• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.3
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• pp.407-414
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• 1996

In this paper we consider the variable structure control for a class of discrete-time uncertain multivariable systems where the nominal system is linear. Discrete-time switching dynamics are introduced so that a new type of state trajectories called sliding mode may exist on the sliding surface by state feedback. The quantitative analysis for the matched uncertainties will show that every response of the system with the proposed switching dynamics is bounded within small neighborhoods of the state-space origin. Also, by the similarity transformation it will be shown that the eigenvalues of the closed-loop systems are composed of those of the subsystems which govern the range-space dynamics and null-space dynamics. It will be also shown that ideal sliding mode can be obtained in the absence of uncertainties due to one-step attraction to the sliding surface regardless of initial position of states. (author). 12 refs., 2 figs.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.49 no.3
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• pp.26-30
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• 2012

This paper presents the observer design method for discrete-time nonlinear systems with delayed output. It is shown that by considering a nonlinear term of error dynamics as an additional state variable, the discrete-time nonlinear error dynamics with time delay can be transformed into the discrete-time linear one with time delay. Sufficient conditions for existence of state observer are characterized by linear matrix inequalities. Finally, an illustrative example is given in order to show the effectiveness of our design method.

• Journal of Korea Society of Industrial Information Systems
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• v.16 no.4
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• pp.45-52
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• 2011

In the real-field of control cases for robot manipulators, there always exists a modeling error, which results the model has the uncertainties in its parameters and/or structure. In many modem applications, digital computers are extensively used to implement control algorithms to control such systems. The discretization of the nonlinear dynamic equations of such systems results in a complicated discrete dynamic equations. Therefore, it will be difficult to design a discrete-time controller to give good tracking performances in the presence of certain uncertainties. In this paper, a discrete-time sliding mode control algorithm for nonlinear and time varying robot manipulators with uncertainties is presented. Sufficient conditions for guaranteeing the convergence of the discrete-time SMC system are derived. As example simulations, the proposed SMC algorithm is applied to a two-link robotic manipulator with unknown dynamics. The results of the simulation indicate that the developed control scheme is effective in manipulators and electro-mechanical system control.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.4
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• pp.330-340
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• 2002

In this Paper. a non-linear approach to a design of model reference adaptive control is presented. The approach is demonstrated by a case study of a simple single-pole and no zero, linear, discrete-time plant. The essence of the idea is to generate a full non-linear model of the plant dynamics and the parameter adaptation dynamics as a gradient descent algorithm with respect to a Riemannian metric. It is shown how a Riemannian metric can be chosen so that the modelled plant dynamics do in fact match the true plant dynamics. The performance of the proposed scheme is compared to a traditional model reference adaptive control scheme using the classical sensitivity derivatives (Euclidean gradients) for the descent algorithm.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.12
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• pp.1610-1617
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• 1988

In this paper, a robust discrete-time adaptive control with compensation is proposed for single-input single-output discrete-time plants which have unmodeled dynamics. The stability of the overall system is studied using the conic sector stability theorems when a normalized constant gain parameter adaptation algorithm and a properly chosen compensation are used. An illustrative exmple shows that this compensation can also increase the parameter adaptation speed. And a method of compensation using the adaptive observation is also discussed.

• Smart Structures and Systems
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• v.20 no.4
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• pp.483-498
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• 2017

Real-Time Hybrid Simulation (RTHS) is a powerful and cost-effective dynamic experimental technique. To implement a stable and accurate RTHS, time delay present in the experiment loop needs to be compensated. This delay is mostly introduced by servo-hydraulic actuator dynamics and can be reduced by applying appropriate compensators. Existing compensators have demonstrated effective performance in achieving good tracking performance. Most of them have been focused on their application in cases where the structure under investigation is subjected to inputs with relatively low frequency bandwidth such as earthquake excitations. To advance RTHS as an attractive technique for other engineering applications with broader excitation frequency, a discrete-time feedforward compensator is developed herein via various optimization techniques to enhance the performance of RTHS. The proposed compensator is unique as a discrete-time, model-based feedforward compensator. The feedforward control is chosen because it can substantially improve the reference tracking performance and speed when the plant dynamics is well-understood and modeled. The discrete-time formulation enables the use of inherently stable digital filters for compensator development, and avoids the error induced by continuous-time to discrete-time conversion during the compensator implementation in digital computer. This paper discusses the technical challenges in designing a discrete-time compensator, and proposes several optimal solutions to resolve these challenges. The effectiveness of compensators obtained via these optimal solutions is demonstrated through both numerical and experimental studies. Then, the proposed compensators have been successfully applied to RTHS tests. By comparing these results to results obtained using several existing feedforward compensators, the proposed compensator demonstrates superior performance in both time delay and Root-Mean-Square (RMS) error.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.2
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• pp.112-124
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• 2004

