Kyung-Jinn Yang

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 Hamiltons 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.

Energy-based control of axially translating beams: varying tension, varying speed, and disturbance adaptation

In this brief, the investigational results for a robust adaptive vibration control of a translating tensioned beam with a varying traveling speed are presented. The dynamics of beam and actuator is modeled via the extended Hamiltons principle, in which the tension applied to the beam is given as a nonlinear spatiotemporally varying function. The moving beam is divided into two parts, a controlled span and an uncontrolled span, by a hydraulic touch-roll actuator that is located in the middle section of the beam. The transverse vibration of the controlled span is suppressed by the touch-roll actuator, whereas the vibration of the uncontrolled span is treated as a disturbance, and the magnitude of unknown disturbance is estimated. In a proper mathematical manner, the Lyapunov method is employed to design robust adaptive boundary control laws for ensuring the vibration reduction of the nonlinear time-varying system, and also to ensure the stability of the closed-loop system. The effectiveness of the proposed controller is demonstrated via numerical simulations.

Robust boundary control of an axially moving string by using a PR transfer function

In this note, a scheme for the vibration suppression of a translating string using a positive real (PR) transfer function is investigated. The transverse vibration of the string is controlled by hydraulic touch-rolls located at the right end of the string. The mathematical model of the system, which consists of a hyperbolic partial differential equation (PDE) describing the dynamics of the moving string and an ordinary differential equation (ODE) for the actuator dynamics, is derived by using Hamiltons principle for translating continua. The transfer function of the proposed boundary controller is a nonproper but PR function. The asymptotic stability of the closed-loop system in the presence of output disturbance is proved.

Exponential Stabilization of an Axially Moving Tensioned Strip by Passive Damping and Boundary Control

In this paper, we investigate an active vibration control of a translating tensioned steel strip in the zinc galvanizing line. The dynamics of the moving strip is modeled as a Euler-Bernoulli beam with non-linear tension. The control objective is to suppress the transverse vibrations of the strip via boundary control. A right boundary control law based upon the Lyapunov second method is derived. It is revealed that a time-varying boundary force and a suitable passive damping at the right boundary can successfully suppress the transverse vibrations. The exponential stability of the closed-loop system is proved. The effectiveness of the control laws proposed is demonstrated via simulations.

Boundary control of a translating tensioned beam with varying speed

The investigational results for an active vibration control of a translating tensioned beam with a varying traveling speed are presented. The dynamics of beam and actuator is modeled via the extended Hamiltons principle. In a proper mathematical manner, the Lyapunov method is employed to design a boundary control law for ensuring the vibration reduction of the nonlinear time-varying system and also to ensure the exponential stability of the closed-loop system.

THE RATE OF CHANGE OF AN ENERGY FUNCTIONAL FOR AXIALLY MOVING CONTINUA

Abstract In this paper, with the utilization of a transport theorem and three-dimensional version of Leibnizs rule, the procedure for deriving the time rate of change of an energy functional for axially moving continua is investigated. In the control engineering, the correct solution of the time derivation of an energy functional is essential for designing an effective controller, especially, in the Lyapunov method. The key point to get the correct solution for axially moving continua is that the time derivation of an energy functional should be taken into account under Eulerian description with a physical concept. A novel way of deriving the time rate of change of the energy functional, then, is proposed.

An Object-Oriented Modular Simulation Model for Integrated Gasoline Engine and Automatic Transmission Control

In this paper a computer simulation model for control system design of gasoline engines with an automatic transmission is presented. A modular programming approach has been pursued, and MATLAB/SIMULINK has been utilized as a programming environment. Engine/transmission systems are analyzed in the objectoriented fashion. Thus, easy construction of various computer models by assembling various objects is possible. An object in this paper represents a physical part, an equation, or an algorithm. The top level in the powertrain model consists of three classes: an engine, a transmission, and a driveline. Each class is designed to perform by itself. The construction procedure of a typical powertrain model together with supplementary explanation is demonstrated. It is expected that the whole program and individual class constructed in this paper are useful for the automotive engineers who design a new engine/transmission system and/or modify an existing system. INTRODUCTION In the automotive industry, the enhancement of the ride quality, fuel efficiency, and exhaust emission of a newly introduced vehicle has been continuously emphasized. This endeavor can be substantially achieved by improving the performance of the powertrain, which is a primary element of the noise, vibration, harshness, and fuel efficiency of a vehicle. Fig. 1 shows the schematic diagram of a typical powertrain system. An integrated control of the powertrain system refers to a combined control of the hitherto separated engine and transmission controls as shown in Fig. 2. The subject of powertrain control will play a central role among the many issues related to the control of the vehicle[1,2]. One challenging engineering problem is to build a software model with a computer which imitates or reproduces the behavior of a real plant. If this goal is achieved, then the cost and time needed to develop a better performing machine can be greatly reduced. It would be very effective if the dynamic performance of a newly configured powertrain system could be evaluated from the early stages of its design with a computer model before making its prototype.

Object‐oriented modeling for gasoline engine and automatic transmission systems

In this article a computer model for control system design of gasoline engines with an automatic transmission is presented. A modular programming approach has been pursued, and MATLAB/SIMULINK has been used as a programming environment. Engine/transmission systems are analyzed in the object‐oriented fashion that provides and ensures easy construction of various computer models by assembling various objects. An object in this article represents a physical part, an equation, or an algorithm. The top level in the powertrain model consists of three classes: an engine, a transmission, and a driveline. Each class is designed to perform by itself. The construction procedure of a typical powertrain model together with supplementary explanation is demonstrated. It is expected that the whole program and individual class constructed in here are useful for the automotive engineers who design a new engine/transmission system and/or modify an existing system.

Advanced sliding mode idle speed control for a nonlinear engine model: coordinated throttle/spark advance control

The engine idle speed should be as low as possible for reduced fuel consumption. But, since idle speed is set at a low value, even slight fluctuations of the idle speed due to torque disturbances cause not only deterioration of vehicle performance but also unpleasant vibrations of the vehicle. Therefore, the primary goal of the idle speed control is to maintain a desired engine speed despite torque disturbances. In this paper, the coordinate throttle/spark advance control using a sliding mode scheme is designed for nonlinear engine speed control which has superior ability to minimize idle speed variations under rapid torque disturbances and the system nonlinearities/uncertainties.

ROBUST BOUNDARY CONTROL OF AN AXIALLY MOVING STEEL STRIP

Abstract In this paper, a robust vibration control scheme of the axially moving steel strip in the zinc galvanizing line is considered. The boundary control force is applied to the strip through the two touch rolls connected to a hydraulic actuator. The mathematical model of the system, which consists of a partial differential equation describing the dynamics of the traveling steel strip and an ordinary differential equation describing the actuator dynamics, is derived by using the Hamiltons principle for the systems with changing mass. The total mechanical energy of the system is considered as a Lyapunov function candidate. For vibration suppression purpose, a robust boundary feedback control law is designed. The asymptotic stability of the closed loop system is verified through the Lyapunov analysis and the semigroup theory.