scholarly journals Design of IIR Digital Filters with Arbitrary Flatness Using Iterative Quadratic Programming

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yasunori Sugita
Keyword(s):  
Transfer Function ◽  
Digital Filters ◽  
Design Method ◽  
Infinite Impulse Response ◽  
Linear Matrix ◽  
Linear Phase ◽  
Iir Filters ◽  
Matrix Equality ◽  
Iir Digital Filters ◽  
The Stability

This paper presents a design method of Chebyshev-type and inverse-Chebyshev-type infinite impulse response (IIR) filters with an approximately linear phase response. In the design of Chebyshev-type filters, the flatness condition in the stopband is preincorporated into a transfer function, and an equiripple characteristic in the passband is achieved by iteratively solving the QP problem using the transfer function. In the design of inverse-Chebyshev-type filters, the flatness condition in the passband is added to the constraint of the QP problem as the linear matrix equality, and an equiripple characteristic in the stopband is realized by iteratively solving the QP problem. To guarantee the stability of the obtained filters, we apply the extended positive realness to the QP problem. As a result, the proposed method can design the filters with more high precision than the conventional methods. The effectiveness of the proposed design method is illustrated with some examples.

Lth-Band Digital Filters

2009 ◽  
pp. 206-241
Author(s):  
Ljiljana Milic
Keyword(s):  
Transfer Function ◽  
Digital Filters ◽  
Intersymbol Interference ◽  
Transfer Functions ◽  
Sampling Rate ◽  
Angular Frequency ◽  
Efficient Implementation ◽  
Fir Filters ◽  
Linear Phase ◽  
Iir Filters

Digital Lth-band FIR and IIR filters are the special classes of digital filters, which are of particular interest both in single-rate and multirate signal processing. The common characteristic of Lth-band lowpass filters is that the 6 dB (or 3 dB) cutoff angular frequency is located at p/L, and the transition band is approximately symmetric around this frequency. In time domain, the impulse response of an Lth-band digital filter has zero valued samples at the multiples of L samples counted away from the central sample to the right and left directions. Actually, an Lth-band filter has the zero crossings at the regular distance of L samples thus satisfying the so-called zero intersymbol interference property. Sometimes the Lthband filters are called the Nyquist filters. The important benefit in applying Lth band FIR and IIR filters is the efficient implementation, particularly in the case L = 2 when every second coefficient in the transfer function is zero valued. Due to the zero intersymbol interference property, the Lth-band filters are very important for digital communication transmission systems. Another application is the construction of Hilbert transformers, which are used to generate the analytical signals. The Lth-band filters are also used as prototypes in constructing critically sampled multichannel filter banks. They are very popular in the sampling rate alteration systems as well, where they are used as decimation and interpolation filters in single-stage and multistage systems. This chapter starts with the linear-phase Lth-band FIR filters. We introduce the main definitions and present by means of examples the efficient polyphase implementation of the Lth-band FIR filters. We discuss the properties of the separable (factorizable) linear-phase FIR filter transfer function, and construct the minimum-phase and the maximum-phase FIR transfer functions. In sequel, we present the design and efficient implementation of the halfband FIR filters (L = 2). The class of IIR Lth-band and halfband filters is presented next. Particular attention is addressed to the design and implementation of IIR halfband filters. Chapter concludes with several MATLAB exercises for self study.

scholarly journals Suboptimal Disturbance Observer Design Using All Stabilizing Q Filter for Precise Tracking Control

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1434 ◽  
Author(s):  
Wonhee Kim ◽  
Sangmin Suh
Keyword(s):  
Design Method ◽  
Industrial Applications ◽  
Point Of View ◽  
Observer Design ◽  
Linear Matrix ◽  
External Disturbances ◽  
Closed Loop Systems ◽  
Control Target ◽  
The Stability ◽  
Unified Index

For several decades, disturbance observers (DOs) have been widely utilized to enhance tracking performance by reducing external disturbances in different industrial applications. However, although a DO is a verified control structure, a conventional DO does not guarantee stability. This paper proposes a stability-guaranteed design method, while maintaining the DO structure. The proposed design method uses a linear matrix inequality (LMI)-based H∞ control because the LMI-based control guarantees the stability of closed loop systems. However, applying the DO design to the LMI framework is not trivial because there are two control targets, whereas the standard LMI stabilizes a single control target. In this study, the problem is first resolved by building a single fictitious model because the two models are serial and can be considered as a single model from the Q-filter point of view. Using the proposed design framework, all-stabilizing Q filters are calculated. In addition, for the stability and robustness of the DO, two metrics are proposed to quantify the stability and robustness and combined into a single unified index to satisfy both metrics. Based on an application example, it is verified that the proposed method is effective, with a performance improvement of 10.8%.

