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The problem of sensor noise rejection in digital control systems with nonlinear plant is discussed. The design method based on the formation of two-time-scale motions in the closed loop system is used. It has been shown that if a sufficient time-scale separation between the fast and slow modes in the discussed closed loop system and stability of fast modes are provided then slow modes have the desired form. The relationships for the control law parameters calculation in accordance with the requirement to high-frequency noise rejection are obtained. Finally, an example with simulation results is presented.

In this paper, we address the dynamic modeling of reactive distillation processes, where the presence of fast reaction or momentum transport induces two time scale dynamics. We present a systematic modeling framework that allows identifying the source of time Scale multiplicity and deriving nonlinear non-stiff models of the slow dynamics.

The problems of the robust digital controller design and control accuracy analysis are discussed. The design method based on the formation of two-time scale motions in the closed loop system is used. If a sufficient time-scale separation between the fast and slow modes in the discussed closed loop system and stability of fast modes are provided then slow modes have the desired form. Thus the output transient performance indices are insensitive to external disturbances. The relationships for control accuracy analysis and choice of the sampling period are obtained. Finally, an example with simulation results is presented.

In this paper, the H 2 guaranteed cost output feedback control for uncertain singularly perturbed systems is addressed. The design procedure shows how the fullorder uncertain system can be stabilized for small value of G > 0 avoiding high dimensionality and ill-conditioning. It is shown that when necessary and sufficient conditions formulated for the slow and fast subsystems are satisified, a singularly perturbed controller which stabilizes the full-order system is obtained. The solution of the H 2 guaranteed cost problem is searched in the set of such two time scale controllers.

The problem of forming desired output transients for discrete-time system is discussed under assumption of incomplete information about varying parameters of the system and unknown external disturbances. The main result of the paper is the procedure to analyse of fast and slow motions in the discrete-time control system with small parameter where control system is designed by dynamic contraction method. It is shown, that if a sufficient time-scale separation between the fast and slow modes in the closed loop system and stability of fast motions are provided then in the closed loop system the output transient performance indices are insensitive to parameter variations of the plant and external disturbances. Finally, in order to guaranteed cost control an universal digital control law for a sampled-data system with small sampling period is received and numerical example is presented.

The indirect method of solving optimal control problems requires the solution of a Hamiltonian boundary-value problem (HBVP). Geometric properties of Hamiltonian systems and the notion of a dichotomy guide the development of a solution approach for HBVPs that involve two distinct time scales and boundary layers.

This paper concerns two-time-scale single-input single-output nonlinear processes. For such processes, we address and solve the problem of synthesizing well-conditioned state feedback control laws that induce a well-characterized input/output behavior and guarantee stability of the closed-loop system.

In the quarter car model, the active suspension with nonlinear characteristics is investigated. An active suspension model is made by two time scale modeling. Two models have relation to handling and the ride comfort respectively. A new control method that is based on the singular perturbation approach is proposed. Our control law for the full model combines with control laws for slow and fast submodels. The simulation shows that the new design approach is very useful.

A matrix norm condition is given under which the large eigenvalues of a two-time scale system will be sufficiently separated from the small eigenvalues. A feedback control design is proposed in which two gain matrices are used for separate placement of small and large eigenvalues.

This paper contains a brief discussion of various model simplification techniques currently available in the literature. The main intention is to highlight some of the unifying features of the different model simplification techniques. Directions for possible future research are also indicated.