The exact and unique solution for phase-lead and phase-lag compensation

Intelligent Control & Syst. Eng. Center, Chinese Acad. of Sci., Beijing, China
IEEE Transactions on Education (Impact Factor: 0.84). 06/2003; 46(2):258 - 262. DOI: 10.1109/TE.2002.808279
Source: IEEE Xplore


Phase-lead and -lag compensation is one of the most commonly used techniques for designing control systems in the frequency domain, especially when the Bode diagram or root locus is used. In most cases, the graphic-based approximation or trial-and-error approach has been utilized in the design process. This paper presents the exact and unique solution to the design of phase-lead and phase-lag compensation when the desired gains in the magnitude and phase are known at a given frequency. It also gives the concise condition for determining the existence of single-stage lead or lag compensation.

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    • "4 . Design of the proposed first order compensator A first order compensator such as lag and lead com - pensators may be designed for the desired specifications ( Teixeira and Assuncao , 2002 ; Wang , 2003 ; Loh , et al . , 2004 ; Lee , 2005 ; Wang et al . "
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    • "In the last four decades, several other design methods [2] [3] [4] [5] [6] [7] [8] [9] have been proposed. Analytical design procedures have been developed for single continuous phase-lag and phase-lead compensa- tors [8] . However, there are no known non-trial-anderror design procedures for the four-parameter lag-lead compensators. "
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    ABSTRACT: The four-parameter lag-lead compensator design has received much attention in the last two decades. However, most approaches have been either trial-and-error or only for special cases. This paper presents a non-trial-and-error design method for four-parameter lag-lead compensators. Here, the compensator design problem is formulated into a polynomial function optimization problem and solved by using the recently developed sum-of-squares (SOS) techniques. This result not only provides a useful design method but also shows the power of the SOS techniques.
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    • "The analytical design procedures for single continuous phase-lag and phase-lead compensator have been given in several literatures, e.g. [8]. An analytical solving procedure is constructed for three-parameter lag-lead compensators in [9]. "
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    ABSTRACT: In this paper, we first give the analytical solution of the general lag-lead compensator design problem. Then, we show why a series of more than 5 phase-lead/phase-lag compensator cannot be solved analytically using the Galois Theory.
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