A new structure for the design of wideband variable fractional-order FIR differentiators
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Differentiator
Wideband
Finite impulse response
Differentiator
Wideband
Finite impulse response
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The nano quadrotor is a nonlinear multi-input and multi-output system with strong coupling, which causes difficulties in control law design. In order to achieve a favorable performance, an extended state observer–based nonlinear cascade proportional–integral–derivative controller is proposed in this article. First, the nano quadrotor platform is built, and the dynamic model is established. Second, a novel and practical measuring method is given to obtain model parameters. Then, based on the active disturbance rejection control method, the design procedure of the extended state observer–based nonlinear cascade proportional–integral–derivative controller is presented. In the developed controller, a tracking differentiator is involved to extract the signals of gyroscope, and extended state observer is used to estimate the disturbance. To obtain a better performance of tracking differentiator and extended state observer, a systematic parameter-tuning method is studied. Finally, simulation results are given to demonstrate the efficiency of the proposed controller.
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Optimum (in a minimax relative error sense) linear phase FIR digital differentiators can be designed in an efficient manner using a Remez optimization procedure. This paper presents data on wideband differentiators designed with even and odd values of N, the filter impulse response duration in samples. Based on these data, several interesting observations can be made, including: (i) Differentiators with even values of N have peak relative errors which are approximately one to two orders of magnitude smaller than identical bandwidth differentiators with odd values of N, and with the same number of multiplications per sample in a direct convolution realization. (ii) The smaller the bandwidth of the differentiator, the faster the decrease of the peak relative error with increasing N. (iii) The larger the value of N, the faster the decrease of the peak relative error with decreasing bandwidth. These observations lead to the conclusions that the bandwidth of a differentiator should be made as small as possible, and that even values of N should be used whenever possible. Complete tables of values of the impulse response coefficients are included for several wideband differentiators for even and odd values of N.
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Finite impulse response
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This study proposes a finite-time dynamic surface control (DSC) combined with a nonlinear differentiator disturbance observer for nonlinear systems, in which dynamics are partially known. The nonlinear differentiator disturbance observer, virtual stabilizing controllers, and final controller were designed based on finite-time convergent theorem via the recursive steps in conventional DSC system. In conclusion, the study results show that the filtered output error due to the first-order filter in a conventional DSC, which is the source of controller design complexity and stability, can be bypassed; this is because stability is provided by a finite-time Lyapunov function comprised of newly defined variables instead of the tracking error variables used in conventional DSCs. Thus, the controller design procedure and stability analysis can be more intuitive than those of a conventional DSC. Another important study result is the design of a nonlinear differentiator disturbance observer for nonlinear systems to estimate uncertainty in finite-time. The study shows that very competitive results can be achieved using the proposed method, as shown by the simulation results for an articulated manipulator system.
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Abstract The cascade proportional‐integral‐derivative (PID) control method is widely used in power plant control field. In this paper, an active disturbance rejection control (ADRC) for a power plant with a single loop is introduced for eliminating the shortcomings of the cascade PID control method. The proposed controller based on the ADRC method consists of a tracking differentiator (TD), an extended state observer (ESO) and a nonlinear combination of errors. In this approach, the processes with higher orders, uncertainties and unmodeled dynamics are viewed as lower‐ordered systems with general disturbances, and the general disturbances are estimated by ESO, and then actively compensated. Besides, only one measured output is needed in the proposed method instead of two or three in the cascade PID control method. Some simulation studies compared with the regular cascade PID control method show the proposed method has better performance beyond the regular cascade PID control method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society
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In this correspondence, the design of variable maximally linear (VML) FIR differentiators by least-squares method is proposed. The VML differentiator is designed such that its maximally flat frequency is adjustable. The used transfer function is formulated in a variable frame, and the Farrow structure can be applied for the implementation of VML FIR differentiators. For comparison, the non-variable optimal design of maximally linear FIR differentiators is also proposed. The experiments show that the variable design indeed possesses the flat characteristics as the independent optimal design.
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In this brief, the problems of stability and tracking control for multimotor servomechanism with unmodeled dynamics are addressed by neural active disturbance rejection control. For realizing output feedback, an extended state observer based on high-order sliding mode (HOSM) differentiator is designed to estimate the unmeasured velocity. Moreover, HOSM differentiator is introduced to modify the traditional dynamic surface control method. The designed controller solves the contradiction between rapidness and overshoot, which comes from the traditional proportional-integral-derivative that deals with a large number of practical systems with unknown disturbances. In addition, unknown functions, including friction and disturbances, are approximated by Chebyshev neural networks (CNNs), in which adaptive laws are provided by Lyapunov method. Especially, steady state and transient performance of closed-loop system are maintained by performance function in theoretical analysis. Finally, extensive experimental results are provided to illustrate our proposed approach.
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Servomechanism
Overshoot (microwave communication)
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This paper introduces a structure for the realization of wide-band linear-phase finite-length impulse response (FIR) differentiators. It is based on multirate and frequency-response masking techniques. Examples show that this structure achieves computational savings between some 10% and 65% for bandwidths in the range between 0.9 pi and 0.98 pi in comparison with conventional linear-phase differentiators.
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Finite impulse response
Linear phase
Wideband
Impulse response
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Continuous Differentiator Based on Adaptive Second-Order Sliding-Mode Control for a 3-DOF Helicopter
A novel control scheme for the regulation and trajectory tracking in spite of external perturbations of the three degrees of freedom (3-DOF) helicopter is presented. The scheme allows reduced control effort, vibration reduction, and accurate tracking. The proposed approach combines a continuous differentiator with an adaptive super twisting controller. The differentiator provides state estimation, whereas the adaptive super twisting algorithm is chosen such that the gains of the controller are adapted to reduce the control effort and do not require the knowledge of the bounds of the uncertainties and perturbations. Furthermore, finite time convergence of the continuous differentiator to a neighborhood of the desired trajectory, allows to design independently controller and the differentiator, satisfying the principle of separation. Finally, the proposed control scheme is validated by experimental tests under external disturbances.
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3 Abstract: An ideal differentiator has a frequency response that is linearly proportional to frequency. Full Wideband differentiator has an anti-symmetric unit sample response. FIR approximations are preferred to IIR because of the stability and linear phase response offered. In this paper we consider the design of an FIR differentiator based on frequency sampling technique.
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Wideband
Finite impulse response
Linear phase
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