• International Journal of Precision Engineering and Manufacturing
• /
• v.1 no.2
• /
• pp.24-34
• /
• 2000

In this paper we propose a controller design method, called Quasi-LQG/$H_{\infty}$/LTR for nonlinear servo systems with hard nonlinearities such as Coulomb friction, dead-zone. Introducing the RIDF method to model Coulomb friction and dead-zone, the statistically linearized system is built. Then, we consider $H_{\infty}$ performance constraint for the optimization of statistically linearized systems, by replacing a covariance Lyapunov equation into a modified Riccati equation of which solution leads to an upper bound of the LQG performance. As a result, the nonlinear correction term is included in coupled Riccati equation, which is generally very difficult to thave a numerical solution. To solve this problem, we use the modified loop shaping technique and show some analytic proofs on LTR condition. Finally, the Quasi-LQG/$H_{\infty}$/LTR controller for a nonlinear system is synthesized by inverse random input describing function techniques (ITIDF). It is shown that the proposed design method has a better performance robustness to the hard nonlinearity than LQG/$H_{\infty}$/LTR method via simulations and experiments for the timing-belt driving servo system that contains the Coulomb friction and dead-zone.

• 제어로봇시스템학회:학술대회논문집
• /
• 1991.10a
• /
• pp.55-59
• /
• 1991

This paper presents a method for designing a full state feedback linear static control law. This will stabilize a given linear uncertain system and also guarantee the performance of the system. The uncertain systems are described by state equation which contains uncertain parameters in system and input distribution matrices. The method is based on the guaranteed cost control of Chang and Peng(1972). The controller gain can be obtained by the solution of a algebraic Riccati equation in which the input weighting matrices depend on the uncertainty bounds. The algebraic Riecati equation in this paper is same as that of weighted LQ regulator problem.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1165-1176
• /
• 2009

This paper is concerned with the interval oscillation of the second order nonlinear ordinary differential equation (r(t)|y'(t)|$^{{\alpha}-1}$ y'(t))'+p(t)|y'(t)|$^{{\alpha}-1}$ y'(t)+q(t)f(y(t))g(y'(t))=0. By constructing ageneralized Riccati transformation and using the method of averaging techniques, we establish some interval oscillation criteria when f(y) is not differetiable but satisfies the condition $\frac{f(y)}{|y|^{{\alpha}-1}y}$ ${\geq}{\mu}_0$ > 0 for $y{\neq}0$.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.37 no.3
• /
• pp.28-34
• /
• 2000

In this paper, we derive a spectral function and a new impedance profile of non-uniform tapered transmission lines by applying the Fourier transform to a linearized Riccati equation. We compensate the error which is from a linearized Riccati equation by adding a Taylor series to the impedance profile. Added terms remove discontinuities In the impedance profile at both ends of the non-uniform section. We show that a calculated spectrum approaches to a target spectrum of filter by an iterative method and numerical examples are given to illustrate the role of the phase function. As the design method which is shown in present paper provides a excellent adaptability for the design of non-uniform tapered transmission lines, the present method can be applied to design filters and impedance matching circuits with various passband characteristics.

• Honam Mathematical Journal
• /
• v.16 no.1
• /
• pp.103-109
• /
• 1994

Piezoceramic patches as collocated actuator and sensors are widely used in mechanical control systems. An approximation scheme for computing feedback gains arising in heat flux stabilization problem with such control mechanism is introduced. The scheme is based on a finite element method and a variational approach.

• Journal of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.73-82
• /
• 2018

In this article we consider certain types of nonlinear matrix equations including the stochastic rational Riccati equation and show the existence and uniqueness of the positive definite solution by using Bhaskar-Lakshmikantham's coupled fixed point theorem.

• Bulletin of the Korean Space Science Society
• /
• 2005.10a
• /
• pp.65-65
• /
• 2005

• 제어로봇시스템학회:학술대회논문집
• /
• 1988.10b
• /
• pp.749-752
• /
• 1988

In this paper, the delay margins of the LQ and the LQG regulators are obtained in the time domain. These margins are represented in terms of the singular values of system matrices and the solutions of a Riccati equation and a Lyapunov one. And their asymptotical properties when gains tend to infinity are investigated.

• 제어로봇시스템학회:학술대회논문집
• /
• 1987.10b
• /
• pp.223-227
• /
• 1987

This paper presents the extended interaction prediction method for large scale discrete-time systems with interconnected state and control. Feedback gain is obtained from decentralized calculation without solving Riccati equation. Hence, Computer storage and calculation time is reduced.

• 제어로봇시스템학회:학술대회논문집
• /
• 1992.10b
• /
• pp.219-224
• /
• 1992

This paper deals with the linear quadratic optimal regulator problem for descriptor systems without performing a preliminary transformation for a descriptor system. We derive a generalized Riccati differential equation (GRDE) based on the two-point boundary value problem for a Hamiltonian equation. We then obtain an optimal feedback control and the optimal cost in terms of the solution of GRE. A simple example is included.