English

This paper presents results from a follow-up study of fractional damping and time delay. Fractional damping has been used in the literature to demonstrate certain advantages over integer-order damping in many applications involving viscoelastic characteristics. It is observed that fractional damping can be used to influence stability boundaries, natural frequencies and vibration amplitudes, thus providing modeling flexibility in predicting the response of an isolated system during preliminary design. Additionally, time delay or lag is known to be inherent in a damped system, therefore a direct representation of time delay in modeling the damping force is expected to enhance model fidelity. This paper investigates the use of Voigt and Maxwell-Voigt models that incorporate fractional damping and time delay. In this paper, fractional damping has been particularly introduced to investigate possible improvements in the frequency response. Results indicate that fractional damping can be used to significantly enhance the capability of the Voigt model. The influence of the fractional order is found to be analogous to the damping ratio in an integer-order model. Fractional order is seen to exhibit a somewhat limited influence on the Maxwell-Voigt model. However, attributes such as the peak frequency and maximum amplitude are seen to be directly influenced by the fractional order. Although time delay is seen to exhibit an influence on the frequency response, it needs to be limited within useful bounds. Overall, it is observed that fractional order and time delay can be used to improve the accuracy of the Voigt and Maxwell-Voigt models. These enhanced models can be used for the design and development of elastomeric isolators and vibration isolation systems.

related to the use of Fractional-order (FO) differential equations in modeling and control. FO differential equations are found to provide a more realistic, faithful, and compact representations of many real world, natural and manmade systems. FO controllers, on the other hand, have been able to achieve a better closed-loop performance and robustness, than their integer-order counterparts. In this paper, we provide a systematic and rigorous time and frequency domain analysis of linear FO systems. Various concepts like stability, step response, frequency response are discussed in detail for a variety of linear FO systems. We also give the state space representations for these systems and comment on the controllability and observability. The exercise presented here conveys the fact that the time and frequency domain analysis of FO linear systems are very similar to that of the integer-order linear systems.

This paper proposes a new method named as impedance steering to improve the frequency response of the AC coupled instrumentation amplifier (IA) which is widely used for processing of biomedical (BM) signals. The method makes use of steering a high impedance in chain of resistors used at the input of IA with balanced AC coupling to achieve very high impedance during amplification of the input voltage. This results in uniform frequency response even at the lower frequencies which is major concern for processing of BM signals. This impedance steering technique can be used at input of any IA to construct a standalone amplification system for BM signals. However, in many applications, the output of IA is digitized using high resolution A/D conversion. A new method named a synchronized sampling and A/D conversion has been proposed in this paper for such applications. This method makes use of sampling and digitization of the signal which is synchronized with the process of steering the impedances to obtain high performance AC coupled BM signal processing system. The circuit has been designed and simulated using NI Multisim software, version 12. The results obtained using this method confirms the efficacy of the method for obtaining high performance signal processing required for BM signal applications. Though the system is preliminary designed for BM application, it can be used for wide range of signal processing.

In this paper, analysis of fractional order passive RC low-pass filter circuit is presented. The time domain behaviors were expressed for different values of fractional order α. The output of fractional order low-pass filter for order α has been simulated by MATLAB software. The effect of fractional order α on frequency response is represented as simulation results. The design of these filters using an approximation of the fractional Laplacian operator is outlined. A fractance device of order α which uses usual expression sα is analyzed and presented using continuous fraction expansion (CFE) method. The fractional order operator α is rationalized approximately by using different methods (Oustaloup, Newton and CFE method) and is presented and compared with the ideal response of the filter circuit. The fractional order circuits have better design flexibility than the integer-order circuits. The performance of integer-order circuit is improved by the replacement of fractional component as it has greater degree of freedom.

