• International Journal of Control, Automation, and Systems
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• v.6 no.6
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• pp.960-967
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• 2008

This paper shows that design of a robustly stable repetitive control system is equivalent to that of a feedback control system for an uncertain linear time-invariant system satisfying the well-known robust performance condition. Once a feedback controller is designed to satisfy the robust performance condition, the feedback controller and the repetitive controller using the performance weighting function robustly stabilizes the repetitive control system. It is also shown that we can obtain a steady-state tracking error described in a simple form without time-delay element if the robust stability condition is satisfied for the repetitive control system. Moreover, using this result, a sufficient condition is provided, which ensures that the least upper bound of the steady-state tracking error generated by the repetitive control system is less than or equal to the least upper bound of the steady-state tracking error only by the feedback system.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.5
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• pp.470-477
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• 1990

Singh's multi-level method is extended to the optimal tracking control of a large interconnected dynamical system which has coupled states and coupled inputs. The steady-state tracking error and a convergence condition for the extended multi-level method are derived analytically and the results show that the steady-state tracking error and a convergence rate have to be compromised. Also, a new multi-level method which is advantageous over the Singh's method in steady-state tracking error and computational burden is proposed by introducing nominal inputs into the performance index. The resulting feedback gain matrix and the compensation vector are optimal for all initial conditions so that eventual on-line computation is minimal.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.473-476
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• 1989

Quadratic weighting matrices have an effect on the transition and steady state responses in a LQ tracking problem. They are usually decided on trial and error in order to get a good response. In this paper a method is presented which calculates a steady - state deviation without solving Riccati equation. By using this method, a new procedure for selecting the weighting matrices is proposed when a tolerance on the steady - state deviation is given.

• Journal of Environmental Science International
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• v.4 no.1
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• pp.71-80
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• 1995

A discrete state space model for a multiple-reach river system is formulated using the dynamics of biochemical oxygen demand(BOD) and dissolved oxygen(DO). A hierarchical optimization technique, which is applicable to large-scale systems with time-delays in states, is also described to control stream quality in a river as an optimal manner based on the interaction prediction method. The steady state tracking error of the proposed method is determined analytically and a necessary and sufficient condition on which a constant target tracking problem has zero steady-state error is derived. Computer simulations for the river pollution model illustrate the algorithm.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.2
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• pp.101-105
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• 2006

Disk radial runout creates a periodic relative motion between the laser beam spot and tracks formed on an optical disk. While only focus control is activated, the periodic relative motion yields sinusoid-like waves in the tracking error signal, where one cycle of the sinusoid-like waves corresponds to one track. The frequency of the sinusoid-like waves varies depending on the disk rotational speed and the amount of the disk radial runout. If the frequency of the tracking error signal in the off-track state is too high due to large radial runout of the disk, it is not a simple matter to begin track-following control stably. It might take a long time to reach a steady state or tracking control might fail to reach a stable steady state in the worst case. This article proposes a simple method for reducing the relative motion caused by the disk radial runout in the off-track state. The relative motion in the off-track state is effectively reduced by a drive input obtained through measurements of the tracking error signal and simple calculations based on the measurements, which helps reduce the transient response time of the track-following control. The validity of the proposed method is verified through an experiment using an optical disk drive.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.04a
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• pp.64-69
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• 2004

The work presented here deals with controller design using error model constructed with proportional control ramp response. The design aims at the improvement of transient response, steady-state error reduction with stability preservation, generation of the consistent contour error through the proportional gain regulation of a mismatched system. The first step is to generate tracking-error curve with proportional control only and decide the added error signal shape on the error curve. The next is to construct a table for the steady-state loop gain with step input. The table is used for selecting the proportional gain. The effectiveness of the proposed controller is confirmed through the simulation and experiment.

• The Journal of the Korea institute of electronic communication sciences
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• v.17 no.5
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• pp.859-866
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• 2022

Active disturbance rejection control is a method in which the disturbance is removed from the controller by estimating the state variable using the Luenberger observer. The Luenberger observer is estimated by defining a nonlinear term including disturbance with constant characteristics in a steady state as a state variable. It can be shown that the speed tracking performance is improved by compensating the estimated state variable to the PI controller and the IP controller. The disturbance removal performance of the tracking control can be confirmed by observing that the estimated state error is within 1.9 [%] in the case of load fluctuation and the steady-state state tracking error converges to zero.

• Journal of Drive and Control
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• v.13 no.3
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• pp.24-31
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• 2016

The performance characteristics of a dynamic control system are evaluated according to the transient and steady-state responses. The transient performance is the controllability of the output for the tracking of the reference or the ability to reduce or reject the effects of unwanted disturbances; alternatively, the steady-state performance is represented by the magnitude of the control error at the steady state. As the effects of the two performances on each other are reciprocal, a controller design that shows a zero steady-state error for the ramp input is uncommon because of the challenge regarding the achievement of an acceptable transient response. This paper proposes a PI+double-integral controller for the elimination of the steady-state error for the ramp input while a sound transient performance is maintained. The control-gain design procedure is described by the second-order response for the step input and the response of the error dynamics for the ramp input. The PI+double-integral controller is designed for the first-order transfer function that is derived from a system identification with the open-loop experiment data of the dc-motor. The simple structure of the proposed controller enables the adoption of a low-end microcontroller for the implementation of a real-time control. The experiment results show that the control performance is as effective as that of the simulation analysis for the operating point of linear system; furthermore, the PI+double-integral controller can be conveniently applied to the control system, which is desirable for the improvement of the steady-state error.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.8
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• pp.71-78
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• 2006

When a tracking filter may be designed in the Cartesian coordinate, the covariance of the measurement errors varies according to the range and the bearing of an interested target. In this paper, interacting multiple model based tracking filter is formulated in the Cartesian coordinate utilizing the analytic solution of the steady state Kalman filter, which can be able to consider the variation of the measurement error covariance. 100 Monte Carlo runs performed to verify the proposed method. The performance of the proposed method is compared with the conventional fixed gain and Kalman filter based IMM tracking filter in terms of the root mean square error. The simulation results show that the proposed approach meaningfully reduces the computation time and provides a similar tracking performance in comparison with the conventional Kalman filter based IMM tracking filter.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.12
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• pp.2189-2196
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• 2016

This paper proposes a new finite control set-model predictive control (FCS-MPC) method for induction motors. In the method, the reference state that satisfies the given torque and rotor flux requirements is derived. Cost indices for the FCS-MPC are defined using the state tracking error, and a linear matrix inequality is formulated to obtain a proper weighting matrix for the state tracking error. The on-line procedure of the proposed FCS-MPC comprises of two steps: select the output voltage vector of the two level inverter minimizing the cost index and compute the optimal modulation factor of the minimizing output voltage vector in order to reduce the state tracking error and torque ripple. The steady state tracking error is removed by using an integrator to adjust the reference state. The simulation and experimental results demonstrated that the proposed FCS-MPC shows good torque, rotor flux control performances at different rotating speeds.