• Title/Summary/Keyword: polynomial law

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Time-to-go Polynomial Guidance Law for Target Observability Enhancement (표적 가관측성 향상을 위한 Time-to-go 다항식 유도법칙)

  • Kim, Tae-Hun;Lee, Chang-Hun;Tahk, Min-Jea
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.39 no.1
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    • pp.16-24
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    • 2011
  • In this paper, we propose a new guidance law for target observability enhancement, which can control both terminal impact angle and acceleration. The proposed guidance law is simple form, combined conventional time-to-go polynomial guidance and a additional bias term which consists of relative position and proportional gain. The guidance law provides oscillatory flight trajectory and it maintains the conventional time-to-go polynomial guidance performance. To investigate the characteristics of the guidance law, we derive the closed-form solution, and various simulations are performed for proving the validity of the proposed guidance.

Nonlinear Backstepping Control of SynRM Drive Systems Using Reformed Recurrent Hermite Polynomial Neural Networks with Adaptive Law and Error Estimated Law

  • Ting, Jung-Chu;Chen, Der-Fa
    • Journal of Power Electronics
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    • v.18 no.5
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    • pp.1380-1397
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    • 2018
  • The synchronous reluctance motor (SynRM) servo-drive system has highly nonlinear uncertainties owing to a convex construction effect. It is difficult for the linear control method to achieve good performance for the SynRM drive system. The nonlinear backstepping control system using upper bound with switching function is proposed to inhibit uncertainty action for controlling the SynRM drive system. However, this method uses a large upper bound with a switching function, which results in a large chattering. In order to reduce this chattering, a nonlinear backstepping control system using an adaptive law is proposed to estimate the lumped uncertainty. Since this method uses an adaptive law, it cannot achiever satisfactory performance. Therefore, a nonlinear backstepping control system using a reformed recurrent Hermite polynomial neural network with an adaptive law and an error estimated law is proposed to estimate the lumped uncertainty and to compensate the estimated error in order to enhance the robustness of the SynRM drive system. Further, the reformed recurrent Hermite polynomial neural network with two learning rates is derived according to an increment type Lyapunov function to speed-up the parameter convergence. Finally, some experimental results and a comparative analysis are presented to verify that the proposed control system has better control performance for controlling SynRM drive systems.

Guidance Law for Vision-Based Automatic Landing of UAV

  • Min, Byoung-Mun;Tahk, Min-Jea;Shim, Hyun-Chul David;Bang, Hyo-Choong
    • International Journal of Aeronautical and Space Sciences
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    • v.8 no.1
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    • pp.46-53
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    • 2007
  • In this paper, a guidance law for vision-based automatic landing of unmanned aerial vehicles (UAVs) is proposed. Automatic landing is a challenging but crucial capability for UAVs to achieve a fully autonomous flight. In an autonomous landing maneuver of UAVs, the decision of where to landing and the generation of guidance command to achieve a successful landing are very significant problem. This paper is focused on the design of guidance law applicable to automatic landing problem of fixed-wing UAV and rotary-wing UAV, simultaneously. The proposed guidance law generates acceleration command as a control input which derived from a specified time-to-go ($t_go$) polynomial function. The coefficient of $t_go$-polynomial function are determined to satisfy some terminal constraints. Nonlinear simulation results using a fixed-wing and rotary-wing UAV models are presented.

SynRM Servo-Drive CVT Systems Using MRRHPNN Control with Mend ACO

  • Ting, Jung-Chu;Chen, Der-Fa
    • Journal of Power Electronics
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    • v.18 no.5
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    • pp.1409-1423
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    • 2018
  • Compared with classical linear controllers, a nonlinear controller can result in better control performance for the nonlinear uncertainties of continuously variable transmission (CVT) systems that are driven by a synchronous reluctance motor (SynRM). Improved control performance can be seen in the nonlinear uncertainties behavior of CVT systems by using the proposed mingled revised recurrent Hermite polynomial neural network (MRRHPNN) control with mend ant colony optimization (ACO). The MRRHPNN control with mend ACO can carry out the overlooker control system, reformed recurrent Hermite polynomial neural network (RRHPNN) control with an adaptive law, and reimbursed control with an appraised law. Additionally, in accordance with the Lyapunov stability theorem, the adaptive law in the RRHPNN and the appraised law of the reimbursed control are established. Furthermore, to help improve convergence and to obtain better learning performance, the mend ACO is utilized for adjusting the two varied learning rates of the two parameters in the RRHPNN. Finally, comparative examples are illustrated by experimental results to confirm that the proposed control system can achieve better control performance.

