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Proceedings ArticleDOI

Design of robust PID controller for an interval plant

TL;DR: In this article, a method based on stability boundary plot is considered for an unstable second order process with dead time, and an optimization based design of robust Proportional-Integral-Derivative (PID) controller that guarantees both the stability and performance of an interval plant is proposed.
Abstract: In this paper, a method based on stability boundary plot is considered for an unstable second order process with dead time. All the controllers that satisfy the gain margin and phase margin requirements are found by plotting the K p -K i curve. The technique is based on Kharitonov theorem for stability of interval plants. Limiting values of the controller parameters that stabilize the given system are found using the curves obtained. In addition to this, an optimization based design of robust Proportional-Integral-Derivative (PID) controller that guarantees both the stability and performance of an interval plant is proposed. The controller design involves two steps. First, a controller setting is obtained for the nominal plant and then optimization is done to find a setting which will work on the entire range of the uncertainties specified. Optimization is based on the necessary and sufficient conditions for a system to be Hurwitz stable. A set of constraints are framed based on these conditions and it is used to minimize an objective function using non-linear programming (NLP). This technique is applied to i) Stable FOPTD process ii) Unstable FOPTD process. Further, Nonlinear simulation is performed for an unstable CSTR plant under three operating regions. The results obtained show the effectiveness of optimization taking into account the uncertainties associated with the plant.
Citations
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31 Dec 2018
TL;DR: In this paper, an analytical design method of a Proportional Integral controller for the stability and performance of first order plus time delay systems is proposed, which achieves general computation equations for such systems.
Abstract: This study proposes an analytical design method of a Proportional Integral controller for the stability and performance of first order plus time delay systems. The method proposed in the study achieves general computation equations for such systems. Inspired from Bode’s ideal loop, gain crossover frequency and phase margin specifications are considered for the system. Then, these specifications are used to obtain the parameters of the proportional integral controller. Analytically derived formulas by the proposed method are tested with existing plants in the literature and the results are illustrated graphically. It is shown that the tuning method satisfies desired gain crossover frequency and phase margin specifications.

5 citations

Proceedings ArticleDOI
01 Sep 2018
TL;DR: This study intends to present the systematic design procedure of stabilizing fractional order proportional integral controllers for first order plus time delay plants via the stability boundary locus (SBL) method, which gives generalized computation equations for tuning related controllers within desired frequency ranges.
Abstract: This study intends to present the systematic design procedure of stabilizing fractional order proportional integral controllers for first order plus time delay (FOPTD) plants via the stability boundary locus (SBL) method. Proposed method gives generalized computation equations for tuning related controllers within desired frequency ranges. Besides, equations to compute the real root boundary (RRB) of the SBL are presented. In spite of the classical design technique, this paper proposes to find the starting and ending points and the stability region of the stability boundary of the system by heuristic approach. This method ensures the stability by analytically obtained formulas instead of testing the regions of the SBL with arbitrary selected points. This proves the advantage and the contribution of the proposed procedure. Obtained equations are applied on examples and the results are illustratively given. Comparisons with the literature showed the effectiveness of the proposal.

2 citations

References
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Journal ArticleDOI
TL;DR: For a large number of single input-single output (SISO) models typically used in the process industries, the Internal Model Control design procedure is shown to lead to PID controllers, occaslonally augmented with a first-order lag.
Abstract: For a large number of single input-single output (SISO) models typically used in the process industries, the Internal Model Control (IMC) design procedure is shown to lead to PID controllers, occaslonally augmented with a first-order lag. These PID controllers have as their only tuning parameter the closedloop time constant or, equivalently, the closed-loop bandwidth. On-line adjustments are therefore much simpler than for general PID controllers. As a special case, PIand PID-tuning rules for systems modeled by a first-order lag with dead time are derived analytically. The superiority of these rules in terms of both closed-loop performance and robustness is demonstrated.

1,424 citations

Journal ArticleDOI
TL;DR: It is shown, in particular, that for a fixed value of the proportional term (K"p) the resulting stabilizing PID compensators form a finite set of disjoint polyhedral sets in the parameter space.

229 citations

Journal ArticleDOI
TL;DR: In this paper, a new method for the calculation of all stabilizing PI controllers is given, which is based on plotting the stability boundary locus in the (kp, ki)-plane and then computing the stabilizing values of the parameters of a PI controller.

217 citations

Proceedings ArticleDOI
04 Jun 1997
TL;DR: In this paper, the authors provide a computationally constructive characterization of all stabilizing PID controllers that stabilize a given plant, which is an extension of the YJBK characterization restricted to PIDs and opens up the possibility of optimal design using PIDs.
Abstract: The YJBK parametrization characterizes all stabilizing controllers. In industry, most controllers are PID and there is no solution to the problem: can a plant P(s) be stabilized by a PID controller? In this paper, we provide an answer to this question. Besides settling the question of existence, we provide a computationally constructive characterization of all stabilizing PID controllers that stabilize a given plant. Thus this result is essentially an extension of the YJBK characterization restricted to PIDs and opens up the possibility of optimal design using PIDs.

143 citations


"Design of robust PID controller for..." refers methods in this paper

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  • ...A technique based on linear programming used for finding the controller parameters that stabilize a given plant is obtained in [2]....

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Proceedings ArticleDOI
11 Dec 1996
TL;DR: In this paper, an appropriately generalized version of the Hermite-Biehler Theorem is given and shown to be useful in providing a solution to the constant gain stabilization problem.
Abstract: This paper considers the problem of stabilizing a given linear time-invariant plant using a fixed order compensator. As a first step, attention is focused on the constant gain stabilization problem. An appropriately generalized version of the Hermite-Biehler Theorem is given and shown to be useful in providing a solution to this problem. A complete analytical characterization of all stabilizing feedback gains is provided as a closed form solution. This is in stark contrast to the highly nonlinear inequalities that one may have to deal with in trying to solve this problem using the Routh-Hurwitz criterion or the graphical procedures which must be followed while using the Nyquist criterion or the Root Locus technique. The development of similar approaches for stabilization using PID or first order controllers is a topic of current research.

65 citations


"Design of robust PID controller for..." refers methods in this paper

  • ...[1-3]....

    [...]

  • ...The Hermite-Biehler theorem, which makes use of an analytical solution based approach has been provided in [1]....

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