Strict Positive Real Property Research Articles

보의 진동제어를 위한 압전 액추에이터의 길이변화 효과 연구

This paper presents an approach to define an optimal piezoactuator length to actively control structural vibration. The optimal ratio of the piezoactuator length against the beam length when a pair of piezoceramic actuator and accelerometer is used to suppress unwanted vibration with direct velocity feedback(DVFB) control strategy is not clearly defined so far. It is well known that DVFB control can be very useful when a pair of sensor and actuator is collocated on structures with a high gain and excellent stability. It is considered that three different collocated Pairs of piezoelectric actuators (20, 50 and 100 mm long) and accelerometers installed on three identical clamped-clamped beams(<TEX>$30{\times}20{\times}1mm$</TEX>). The response of each sensor-actuator pair requires strictly positive real(SPR) property to apply a high feedback gain. However the length of the piezoactuator affects the SPR property of the sensor-actuator response. Intensive simulation and experiment show the effect of the actuator length variation is strongly related with the frequency range of the SPR property. Thus an optimal length ratio was suggested to obtain relevant performance with a good stability under the DVFB strategy.

A New Active Noise Control Algorithm That Requires No Secondary Path Identification Based on the SPR Property

Active noise control (ANC) has been widely applied in industry to reduce environmental noise and equipment vibrations. Most available control algorithms require the identification of the secondary path, which increases the control system complexity, contributes to an increased residual noise power, and can even cause the control system to fail if the identified secondary path is not sufficiently close to the actual path. In this paper, based on the geometric analysis and the strict positive real (SPR) property of the filtered-x LMS algorithm, we introduce a new ANC algorithm suitable for single-tone noises as well as some specific narrowband noises that does not require the identification of the secondary path, though its convergence can be very slow in some special cases. We are able to extend the developed ANC algorithm to the case of active control of broadband noises through our use of a subband implementation of the ANC algorithm. Compared to other available control algorithms that do not require secondary path identification, our developed method is simple to implement, yields good performance, and converges quickly. Simulation results confirm the effectiveness of our proposed algorithm

능동음향진동제어를 위한 센서와 액추에이터의 동위치화 연구

The problem considered in this paper is about the collocation of sensor and actuator for the active control of sound and vibration. It is well-known that a point collocated sensor-actuator pair offers an unconditional stability with very high performance when it is used with a direct velocity feedback (DVFB) control, because the pair has strictly positive real (SPR) property. In order to utilize this SPR characteristics, a matched piezoelectric sensor and actuator pair is considered. but this pair suffers from the in-plane motion coupling problem with the out-of-plane motion due to the piezo sensor and actuator interaction. This coupling phnomenon limits the stability and performance of the matched pair with DVFBcontrol. As a new alternative, a point sensor and distributed piezoelectric actuator pair is also considered, which provides SPR property in all frequency range when the pair is implemented on a clamped-clapmed beam. The use of this sensor-actuator pair is highly expected for the applications to more practical active control of sound and vibration systems with the DVFB control strategy.

SPR criteria for uncertain rational matrices via polynomial positivity and Bernstein's expansions

The main purpose of this brief is to convert the strict positive real (SPR) conditions for rational matrices to conditions involving only positivity of polynomials. The polynomial formulation provides efficient SPR criteria for matrices with uncertain interval parameters. To establish the robust SPR property, it is sufficient to test positivity of only three uncertain polynomials regardless of the order of the matrix. The most interesting feature of the proposed polynomial formulation is that the coefficients of uncertain matrices are allowed to have polynomic uncertainty structure. This generality is easily handled by using the Bernstein expansion algorithm. The efficiency of the proposed polynomial approach is illustrated by testing absolute stability of a MIMO Lur'e-Postnikov system having interval parameters.

Design of strictly positive real systems using constant output feedback

The authors present a linear matrix inequality (LMI) approach to the strictly positive real (SPR) synthesis problem: find an output feedback K such that the closed loop system T(s) is SPR. The authors establish that if no such constant output feedback K exists, then no dynamic output feedback with a proper transfer matrix exists to make the closed-loop system SPR. The existence of K to guarantee the SPR property of the closed-loop system is used to develop an adaptive control scheme that can stabilize any system of arbitrary unknown order and unknown parameters.

On the existence of robust strictly positive real rational functions

A new approach for the analysis of the strict positive real property of rational functions of the form H(s)=p(s)/q(g) is proposed. This approach is based on the interlacing properties of the roots of the even and odd parts of p(s) and q(s) over the imaginary axis. From the analysis of these properties, an algorithm to obtain p(s) such that p(s)/q(s) is strictly positive real (SPR) for a given Hurwitz q(s) is developed. The problem of finding p(s) when q(s) is an uncertain Hurwitz polynomial is also considered, using this new approach. An algorithm for obtaining p(s) such that p(s)/q(s) is SPR, when q(s) has parametric uncertainties, is presented. This algorithm is easy to use and leads to p(s) in cases where previously published methods fail.

Least squares identification and the robust strict positive real property

Certain problems of adaptive systems revolve round finding a transfer function q(s) (which is not proper) such that a set of transfer functions q(s)/b(s)- 1/2 is strictly positive real for all polynomial b(s) in a certain set. This paper treats this and some related problems. >

Strict positive realness of a family of polytopic plants

Some strict positive realness results for a family of polytopic plants are presented. More specifically, it is shown that the strict positive real property of such a family of plants can be ascertained from its vertex plants.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the strictly positive realness of Schur interval functions

Necessary and sufficient conditions for strictly positive realness of discrete-time interval functions, which may be associated in parameter space by a multidimensional boxed domain, are provided. Positive realness of interval functions are studied, and both necessary and sufficient conditions are provided for such functions to be strictly positive real (SPR) in the presence of interval variations of the function's parameters corresponding to a Kharitonov-type box domain. The number of checking functions that have to be tested for SPR property in order to establish the interval SPR property grows with the order of the interval function. These tests give both necessary and sufficient conditions for SPR. The approach presented for interval functions does not require the checking of all the vertices for unit circle positive realness. >