A neural network based adaptive reconfigurable flight controller is presented for a class of discrete-time nonlinear flight systems in the presence of variations of aerodynamic coefficients and control effectiveness decrease caused by control surface damage. The proposed adaptive nonlinear controller is developed making use of the backstepping technique for the angle of attack, sideslip angle, and bank angle command following without two time separation assumption. Feedforward multilayer neural networks are implemented to guarantee reconfigurability for control surface damage as well as robustness to the aerodynamic uncertainties. The main feature of the proposed controller is that the adaptive controller is developed under the assumption that all of the nonlinear functions of the discrete-time flight system are not known accurately, whereas most previous works on flight system applications even in continuous time assume that only the nonlinear functions of fast dynamics are unknown. Neural networks learn through the recursive weight update rules that are derived from the discrete-time version of Lyapunov control theory. The boundness of the error states and neural networks weight estimation errors is also investigated by the discrete-time Lyapunov derivatives analysis. To show the effectiveness of the proposed control law, the approach is i]lustrated by applying to the nonlinear dynamic model of the high performance aircraft.

• Advances in nano research
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• v.15 no.1
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• pp.25-34
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• 2023

This paper investigates the dynamics and stability of steady states in a continuous and discrete-time single-mode laser system. By using an explicit criteria we explored the Neimark-Sacker bifurcation of the single mode continuous and discrete-time laser model at its positive equilibrium points. Moreover, we discussed the parametric conditions for the existence of period-doubling bifurcations at their positive steady states for the discrete time system. Both types of bifurcations are verified by the Lyapunov exponents, while the maximum Lyapunov ensures chaotic and complex behaviour. Furthermore, in a three-dimensional discrete-time laser model, we used a hybrid control method to control period-doubling and Neimark-Sacker bifurcation. To validate our theoretical discussion, we provide some numerical simulations.

• Wind and Structures
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• v.20 no.2
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• pp.169-189
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• 2015

To investigate the effects of "sudden change" of wind fluctuations on vehicle running performance, which is caused by the artificial discrete simulation of wind field, a three-dimensional vehicle model is set up with multi-body dynamics theory and the vehicle dynamic responses in crosswind conditions are obtained in time domain. Based on Hilbert Huang Transform, the effects of simulation separations on time-frequency characteristics of wind field are discussed. In addition, the probability density distribution of "sudden change" of wind fluctuations is displayed, addressing the effects of simulation separation, mean wind speed and vehicle speed on the "sudden change" of wind fluctuations. The "sudden change" of vehicle dynamic responses, which is due to the discontinuity of wind fluctuations on moving vehicle, is also analyzed. With Principal Component Analysis, the comprehensive evaluation of vehicle running performance in crosswind conditions at different simulation separations of wind field is investigated. The results demonstrate that the artificial discrete simulation of wind field often causes "sudden change" in the wind fluctuations and the corresponding vehicle dynamic responses are noticeably affected. It provides a theoretical foundation for the choice of a suitable simulation separation of wind field in engineering application.

• Journal for History of Mathematics
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• v.27 no.3
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• pp.197-210
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• 2014

Species like insects and fishes have, in many cases, non-overlapping time intervals of one generation and their descendant one. So the population dynamics of such species can be formulated as discrete models. In this paper various discrete population models are introduced in chronological order. The author's investigation starts with the Malthusian model suggested in 1798, and continues through Verhulst model(the discrete logistic model), Ricker model, the Beverton-Holt stock-recruitment model, Shep-herd model, Hassell model and Sigmoid type Beverton-Holt model. We discuss the mathematical and practical significance of each model and analyze its properties. Also the stability properties of stationary solutions of the models are studied analytically and illustratively using GSP, a computer software. The visual outputs generated by GSP are compared with the analytical stability results.