Kyu-Hong Shim

Near-optimal state feedback design for singularly perturbed systems by unified approach

A near optimal state feedback design for singularly perturbed systems by a unified approach using the delta operator is presented with an example of the aircraft longitudinal motion. The main contribution of this paper is to explore the use of the i -operator that has attracted a new attention in systems science. The i -operator system unifies the continuous system and the discrete system together without loosing any characteristics of both systems. The paper offers the following; Finite-word-length-characteristics are improved using the i -operator. Floating-point-operations are reduced by block diagonalization and by time-invariant optimal feedback gain from the algebraic Riccati equation. The results of adopting those approaches are illustrated in the simulation figures and compared with the earlier one.

Singularly perturbed unified time systems with low sensitivity to model reduction using delta operators

A method of designing a state feedback gain achieving a specified insensitivity of the closed-loop trajectory by the singularly perturbed unified system using the δ operators is proposed. The order of system is reduced by the singular perturbation technique by ignoring the fast mode in it. The proposed method takes care of the actual trajectory variations over the range of the singular perturbation parameter. Necessary conditions for optimality are also derived. The previous study was done in the continuous time system. The present paper extends the previous study to the discrete system and the δ-operating system that unifies the continuous and discrete systems. Advantages of the proposed method are shown in the numerical example.

Unified modeling for singularly perturbed systems by delta operators: pole assignment case

A unified modeling method by using the δ-operators for the singularly perturbed systems is introduced. The unified model unifies the continuous and the discrete models. When compared with the discrete model, the unified model has an improved finite word-length characteristics and its δ-operator is handled conveniently like that of the continuous system. In additions, the singular perturbation method, a model approximation technique, is introduced. A pole placement example is used to show such advantages of the proposed methods. It is shown that the error of the reduced model in its eigenvalues is less than the order of e (singular perturbation parameter). It is shown that the error in the unified model is less than that of the discrete model.

Singularly perturbed unified systems with low sensitivity to model reduction

A method of designing a state feedback gain achieving a specified insensitivity of the closed-loop trajectory by the singularly perturbed unified system using the delta operators is proposed. The order of system is reduced by the singular perturbation technique by ignoring the fast mode in it. The proposed method takes care of the actual trajectory variations over the range of the singular perturbation parameter. Necessary conditions for optimality are also derived. The previous study was done in the continuous time system. The present paper extends the previous study to the discrete system and the delta operating system that unifies the continuous and discrete systems. Advantages of the proposed method are shown in the numerical example.

Rationalization of singularly perturbed continuous systems with time delays

The state equation of a continuous time system with time delay is nonlinear. Therefore, its transfer function is irrational, which is difficult to solve. However, the transfer function of a discrete time state equation with time delay is rational. Hence, the problem can be solved easily. A rationalization of the singularly perturbed continuous system of single and multiple time delays is presented by setting a delay coefficient. The technique is a powerful tool when solving the singularly perturbed continuous equation with single and multiple time delays instead of when using numerical methods such as the Runge-Kutta algorithm.

H∞ CONTROLLER DESIGN FOR SINGULARLY PERTURBED SYSTEMS BY DELTA OPERATOR APPROACH

Abstract This paper presents a standard H∞ controller design for singularly perturbed systems with frequency domain by unified approach using the delta operators. Decomposition of the singularly perturbed systems into the fast and slow subsystems is shown. And the delta operator approach is implemented to improve a finite word-length (FWL) characteristics. The delta operator systems have the better FWL characteristics over the shift operator systems. The result is shown in the example.