• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1741-1747
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• 2011

Though various techniques have been studied as a way of adjusting parameters of PID controllers, no perfect method of determining parameters is available to date. This paper proposes a new method for enhancing performance of PID controllers by using the characteristics of dual-input describing function (DIDF). In other words, if nonlinear elements with two inputs (DIDF) are connected in series to the plant, the critical point (-1+j0) for Nyquist stability theory can be moved to a position arbitrarily selected on the complex plane by determining necessary coefficients of the DIDF appropriately. This makes the application of the existing conventional PID parameter tuning methods a lot easier, and stability and robustness of the system are improved simultaneously due to the DIDF inserted.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.1
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• pp.168-175
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• 2010

The issue of rejecting periodic disturbances arises in various applications dealing with rotating machinery. A new method using DIDF (Dual-Input Describing Function) is presented for the rejection of periodic disturbances with uncertain frequency. This can be added to an existing feedback control system without altering the closed-loop system stability. The objective is to design a nonlinear compensator to secure specified oscillation amplitude and frequency which are the same as disturbances. We suggest two procedures to determine coefficients for DIDF's synthesis. The structure of the proposed DIDF is so simple that we can easily synthesize. A number of computer simulations were carried out to demonstrate the salient feature of the proposed DIDF compared to the conventional ones(that is, adaptive algorithms).

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.5
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• pp.644-650
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• 1998

In this paper , a state space model for flexible beam is presented using the assumed-modes approach. The state space equation is derived for a flexible beam in which one end is connected to a motor and is driven by a torque equation and the other end is free. Many of the transfer function proposed thus far use the torque to the flexible beam as the input and the tip deflection of the flexible beam as the output. The Technique for the analysis and synthesis of the dual-input describing function(DIDF) is introduced here and the construction of a non-linear compensator, based on this technique, is proposed. This non-linear compensator, properly connected in the direct path of a closed-loop linear or non-linear control system. The above non-linear network is used to compensate linear and non-linear systems for instability, limit cycles, low speed of response and static accuracy. The effectiveness of the proposed scheme is demonstrated through computer simulation and experimental results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.4
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• pp.509-518
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• 2014

Though various techniques have been studied as a way of adjusting parameters of PID controllers, no perfect method of determining parameters is available to date. Especially the deign of PID controller for unstable processes with dead time(UPWDT) is even more difficult due to various reasons. Generally the existing design procedures for UPWDT involve deriving formulas to meet gain and phase margin specifications, or using inner loop to stabilize UPWDT before applying PID controller. In this paper, the dual-input describing function(DIDF) method is proposed, by which the performance and robustness of the closed-loop system can be improved. The method is based on moving the critical point (-1+j0) of Nyquist stability to a new position arbitrarily selected on the complex plane. This can be done by determining appropriate coefficients of the DIDF. As a result, we can easily determine parameters of PID-type controller by using existing conventional tuning methods for stable or unstable systems. Simulation results are included to show the effectiveness of the proposed method.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.37 no.2
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• pp.130-137
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• 1988

The technique of dual-input describing function's synthesis is introduced and the construction of a nonlinear compensator, based on this technique, is proposed. A nonlinear compensator, describing a complex DIDF depending upon amplitude of the second sinusoidal input signal only, is also proposed, where the second sinusoidal input signal is supplied to the nonlinear compensator by external generator. This compensator, connected in a closed loop of the PI speed control of DC motor, can improve the speed response in view instability limit cycle, low speed response and disturbance of the dynamic shift of the Nyquist's critical point -1 + j O. It is verified theoretically that the improvement of speed response of DC motor using the proposed compensator is achieved by means of the dynamic shift of the Nyquist's critical point on the complex plane, and the speed characterstics of DC motor is to be tested through experiment for its performance.

• Journal of the Institute of Convergence Signal Processing
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• v.3 no.4
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• pp.49-56
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• 2002

In this paper, a new controller using non-linear compensator for position control is presented, which we can satisfy the given specifications more easily than the existing one. We suggest an improved PDFE(Integral with Proportional-Derivative-plus-Feedforward) controller by which both phase margin and bandwidth are controlled simultaneously in the controller design problem. Replacing the feed forward term in the PDFF system with a CDIDF(Complex Dual Input Describing Function), the desired phase margin is obtained without diminishing the bandwidth of the closed loop system. The effectiveness of the proposed controller is confirmed through simulations and experiments. As The results of these, we know that it is possible to adjust overall specifications by varying parameters in the improved PDFF system.