vibrations of the flexible link. Considering the unknown spatiotemporally varying disturbance, the developed boundary control schemes achieve uniform boundedness of the steady state error between the boundary payload and the desired position. Simulations are provided to illustrate the applicability and effectiveness of the proposed control.

Observer-based partial differential equation boundary control for a flexible two-link manipulator in task space

This study addresses the problem of trajectory control of a flexible two-link manipulator on the basis of the partial differential equation (PDE) dynamic model. One of the key contributions of this study is that a novel non-linear PDE observer is proposed to estimate distributed positions and velocities along flexible links, which cannot be achieved by the typical ordinary differential equation observer. In addition, the rigidity-flexibility coupling dynamics is decomposed using the singular perturbation approach, thus providing convenience for control design. Based on the proposed observer and the decoupled PDE model, a boundary control scheme is designed to regulate the end effector along reference trajectory in task space and suppress vibration simultaneously. The asymptotic stability of both the proposed observer and the control algorithm is validated by theoretical analysis and demonstrated by simulation results, respectively.

High Performance Boundary Control of Boost-Derived PFCs: Natural Switching Surface Derivation and Properties

This study presents the application of the natural switching surface (NSS) to control single-phase power factor correctors (PFCs). The proposed boundary control scheme provides tight regulation and enhanced dynamic characteristics. The analysis is performed in the normalized geometrical domain to provide valuable graphical insight and generality. Low-frequency ripple effects are included as part of the converter reference to improve its behavior in steady state and load transient operation. In addition to the complete characterization of the system, a method to obtain fixed-frequency operation is presented by employing discrete-step references. The resulting switching surface (SS) provides fast output voltage regulation and input current dynamics, and low input harmonic distortion, achieving steady state in only a few switching actions under sudden load disturbances. The enhanced qualities of the natural SS are confirmed with simulation and experimental results of a 300 WPFC.

Improvements in Boundary Control of Boost Converters Using the Natural Switching Surface

A boundary control scheme for boost converters with enhanced performance using the natural switching surface (NSS) is presented in this paper. The derivation of the switching surface (SS) is performed in the normalized domain to obtain a general geometrical representation that is applicable to any combination of boost converter parameters. The resulting SS provides an excellent dynamic response during start-up and sudden load changes, achieving steady state in only one switching action. In order to illustrate the characteristic features and the superior performance of the natural SS, a geometrical analysis is fully developed and compared to other recent SSs. A design example is presented to illustrate the benefits of the normalization technique, and the qualities of the natural SS are confirmed with simulation and experimental results of a 30 W, 10 V/22 V converter.

Adaptive boundary control of a flexible marine installation system

In this paper, boundary control of a marine installation system is developed to position the subsea payload to the desired set-point and suppress the cable’s vibration. Using Hamilton’s principle, the flexible cable coupled with vessel and payload dynamics is described as a distributed parameter system with one partial differential equation (PDE) and two ordinary differential equations (ODEs). Adaptive boundary control is proposed at the top and bottom boundaries of the cable, based on Lyapunov’s direct method. Considering the system parametric uncertainty, the boundary control schemes developed achieve uniform boundedness of the steady state error between the boundary payload and the desired position. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulations are provided to illustrate the applicability and effectiveness of the proposed control.

Motion planning and open loop control design for linear distributed parameter systems with lumped controls

Motion planning and open loop boundary control schemes for linear spatially one dimensional distributed parameter systems with lumped control are discussed. Using Mikusiński's operational calculus the models are formulated as ordinary (operational) boundary value problems. Their solutions are parameterized by introducing a so-called basic variable as an appropriate free parameter. Particular classes of models considered lead to series representations involving derivatives of the basic variable of arbitrary order or to convolution operators which can be interpreted as distributed delays and advances. Examples of bending motions on a ring-shaped plate and a heat exchanger illustrate the results.

Reduced order distributed boundary control of thermal transients in microsystems

We study the problem of regulation of thermal transients in a microsystem using empirical eigenfunctions. Proper orthogonal decomposition (POD) is applied to an ensemble of data to obtain the dominant structures, called empirical eigenfunctions, that characterize the dynamics of the process. These eigenfunctions are the most efficient basis for capturing the dynamics of an infinite dimensional process with a finite number of modes. In contrast to published approaches, we propose a new receding horizon boundary control scheme using the empirical eigenfunctions in a constrained optimization procedure to track a desired spatiotemporal profile. Finite element method (FEM) simulations of heat transfer are provided and used in order to implement and test the performance of the controller.

Asymmetric Radio Resource Assignment Scheme for Connection-less Services in CDMA/Shared-TDD Cellular Packet Communications

The shared time division multiplexing (shared-TDD) scheme has been proposed to accommodate asymmetric communications between uplink and downlink. The accommodation of connection-less services in Shared-TDD systems causes a difficulty of TDD boundary control. This paper proposes a TDD boundary control (resource assignment) scheme, which can optimize a position of the TDD boundary based on the ratio of uplink to downlink traffic in code division multiple access (CDMA)/shared-TDD systems with connection-less services. The proposed scheme controls the TDD boundary based on the estimated uplink and downlink traffic. Computer simulations show that the proposed scheme effectively controls the radio resource, and thus improves total system throughput performance.

Robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension

In this paper, a vibration suppression scheme for an axially moving string under a spatiotemporally varying tension and an unknown boundary disturbance is investigated. The lower bound of the tension variation is assumed to be sufficiently larger than the derivatives of the tension. The axially moving string system is divided into two spans, i.e., a controlled span and an uncontrolled span, by a hydraulic touch-roll actuator which is located in the middle section of the string. The transverse vibration of the controlled span part of the string is controlled by the hydraulic touch-roll actuator, and the position of the actuator is considered as the right boundary of the controlled span part. The mathematical model of the system, which consists of a hyperbolic partial differential equation describing the dynamics of the moving string and an ordinary differential equation describing the actuator dynamics, is derived by using the Hamilton's principle. The Lyapunov method is employed to design a robust boundary control law and adaptation laws for ensuring the vibration reduction of the controlled span part. The asymptotic stability of the closed loop system under the robust adaptive boundary control scheme is proved through the use of semigroup theory. Simulation results verify the effectiveness of the robust adaptive boundary controller proposed.

Transverse Vibration Control of an Axially Moving String by Velocity Boundary Control

In this study, the time varying boundary control using the right boundary transverse motion is suggested to stabilize the transverse vibration of an axially moving string on the basis of the energy flux between the moving string and the boundaries. The effectiveness of the active velocity boundary control is showed through the FDM simulation results. Sliding mode control is adopted in order to achieve velocity tracking control of the time varying right boundary to dissipate vibration energy of the string effectively. Optical sensor system for measuring the transverse vibration of an axially moving string is developed, and the angle of the incident wave to the right boundary, which is the input of the velocity boundary controller, is obtained. Experimental research is carried out to examine the validity and the performance of the transverse vibration control using the suggested velocity right boundary control scheme.