The effects of electrical vestibular stimulation upon movement and perception suggest two evoked sensations: head roll and inter-aural linear acceleration. The head roll vector causes walking subjects to turn in a direction dependent on head pitch, requiring generation of torque around a vertical axis. Here the effect of vestibular stimulation upon vertical torque (T(z)) was investigated during quiet stance. With the head tilted forward, square-wave stimuli applied to the mastoid processes evoked a polarity-specific T(z) response accompanied by trunk yaw. Stochastic vestibular stimulation (SVS) was used to investigate the effect of head pitch with greater precision; the SVS–T(z) cross-correlation displayed a modulation pattern consistent with the head roll vector and this was also reflected by changes in coherence at 2–3 Hz. However, a separate response at 7–8 Hz was unaffected by head pitch. Head translation (rather than rotation) had no effect upon this high frequency response either, suggesting it is not caused by a sense of body rotation induced by an inter-aural acceleration vector offset from the body. Instead, high coherence between medio-lateral shear force and T(z) at the same frequency range suggests it is caused by mechanical coupling to evoked medio-lateral sway. Consistent with this explanation, the 7–8 Hz response was attenuated by 90 deg head roll or yaw, both of which uncouple the inter-aural axis from the medio-lateral sway axis. These results demonstrate two vertical torque responses to electrical vestibular stimulation in standing subjects. The high frequency response can be attributed to mechanical coupling to evoked medio-lateral sway. The low frequency response is consistent with a reaction to a sensation of head roll, and provides a novel method for investigating proprioceptive-vestibular interactions during stance.

This paper presents optimization of fractional order Butterworth filter using a meta-heuristic algorithm. Interior Search Algorithm is used for the algorithm, and performance is compared with the existing optimization technique which is simulated annealing. Global best is calculated using the algorithm for calculating the coefficient for the transfer function, optimizing it using the fitness function. The results are verified with Tow Thomas fractional order filter using Pspice, using an approximated fractional capacitor built using Carlson’s method to obtain the Fractional Order Filter. MATLAB and Pspice results were utilized to calculate the coefficients of the transfer function of the fractional order low pass filter.

Very low-frequency (VLF) communication signals of 15–25 kHz contaminate the transient electromagnetic (TEM) data. The notch filter or Butterworth filter is commonly used to suppress VLF noise in addition to synchronous detection of TEM data such as gating and stacking, while also introducing the TEM signal distortion around the VLF band. We propose a B-spline gating, which suppresses the VLF noise while integrating TEM data in the gate interval without any extra filter. B-spline gating is designed to ensure that the zeros of its amplitude frequency response (AFR) are located around VLF frequencies by optimizing the knot vector of the B-spline. It is available for various VLF frequencies. We apply B-spline gating to synthetic TEM data compared with rectangular gating and full-tapered gating, the AFRs of B-spline and full-tapered gating are 25 dB lower at high frequencies than rectangular gating, and the amplitude of B-spline is more reduced at VLF frequency than full-tapered gating; the standard error of the B-spline gates is reduced by >15% compared to the full-tapered gates. The field example from a TEM survey in the Inner Mongolia Autonomous Region of China shows that the amplitude of B-spline gating frequency response in late gates is reduced by about 20 dB at 24.1 kHz VLF than that of full-tapered gating, and the standard error is lower. It is concluded that B-spline gating can suppress VLF noise while following the normal decay of TEM signal without distortion.

Continuous time filter research has aided in the development of digital filters. To ensure that this chapter is comprehensive, the authors begin by providing an overview of continuous filter synthesis, which is accomplished using analogue components such as resistors, inductors, condensers, and even active components. This chapter establishes a connection between the theoretical introduction of various digital filters and their application in digital image processing for a variety of purposes. Authors will discuss stopband, passband, Butterworth filter, finite impulse filter and infinite impulse filter in this chapter. With numerous applications of digital image filters such as mean, median, Gaussian smoothing, conservation, Crimmins speckle removal and frequency filters.

A Suite of Interactive Programs for Teaching Computer Control

We present a new approach to teaching filter design. In the classroom, students see graphical design methods emphasizing relationships between poles/zeros and frequency response (e.g., Chebyshev pole locations, low-pass to band-pass mapping, and bilinear transformation). In lab, each student develops a MATLAB <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">®</sup> program, capable of designing analog or digital, low-pass/high-pass/band-pass/notch, and Butterworth or Chebyshev filters. Using a ¿bottom-up¿ approach, students write individual functions as topics are covered in class, thereby creating ¿student toolboxes¿ that make no use of inherent MATLAB filter design functions. Students then craft a ¿main program¿ to implement filter design logic by calling their (tested) lower level functions. Finally, students use their programs to filter individually corrupted music files. Students design a digital filter to remove that band-limited noise, while preserving music fidelity, in an iterative process, exploring tradeoffs between maximum passband attenuation, minimum stopband attenuation, filter type, passband and stopband cutoffs, filter order and fidelity. Using graphical techniques, along with bottom-up program development, provides significant insight into fundamental tradeoffs in the filter design process not attainable through design by table lookup or inherent MATLAB function calls. Furthermore, feedback suggests the final design project is very gratifying and unites theory and real world design.

