Design PID controllers for desired time-domain or frequency-domain response

Zhang, Weidong; Xi, Yugeng; Yang, Genke; Xu, Xiaoming

doi:10.1016/s0019-0578(07)60106-2

Cited by 37 publications

(29 citation statements)

References 10 publications

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“…The stability boundary locus divides the parameter plane (K p -K i plane) into stable and unstable regions, as shown in Fig 3. By choosing a test point within each region, the stable region which contains the values of stabilizing K p and K i parameters can be determined [8].…”

Section: Figure 3: Stability Boundary Locus For Pid Controllermentioning

confidence: 99%

“…The overall philosophy in the design procedure presented here is for the compensator to adjust the system's Bode phase curve to establish the required phase margin at the current gain-crossover frequency, without changing the system's magnitude curve at that particular frequency and without reducing the zero-frequency magnitude value [8,9]. The change or shift in the gain crossover frequency is a function of the amount of phase shift that must be added to satisfy the required phase margin.…”

Section: Lead Compensatormentioning

confidence: 99%

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Design and Implementation of PID Controller with Lead Compensator for Thermal Process

Pv¹

2013

IJCA

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PID controller is a conventional controller which uses the advantages of Proportional, derivative and Integral controllers for achieving satisfactory results. PID controller gives better results in the system response, like less overshoot, reduced settling time, less steady state error etc even for nonlinear processes, when perfectly tuned. To achieve more stability for the system, a lead compensator can also be added. Stability Boundary Locus method, a graphical method, is used for tuning the controller parameters, K p , K i and K d . This technique includes less mathematical calculations. The stability of the system can be analyzed very easily with the Stability Boundary plot and Bode Plot analysis.

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Section: Figure 3: Stability Boundary Locus For Pid Controllermentioning

confidence: 99%

Section: Lead Compensatormentioning

confidence: 99%

Design and Implementation of PID Controller with Lead Compensator for Thermal Process

Pv¹

2013

IJCA

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“…Hence, the extra internal stability condition in Eq. (18) can be used to ascertain the form of the decoupled process. This provides convenience for the controller design.…”

Section: Internal Stability Analysismentioning

confidence: 99%

“…On the basis of IMC theory, the controller element C i (s) of the ith loop is designed as the following form [18,19]:…”

Section: Design Of Pi/pid Controller For the Decoupled Processmentioning

confidence: 99%

Improvement on an inverted decoupling technique for a class of stable linear multivariable processes

Chen

Zhang

2007

ISA Transactions

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“…Zhang et al, 2002) are still being reported. Among them, tuning rules based on ultimate gains and ultimate periods (Ziegler and Nichols, 1942;Zhuang and Atherton, 1993) have several advantages over tuning rules based on specific process models.…”

mentioning

confidence: 99%

Analytic Expressions of Ultimate Gains and Ultimate Periods with Phase‐Optimal Approximations of Time Delays

2005

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R&D NOTET here are many tuning rules currently available for PI/PID controllers (Astrom and Hagglund, 1988;Seborg et al., 1989;O'Dwyer, 2003) and new tuning rules (e.g. Zhang et al., 2002) are still being reported. Among them, tuning rules based on ultimate gains and ultimate periods (Ziegler and Nichols, 1942;Zhuang and Atherton, 1993) have several advantages over tuning rules based on specific process models. For example, tuning rules based on the first order plus time delay model cannot be applied directly to the process, G(s)=1/(s+1) 6 . The process should be reduced to a first order plus time delay model before applying those tuning rules. On the other hand, tuning rules based on the ultimate gain and ultimate period can be applied without such a model reduction step. The classical Ziegler-Nichols tuning rule based on the ultimate gain and the ultimate period is often criticized for its oscillatory response. The tuning rule by Zhuang and Atherton (1993) relieves this and is comparable with tuning rules based on specific process models. Recent relay feedback auto tuning method (Astrom and Hagglund, 1984) makes tuning rules based on ultimate parameters be practical. Here, analytic expressions for ultimate periods and ultimate gains have been proposed. For this, the Routh stability method (Seborg et al., 1989) with phase-optimal approximations of the time delay term is utilized. Our analytic equations for ultimate frequencies and ultimate gains show relative errors below 1% for processes, for which analytic equations by Ho et al. (1995) have relative errors over 10%. Analytic Expressions of Ultimate Gains andUltimate gains and ultimate periods have long been used to tune PI/PID controllers since the Ziegler-Nichols tuning. Recently, very simple analytic equations for ultimate gains and ultimate periods by approximating the arctangent function have been presented, which can be used to obtain simple tuning rules. Here, by applying the Routh stability method and phase-optimal approximations of the time delay term, we present analytic expressions of ultimate parameters that are as simple as the existing ones, showing better accuracy.Il est classique d'utiliser des gains et des périodes ultimes pour régler les contrôleurs PI/PID depuis les travaux de Ziegler-Nichols. Récemment, des équations analytiques simples pour des gains et des périodes ultimes par approximation de la fonction arctangente, qui peuvent être utilisées pour obtenir des règles de réglage simple, ont été présentées. En appliquant la méthode de stabilité de Routh et les approximations de phases optimales du terme de délai, on présente ici des expressions analytiques des paramètres ultimes qui sont aussi simples que les paramètres existants, avec une meilleure précision.

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Design PID controllers for desired time-domain or frequency-domain response

Cited by 37 publications

References 10 publications

Design and Implementation of PID Controller with Lead Compensator for Thermal Process

Design and Implementation of PID Controller with Lead Compensator for Thermal Process

Improvement on an inverted decoupling technique for a class of stable linear multivariable processes

Analytic Expressions of Ultimate Gains and Ultimate Periods with Phase‐Optimal Approximations of Time Delays

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