• Proceedings of the IEEK Conference
• /
• 2000.07a
• /
• pp.395-398
• /
• 2000

The method of Variable Structure Control (VSC) design of windmill power systems is proposed. In the design of sliding mode control, we use Riccati equations arising in linear H$\^$$\infty$/ control to decide a stable sliding surface. Then the reachability to the sliding surface is realized by designing a nonlinear controller for the windmill power system. The capability of the proposed controller to damp out the oscillations of power and the robustness with respect to the system parameter variations and model errors are evaluated in the simulation study.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.49 no.3
• /
• pp.136-141
• /
• 2000

This paper presents the design of an H$\infty$ based robust Static Synchronous Compensator (STATCOM) supplementary controller to suppress the subsynchronous resonance (SSR) in the series-compensated system. The IEEE second benchmark, System-l model is employed for this study. In order to design the effective controller, the modal controllability and observability indices to the oscillation modes are considered. Comprehensive time domain simulations using a nonlinear system model that the proposed STATCOM supplementary controller can suppress the SSR efficiently in spite of the variations of power system operating conditions.

• Proceedings of the KIEE Conference
• /
• 1998.11b
• /
• pp.463-465
• /
• 1998

In this paper, we consider the problem of robust stability of large-scale uncertain linear systems with time-varying delays. The considered uncertainties are both unstructured uncertainty which is only known its norm bound and structured uncertainty which is known its structure. Based on Lyapunov stability theorem and $H_{\infty}$ theory. we present uncertainty upper bound that guarantee the robust stability of systems. Especially, robustness bound are obtained directly without solving the Lyapunov equation. Finally, we show the usefulness of our results by numerical example.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.48 no.5
• /
• pp.615-621
• /
• 1999

In this paper, we consider the robust stability of uncertain linear systems with time-delay in the time domain. The considered uncertainties are both the unstructured uncertainty which is only Known its norm bound and the structured uncertainty which is known its structured. Based on Lyapunov stability theorem and{{{{ { H}_{$\infty$ } }}}} theory known as Strictly Bounded Real Lemma (SBRL), we present new conditions that guarantee the robust stability of system. Also, we extend this to multiple time-varying delays systems and large-scale systems, respectively. Finally, we show the usefulness of our results by numerical examples.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.30 no.9 s.252
• /
• pp.1094-1101
• /
• 2006

Recently, a ultra-precision stage is widely used in the fields of the nano-technology, specially in AFMs(Atomic Force Microscope) and STMs(Scanning Tunneling Microscope). In this paper, the ultra-precision stage which consists of flexure hinges, piezoelectric actuator and ultra-precision linear encoder, is designed and developed. The system transfer function of the ultra-precision stage system was derived from the step responses of the system using system identification tool. A $H_{\infty}$ controller was designed using loop shaping method to have robustness for the system uncertainty and external disturbances. For the designed controller, simulations were performed and it was applied to the ultra-precision stage system. From the experimental results it was found that this stage could be controlled with less than 5nm resolution irrespective of hysteresis and creep.

• Journal of the Korean Society for Precision Engineering
• /
• v.15 no.9
• /
• pp.33-42
• /
• 1998

If a ship diesel engine is operated by consolidated control with Controllable Pitch Propeller(CPP), the minimum fuel consumption is achieved together with the demanded ship speed. For this, it is necessary that the ship is operated on the ideal operating line which satisfies the minimum fuel consumption and that the pitch angle of CPP and throtle valve angle are controlled simultaneously. In this point of view, this paper presents a controller design method for a ship propulsion system with CPP based on the decoupling control theory. To do this, Linear Matrix Inequality(LMI) approach is introduced for the control system to satisfy the given $H_\infty$ control performance and robust stability in the presence of physical parameter perturbations. The validity and applicability of this approach are illustrated by simulation in the all operating ranges.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1993.10a
• /
• pp.5-18
• /
• 1993

This paper reports the recent trends in active vibration control in Japan, especially, based on papers selected in the Proceedings of First International Conference on Motion and Vibration Control (1st MOVIC) held at Yokohama, Japan on Sept.7-11, 1992. Firstly, it classifiers vibration control methods and vibration controllers, especially active dynamic absorbers which are widely used in mechanical and civil engineering. Secondly, it covers basic problems in the control of vibration of flexible structures such as formulating a reduced-order model required for designing vibration controller, proper arranging of sensors and actuators, and preventing of spillover instability. Finally, the practical use of control theories such as LQ control theory, $H^{\infty}$ control theory, neural network theory, and other topics are discussed..

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1996.10a
• /
• pp.175-181
• /
• 1996

The magnetic levitation system is utilized in the magnetic bearing of high-speed rotor because of little friction, no lubrication, no noise and so on. The magnetic levitation system need the feedback controller for the stabilization of system, and gap sensors are usually used to measure the gap. The use of sensor is troublesome such as sensor trouble, discord between the measurement point and the control point etc. This paper presents the design of robust stabilizing controller by H$_{\infty}$ control theory using the sensorless method proposed already by authors in the magnetic levitation system. And we investigated both the validity of the designed controller and the usefulness of the sensorless method proposed by authors of magnetic levitation system through results of actual experiment..

• Journal of the Korean Mathematical Society
• /
• v.41 no.1
• /
• pp.1-20
• /
• 2004

Let A be a uniform algebra, and let $\phi$ be a self-map of the spectrum $M_A$ of A that induces a composition operator $C_{\phi}$, on A. It is shown that the image of $M_A$ under some iterate ${\phi}^n$ of \phi is hyperbolically bounded if and only if \phi has a finite number of attracting cycles to which the iterates of $\phi$ converge. On the other hand, the image of the spectrum of A under $\phi$ is not hyperbolically bounded if and only if there is a subspace of $A^{**}$ "almost" isometric to ${\ell}_{\infty}$ on which ${C_{\phi}}^{**}$ "almost" an isometry. A corollary of these characterizations is that if $C_{\phi}$ is weakly compact, and if the spectrum of A is connected, then $\phi$ has a unique fixed point, to which the iterates of $\phi$ converge. The corresponding theorem for compact composition operators was proved in 1980 by H. Kamowitz [17].

• Bulletin of the Korean Mathematical Society
• /
• v.26 no.1
• /
• pp.43-46
• /
• 1989

In this paper, we are concerned with the pointwise-hypoellipticity (see Definition 2.1) of an m-dimensional Frobenious Lie algebra L of analytic complex vector fields in somel open subset .ohm. of $R^{m+1}$. That is, L is a set of complex vector fields in .ohm. with (real-) analytic coefficients satisfying: (A) each point of .ohm. has an open neighborhood in which L is generated by m linearly independent elements of L; (B) L is closed under the commutation bracket [A, B]. The pointwise-analytic hypoellipticity of L is completely characterized by M.S. Baouendi and F. Treves in [1]. Here, we shall prove that if L is hypoelliptic at a point then it must be analytic hypoelliptic in a full neighborhood of the same point. When the coefficients are $C^{\infty}$, hypoellipticity of L was discussed in [2].2].