PID controllers are essential for industrial and academic studies. A robust performance and an easy design of PID controllers have gained them a wide spread usage and they have been utilized over 90 percent of industrial implementation. In recent years, researches have been conducted on fractional order PID controllers that generalize the PID controller. Fractional order allows precise modeling and improvement of performance. However, in the conventional fractional order controller design, controller parameters are often determined by trial and error, and the load of the designer increases. This paper proposes a design method of optimal fractional order controller parameters. The proposed method utilizes frequency responses to design an optimal fractional order controller. The effectiveness of the proposed method is verified through the simulation result.

A digital discrete high-order fast bandpass filter on the TMS320F28377D processor for mobile robot navigation is developed and investigated. The application of the developed band-pass filter in beacon laser navigation systems is proposed in order to increase the speed of mobile robot coordinate computation when solving the fast convolution problem. A fast convolution algorithm based on a digital continuous band-pass Butterworth filter, which is optimal in terms of minimum computation time, is presented. The developed 22-order Butterworth filter is implemented on a digital signal processor TMS320F28377D using a double buffer with parallel recording and processing of data from ADC. The peculiarity of the bandpass filter implementation is its real-time operation for searching signals of navigation beacon lasers in a given frequency band. Two DMA direct memory access modules, CLA accelerator module of the TMS320F28377D processor are used to increase the speed of data processing. The correlation function calculated as a result of convolution of the original signal with the reference signal of a given frequency and filtered by a low-pass filter using the moving average method was obtained. The maximum of the calculated correlation function shows the time delay between the beginning of the beacon pulse transmission and the reception time at the photodiode. This delay time shows the azimuth to the beacon. Laser beacon system (LSM) for robot navigation has the following advantages compared to radio equipment: lower range measurement error, small size of optical systems compared to the size of radar antennas, and high angle resolution due to the narrow beam of sounding radiation. High noise immunity of LSM, including to deliberate interference, allows solving navigation tasks in conditions of suppression of global navigation systems (such as GPS and GLONASS), when the means of autonomous navigation cannot fully provide data to the robot control system. The convolution execution time on the TMS320F28377D processor is 1.8 ms.

Fractional order multifunction filter with 3 degrees of freedom

This study focuses on a piezo-actuated two-degrees-of-freedom (2-DOF) decoupled compliant micro-positioning stage driven by a novel compound bridge-type amplification mechanism embedded with Scott-Russell mechanism. According to the system identification, the transfer functions of two working directions are obtained. Both of the measured dynamic cross couplings between them are also lower than −40 dB, demonstrating that the single-input-single-output control strategy can be adopted reasonably. Based on the identified frequency response, a fractional order proportional-integral (FOPI) controller is designed for the 2-DOF compliant micro-positioning stage. Compared with the integer order proportional-integral (IOPI) controller using same parameters, the amplitude error of the FOPI controller is 2% lower than that of IOPI controller. Additionally, a fractional order zero phase error controller (FOZPETC) is designed by obtaining the inverse of the fractional order closed-loop system in a large frequency range. And the gain of the corrected control system is 1 in a wide frequency band to eliminate the phase error in the close-loop control system. Finally, using the compound control strategy of FOZPETC+FOPI, a series of trajectory tracking tests are carried out on the proposed novel 2-DOF compliant micro-positioning stage. All the experimental results prove that the designed controller can achieve good positioning and tracking performance of the micro-positioning stage, and confirm the effectiveness of the compound control strategy of FOZPETC+FOPI.

An optimal linear system approximation of nonlinear fractional-order memristor–capacitor charging circuit