Time-domain Design Method Research Articles

Normalized Euclid Distance-Based Network Time-Domain Design Method and Its Application in Short-Pulse Differentiator

A time-domain design method for networks with an arbitrary time-domain response is proposed and applied to design a short-pulse differentiator. The proposed method is termed as WAM because it is actually a waveform approach method (WAM) based on the normalized Euclid distance (NED). The NED could naturally characterize the difference between the desired and actual time-domain signals, including their waveforms and amplitudes. The WAM enables the NED to approach zero by tuning the network parameter for the given network topology and thus the actual time-domain response approaches the desired time-domain response. Also, the WAM is utilized to design a short-pulse differentiator with both magnitude and phase responses. Both the theoretical and experimental results verify the feasibility and validity of the WAM.

An Efficient Approach for Stability Analysis and Parameter Tuning in Delayed Feedback Control of a Flying Robot Carrying a Suspended Load

This paper presents an accurate and computationally efficient time-domain design method for the stability region determination and optimal parameter tuning of delayed feedback control of a flying robot carrying a suspended load. This work first utilizes a first-order time-delay (FOTD) equation to describe the performance of the flying robot, and the suspended load is treated as a flying pendulum. Thereafter, a typical delayed feedback controller is implemented, and the state-space equation of the whole system is derived and described as a periodic time-delay system. On this basis, the differential quadrature method is adopted to estimate the time-derivative of the state vector at concerned sampling grid point. In such a case, the transition matrix between adjacent time-delay duration can be obtained explicitly. The stability region of the feedback system is thereby within the unit circle of spectral radius of this transition matrix, and the minimum spectral radius within the unit circle guarantees fast tracking error decay. The proposed approach is also further illustrated to be able to be applied to some more sophisticated delayed feedback system, such as the input shaping with feedback control. To enhance the efficiency and robustness of parameter optimization, the derivatives of the spectral radius regarding the parameters are also presented explicitly. Finally, extensive numeric simulations and experiments are conducted to verify the effectiveness of the proposed method, and the results show that the proposed strategy efficiently estimates the optimal control parameters as well as the stability region. On this basis, the suspended load can effectively track the pre-assigned trajectory without large oscillations.

Time Domain Optimization of Filters Used in a Loudspeaker Array for Personal Audio

This paper describes a time domain design method for calculating the coefficients of FIR filters used to drive a loudspeaker array for personal audio. A motivating application is to boost the television audio in a certain spatial region with the aim of increasing the speech intelligibility of the hearing impaired. As the array is of small size, superdirective beamforming is applied to increase the low and mid frequency directional performance of the radiator. The filters for such arrays have previously been designed one frequency at a time, leading to non-causal filters that require a modeling delay for real time implementation. By posing the filter optimization in the time domain, the filter responses can be causally constrained, and the optimization is performed once for all frequencies. This paper considers the performance of such filters by carrying out off-line simulations, firstly using the impulse responses of point sources in the free field, and then with the measured responses of a loudspeaker array in an anechoic chamber. The simulation results show how the time domain optimization allows the creation of filters with either a low order or a low modeling delay.

Optimal Proportional–Integral–Derivative Control of Time-Delay Systems Using the Differential Quadrature Method

This paper presents an accurate and computationally efficient time-domain design method for the proportional–integral–derivative (PID) control of first-order and second-order plants in the presence of discrete time delays. As time delays would generally deteriorate the achievable performance of the PID controllers, their effects should be thoroughly considered in the controller design and parameter tuning process. This paper is thereby motivated to propose a time-domain semi-analytical method for the parameter tuning and stability analysis of PID controllers of the time-delay systems. To facilitate this development, the transfer functions of the investigated plants associated with the PID controllers are first rewritten as linear periodic delayed differential equations (DDEs) in state-space form. Then, the differential quadrature method (DQM) is adopted to estimate the time derivative of the state-space function at each sampling grid point within a duration of the time delay by the weighted linear sum of the function values over the whole sampling grid points. In this way, the DDEs in the time-delay duration are discretized as a series of algebraic equations, and the transition matrix can be obtained by combining these discretized algebraic equations. Thereafter, the stability boundary can be determined and the optimal control gains are obtained by minimizing the largest absolute eigenvalue of the transition matrix. As the minimum problems are commonly solved by the gradient descent approaches, the analytical form of the gradient of the largest absolute eigenvalue of transition matrix with respect to the control gains is explicitly presented. Finally, extensive numeric examples are provided, and the proposed DQM is proven to be an accurate and computationally efficient way to tune the optimal control gains and estimate the stability region in the control gain space.