Application of Kelvin's approach for material structure of CNT: Polynomial volume fraction law

  • Hussain, Muzamal
    • Structural Engineering and Mechanics
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    • v.76 no.1
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    • pp.129-139
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    • 2020
  • In this piece of work, carbon nanotubes motion equations are framed by Kelvin's method. Employment of the Kelvin's method procedure gives birth to the tube frequency equation. It is also exhibited that the effect of frequencies is investigated by varying the different index of polynomial function. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped, simply supported-simply supported and these frequency curves are higher than that of clamped-free curves. Computer software MATLAB is utilized for the frequencies of single-walled carbon nanotubes.

Generalized Guidance Law with Control Time Constraint for Exoatmospheric Target Interception (외기권 표적 요격을 위한 제어시간 구속조건을 가지는 일반화된 유도법칙)

  • Park, Bong-Gyun;Kim, Tae-Hun
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.46 no.10
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    • pp.814-822
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    • 2018
  • This paper proposes a guidance law for missiles with control time constraint. Because the proposed guidance law is based on a time-to-go polynomial, it has a generalized form. Also, acceleration of the proposed law converges to zero at the end of the control time, which reduces the sensitivity to the time-to-go estimation error and can increase the flight stability when the separation of the missile appears. A prediction method of the time-to-go is proposed for implementing the proposed law, and the possibility of application to the midcourse and terminal guidance phases is dealt with for exoatmospheric interception. The characteristics and performance of the proposed law are analyzed throughout various simulations.

Target Observability Analysis of Time-to-go Polynomial Guidance Law (Time-to-go 다항식 유도 법칙의 표적 가관측성 분석)

  • Lee, Chang-Hun;Kim, Tae-Hun;Tahk, Min-Jea
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.38 no.7
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    • pp.664-672
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    • 2010
  • This paper provides the target observability analysis of time-to-go polynomial guidance law with bearing-only measurement. In this study, a direct approach is used to analyze the target observability. Since the observability condition of a constant-velocity target is given by the function of LOS angle only, the target observability characteristic is determined by substituting the closed form solution of LOS angle to the observability condition directly. The analysis results show that the target observability is depended on the choice of guidance gain, initial intercept condition and guidance command shape. After that this mathematical analysis result is evaluated and demonstrated by number of simulation.

Vibration of SWCNTs: Consistency and behavior of polynomial law index with Galerkin's model

  • Khadimallah, Mohamed A.;Hussain, Muzamal;Khedher, Khaled Mohamed;Bouzgarrou, Souhail Mohamed;Al Naim, Abdullah F.;Naeem, Muhammad Nawaz;Taj, Muhammad;Iqbal, Zafar;Tounsi, Abdelouahed
    • Advances in nano research
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    • v.9 no.4
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    • pp.251-261
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    • 2020
  • In this article, vibration attributes of single walled carbon nanotubes based on Galerkin's method have been investigated. The influence of power law index subjected to different end supports has been overtly examined. Application of the Hamilton's variational principal leads to the formation of partial differential equations. The effects of different physical and material parameters on the fundamental frequencies are investigated for armchair and zigzag carbon nanotubes with clamped-clamped, simply supported and clamped-free boundary conditions. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of Single-Walled Carbon Nanotubes (SWCNTs) are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. MATLAB software package has been utilized for extracting tube frequency spectra. The obtained results are confirmed by comparing with available literature.

Study of Time-to-go Polynomial Guidance Law with Considering Acceleration Limit (가속도 제한을 고려한 Time-to-go 다항식 유도 법칙 연구)

  • Lee, Chang-Hun;Kim, Tae-Hun;Tahk, Min-Jea
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.38 no.8
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    • pp.774-780
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    • 2010
  • This paper deals with the choice of guidance gain for the time-to-go polynomial (POLY) guidance law when the acceleration limit is existed. POLY is derived based on the assumption that guidance commands are formed by a time-to-go polynomial function. The main characteristic of POLY is that any positive values can be used for its guidance gain. For this reason, it is ambiguous to choose a proper guidance gain. To relieve this difficulty, we firstly derive the closed-form solution of acceleration command and figure out the relationship between the maximum acceleration and guidance gain. From this analysis, we provide a guideline for choosing a guidance gain which satisfies the desired acceleration limit. Finally, the proposed method is demonstrated by simulation study.

Optimization-Based Determination of Apollo Guidance Law Parameters for Korean Lunar Lander (달착륙 임무를 위한 최적화 기반 아폴로 유도 법칙 파라미터 선정)

  • Jo, Byeong-Un;Ahn, Jaemyung
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.45 no.8
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    • pp.662-670
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    • 2017
  • This paper proposes an optimization-based procedure to determine the parameters of the Apollo guidance law for Korean lunar lander mission. A lunar landing mission is formulated as a trajectory optimization problem to minimize the fuel consumption and the reference trajectory for the lander is obtained by solving the problem in the pre-flight phase. Some parameters of the Apollo guidance, which are coefficients of the polynomial used to define the guidance command, are selected based on the reference trajectory obtained in the pre-flight phase. A case study for the landing guidance of Korean lunar lander mission using the proposed procedure is conducted to demonstrate its effectiveness.