• Journal of the Institute of Electronics Engineers of Korea SC
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• v.37 no.3
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• pp.33-43
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• 2000

The guarantee of the fast dynamics stability is essential for successful application of singular Perturbation technique to control systems design. Even though the fast dynamics of the control systems is rendered stable by an analog controller, the fast dynamics stability of the control systems resulted from an digital implementation of the analog controller can be impaired severely. In this paper, we first investigate the time sampling effects on singular perturbation based control systems by centering on a design example of recently developed singular perturbation based STT missile autopilot with high performance. The investigation shows that the stability margin the fast dynamics of the STT misile autopilot system decreases rapidly as the sampling interval of discretizing the analog autopilot increases. Under this analysis, we propose a composite digital controller with compensation for the decreasing stability margin of the fast dynamics due to time sampling to achieve better performance with respect to sampling time. The improved performance of the proposed composite digital controller is verified by simulation. This result shows that one needs to investigate time sampling effects in the digital implementation of singular perturbation based controllder, and then can have benefit from the investigation.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.6
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• pp.359-365
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• 2005

This paper presents an reduced-order near-optimal controller for the congestion control of Available Bit Rate (ABR) service in Asynchronous Transfer Mode (ATM) networks. We introduce the model, of a class of ABR traffic, that can be controlled using a Explicit Rate feedback for congestion control in ATM networks. Since there are great computational complexities in the class of optimal control problem for the ABR model, the near-optimal controller via reduced-order technique is applied to this model. It is implemented by the help of weakly coupling and singular perturbation theory, and we use bilinear transformation because of its computational convenience. Since the bilinear transformation can convert discrete Riccati equation into continuous Riccati equation, the design problems of optimal congestion control can be reduced. Using weakly coupling and singular perturbation theory, the computation time of Riccati equations can be saved, moreover the real-time congestion control for ATM networks can be possible.

• Journal of Power Electronics
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• v.17 no.4
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• pp.953-962
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• 2017

Momentum flywheels are widely applied for the generation of small and precise torque for the attitude control and inertial stabilization of satellites and space stations. Due to its inherited system nonlinearity, the tracking performance of the flywheel torque/speed in dynamic/plug braking operations is limited when a conventional controller is employed. To take advantage of the well-separated two-time-scale quantities of a flywheel driving system, the singular perturbation technique is adopted to improve the torque tracking performance. In addition, the composite control law, which combines slow- and fast- dynamic portions, is derived for flywheel driving systems. Furthermore, a novel control strategy for plug braking dynamics, which considers couplings between the Buck converter and the three-phase inverter load, is designed with easy implementation. Finally, experimental results are presented to demonstrate the correctness of the analysis and the superiority of the proposed methods.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.317-329
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• 2006

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.131-145
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• 2013

In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.32 no.2
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• pp.43-49
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• 1983

In this study, model simplification problem using singular perturbation technique is considered. The correctness and errors of simplified model which is obtained by the use of this technique, depends upon the order and the time scaling factor of the simplified model But, unfortunately, there is no explicit criteria for selections of these parameters. In this paper, error equations are derived and expanded by using the useful properties of $L_2$-norm. Then, new criteria for selecting the order of the simplified model and time scaling factor with respect to error bound are suggested. Since these criteria, newly proposed in this study, have strong concern about error bound, it can be used to choose the minimum order of the simplified model and time scaling factor with respect to given error bound. Conversely, if the order of the simplified model and time scaling factor are given, the error induced by the simplification can also be computed easily.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.12
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• pp.95-104
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• 1997

We consider controller design problem to enhance shift quality for automatic transmission. A dynamic modeling related to shifting (mainly 2-3 up-shift) is constructed and nonlinear robust controllers are designed to reduce output torque during shifting. Suggesting a new hydraulic circuit enabling the direct clutch drive, the control activity is extended and more implementable than the conventional design. The designed robust controllers overcome the unmodeled dynamics and the uncertainty embending in the system. Moreover, the dynamic effect between the clutch pressure and the PWM valve duty is considered via singular perturbation technique.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.353-353
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• 2000

To control a light weight flexible manipulator, a composite fuzzy controller is proposed. The controller is designed based on two time scaled models. A singular perturbation technique is applied for deriving the models. The proposed controller, however, does not use the complex equilibrium manifold equations, which are usually needed in the controller based on the two time scaled models. The controller for a slow sub-model and a fast sub-model are T-S type fuzzy controllers, which use 3 linguistic variables for each sub-model. A step trajectory is used in simulations as a reference trajectory of joint motions. The results of simulations with the proposed controller show excellent damping of flexible motions compared to a controller with derivative control of flexible motions.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.8
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• pp.726-732
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• 2005

This paper proposes an autolanding guidance and control algorithm with the lateral guidance law. This algorithm is basically formulated and designed in feedback linearization based on singular perturbation. Main features of this algorithm are two facts. One of those is that when a certain situation happens that airplane must realign to the runway suddenly assigned due to unexpected environment change around the landing site, the heading guidance in this algorithm is very valuable, and the other is the fact that the inner loop control of this algorithm is able to be designed directly based on the Handling Quality Requirements that most flight control systems must be satisfied with. To illustrate the potential of this algorithm, 6-DOF nonlinear simulation based on the nonlinear airplane model shown in Ref.[11] is carried out. The simulation results showed that the altitude response to the given landing trajectory is accurate, and the airplane heading alignment to the assigned runway from the lateral deviation is successful. It is noted that this algorithm is also applicable to unmanned aerial vehicle, which can be retrieved in autolanding technique, where the runway far retrieving the vehicle is in any direction for example at war field.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.3
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• pp.39-49
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• 2003

The delta operator approach and the singular perturbation technique are introduced. The former reduces the round-off error in the numerical computation. The latter reduces computing time by decoupling the original system into the fast and slow sub-systems. The aircraft dynamics consists of the Phugoid and short-period motions whether its model is longitudinal or lateral. In this paper, an approximated solutions of lateral dynamic model of Beaver obtained by using those two methods in compared with the exact solution. For open-loop system and closed-loop system, and approximated solution gets identical to the exact solution with only one iteration and without iteration, respectively. Therefore, it is shown that implementing those approaches is very effective in the flight dynamic and control.