Time-Domain Design of Digital Compensators for PWM DC-DC Converters

A time-domain design method for the digital controller of pulsewidth modulation dc-dc converters was developed. The proposed approach is based on the fact that the closed-loop response of a digitally controlled system is largely determined by the first few samples of the compensator. This concept is used to fit a digital PID template to the desired response. The proposed controller design method is carried out in the time domain and, thus, bypasses errors related to the transformation from the continuous to discrete domain and to discretization. The method was tested by simulations and experimentally. Digital PID controllers for experimental buck- and boost-type converters were designed according to the proposed method and implemented on a TMS320LF2407 DSP core. The measured closed-loop attributes were found to be in good agreement with the design goals. The study was further expanded to investigate the possible realistic closed-loop performance that can be obtained from a system that is controlled by a PID template controller, as well as the stability boundaries of the proposed time-domain controller design approach. The results of the study delineate a normalized map of deviation from the target closed-loop performance goals possible for PID control of switch-mode converters and the areas in which the use of this control law is feasible.

Finite-difference time-domain method for design and analysis of microcavity - Coupled submicron-width waveguides

In this paper the finite-difference time-domain (FDTD) method is reviewed and then used to model and predict the geometric parameters used for the design of the device. The waveguide consists of a periodic array of air gap etched into a silicon (Si) strip on a silicon dioxide (SiO2) layer. The width and the depth of the grooves of the air gap (n = 1) as well as the length of the silicon layer (n = 3.4) are investigated. Using FDTD, the optical parameters are characterized. The effect of the air gap on the field profile distribution of the whole structure is calculated and performed in the range 0.09687 μm –1.55 μm. The field profile, and the response of the microcavity against frequency are calculated from sinusoidal sources. The spectral behavior of the structure is performed and its validity is verified by calculation of the reflectance spectra.

A new class of biorthogonal wavelet systems for image transform coding

We construct general biorthogonal Coifman wavelet systems, a new class of compactly supported biorthogonal wavelet systems with vanishing moments equally distributed for a scaling function and wavelet pair. A time-domain design method is employed and closed-form expressions for the impulse responses and the frequency responses of the corresponding dual filters are derived. The resulting filter coefficients are all dyadic fractions, which is an attractive feature in the realization of multiplication-free discrete wavelet transform. Even-ordered systems in this family are symmetric, which correspond to linear-phase dual filters. In particular, three filterbanks (FBs) in this family are systematically verified to have competitive compression potential to the 9-7 tap biorthogonal wavelet FB by Cohen et al., which is currently the most widely used one in the field of wavelet transform coding. In addition, the proposed FB's have much smaller computational complexity in terms of floating-point operations required in transformation, and therefore indicate a better tradeoff between compression performance and computational complexity.

A Comparison of Multivariable Time- And Frequency-Domain Design Methods for Power System Stabilisers including Links with Reported Field Trials

The paper describes a comparison of multivariable, frequency-domain and time-domain design methods to derive supplementary stabilising signals for a highly oscillatory electrical power system. A direct comparison of different multivariable design approaches is effected on the same power system for the first time. The direct Nyquist array (DNA) method is extended in its application to produce practical stabiliser structures not previously obtained by other multivariable design approaches. All of the controllers designed have been implemented in practice including the DNA extension which produces a stabiliser requiring the measurement of machine terminal quantities only. The different theoretical approaches are also shown to produce essentially the same stabilisers and this, combined with their practical realisability, is a unifying result which is both satisfying and worthwhile emphasising.