scholarly journals Secure Load Frequency Control of Smart Grids under Deception Attack: A Piecewise Delay Approach

Energies ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 2266 ◽  
Author(s):  
Fei Zhao ◽  
Jinsha Yuan ◽  
Ning Wang ◽  
Zhang Zhang ◽  
Helong Wen
Keyword(s):  
Smart Grids ◽  
Controller Design ◽  
Design Method ◽  
Frequency Control ◽  
Functional Method ◽  
Load Frequency Control ◽  
Linear Matrix ◽  
Load Frequency ◽  
The Stability

The problem of secure load frequency control of smart grids is investigated in this paper. The networked data transmission within the smart grid is corrupted by stochastic deception attacks. First, a unified Load frequency control model is constructed to account for both network-induced effects and deception attacks. Second, with the Lyapunov functional method, a piecewise delay analysis is conducted to study the stability of the established model, which is of less conservativeness. Third, based on the stability analysis, a controller design method is provided in terms of linear matrix inequalities. Finally, a case study is carried out to demonstrate the derived results.

GA-BASED DESIGN OF 2D STATE-SPACE DIGITAL FILTERS WITH LINEAR PHASE CHARACTERISTICS

2007 ◽  
Vol 16 (02) ◽  
pp. 287-303 ◽  
Author(s):  
SANG-CHURL NAM ◽  
MASAHIDE ABE ◽  
MASAYUKI KAWAMATA
Keyword(s):  
State Space ◽  
Design Problem ◽  
Digital Filters ◽  
Design Method ◽  
Design Procedure ◽  
Gray Code ◽  
Superior Performance ◽  
Magnitude Response ◽  
The Stability ◽  
Group Delays

This paper proposes a GA-based design method for two-dimensional (2D) state-space digital filters which satisfy simultaneously the magnitude response and constant group delays. The design problem of 2D state-space digital filters is formulated subject to the constraint that the resultant filters are stable. To apply the genetic algorithm to the design problem, all coefficients of 2D state-space digital filters are encoded into the Gray code representation demonstrating the superior performance to the standard binary one. In addition, a stability test routine is embedded in the design procedure in order to ensure the stability for the resultant filters. A numerical example is given to demonstrate the effectiveness of the proposed method.

Stability-Guaranteed Two-Phase Design of Odd-Order Variable-Magnitude Digital Filters

2016 ◽  
Vol 26 (02) ◽  
pp. 1750033
Author(s):  
Tian-Bo Deng
Keyword(s):  
Transfer Function ◽  
Digital Filter ◽  
Digital Filters ◽  
Tuning Parameter ◽  
Second Phase ◽  
Variable Model ◽  
Odd Order ◽  
Order Variable ◽  
The Stability ◽  
Fifth Order

Guaranteeing the stability is one of the most critical issues in designing a variable recursive digital filter. In this paper, we first present an odd-order recursive variable model (transfer function) that is used for designing an odd-order variable-magnitude (VM) digital filter, and then we replace the original coefficients of the denominator of the odd-order transfer function with a set of new parameters. These new parameters can ensure that they can take arbitrary values without incurring instability of the designed odd-order VM filter. To make the VM filter coefficients variable, we find all the VM filter coefficients as polynomial functions of the tuning parameter, which includes two phases. The first phase designs a set of recursive digital filters with fixed coefficients (constant filters), and the second phase utilizes a curve-fitting scheme to represent each coefficient as a polynomial function. As a result, the VM filter coefficients become variable, and the proposed parameter-substitution-based denominator coefficients ensure the filter stability. This is the most important contribution of the parameter-substitution-based design scheme. This paper uses the fifth-order demonstrative example to verify the stability guarantee as well as the design accuracy of the obtained the fifth-order VM filter.

Multiobjective Robust Regulating and Protecting Control for Aeroengines

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Daren Yu ◽  
Xiaofeng Liu ◽  
Wen Bao ◽  
Zhiqiang Xu
Keyword(s):  
Control Method ◽  
Design Method ◽  
Dynamic Performance ◽  
Switching Control ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Proportional Integral Derivative ◽  
Engine Control System ◽  
Switching Performance ◽  
The Stability

The multiobjective regulating and protecting control method presented here will enable improved control of multiloop switching control of an aeroengine. The approach is based on switching control theory, the switching performance objectives and the strategy are given, and a family of H∞ proportional-integral-derivative controllers was designed by using linear matrix inequality optimization algorithm. The simulation shows that using the switching control design method not only can improve the dynamic performance of the engine control system but also can guarantee the stability in some peculiar occasions.

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