On the design of multivariable PID controllers via LMI approach

Zheng, Feng; Wang, Qing‐Guo; Lee, Tong Heng

doi:10.1016/s0005-1098(01)00237-0

Cited by 236 publications

(164 citation statements)

References 4 publications

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“…Simulation results show clearly that Approach 2, described in [26], achieves globally the best compromise between robustness and performance tests compared to Approach 1, described in [24], especially with respect to the multiple time-delays influence test, set-point changes test and performance indices.…”

Section: Discussionmentioning

confidence: 96%

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Multivariable Pid Control Via Ilmis: Performances Assessment

Belhaj

Boubaker

2015

International Journal on Smart Sensing and Intelligent Systems

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Section: Discussionmentioning

confidence: 96%

“…To tackle the problem of computing MIMO PID gain matrices, an Iterative Linear Matrix Inequality (ILMI) algorithm was proposed by [22] and later used to solve several MIMO PID controller design problems [23], [24], [25], [26], [27]. The basic idea is to transform a PID controller into an equivalent static output feedback (SOF) controller.…”

Section: Introductionmentioning

confidence: 99%

Multivariable Pid Control Via Ilmis: Performances Assessment

Belhaj

Boubaker

2015

International Journal on Smart Sensing and Intelligent Systems

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“…For example, the authors of the literature, [1], [2], and [4], have introduced design methods based on the classical approach such as decoupling control or dominant pole placement for two-input two-output PI controller design [5]. The design methods based on the modern approach include those by pole placement [6]- [8], loop shaping for PI control [9], H 2 /H ∞ control [10], [11] or GKYP lemma [12] formulated with linear matrix inequalities, and numerical optimization [13], [14]. Lunze [15] has proposed a unique method that gives an I-gain matrix robustly stabilizable against a given bounded variation of the static transmission matrix of the plant.…”

Section: Introductionmentioning

confidence: 99%

Design of a MIMO PID Controller by Integral-Type Optimal Servomechanism and Fractional Balanced Reduction

Ochi

Kondo

2013

SICE Journal of Control, Measurement, and System Integration

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: The present paper proposes an efficient design method for a multiple-input multiple-output (MIMO) integral preceded by a proportional and derivative (I-PD) controller, which is a type of PID controller. In the proposed method, a given plant model is first reduced to a lower-order model using fractional balanced reduction, and an integral-type or robust optimal servomechanism is then designed for the reduced plant, which is expressed in a peculiar state-space form, where the state vector is composed of outputs, their derivatives, and control inputs. The resultant optimal feedback control law is immediately transformed into a MIMO I-PD control law. The optimal servomechanism, which is based on a linear quadratic regulator, provides a controller with desirable control performance, adequate stability margins, and easy trade-off between the control performance and stability margins attained through weight selection of the quadratic cost function. Although these features are not perfectly guaranteed in the resulting control system due to the model reduction, if the properties are adequately preserved, they make the controller design very simple and efficient. A design example illustrates the effectiveness of the proposed design method as well as its limitations.

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“…In [14], a third approach for the design of an optimal PID controller is proposed, which involves solving a high-order static state-feedback problem and then reducing the size of the controller by retaining the "dominant" dynamics of the closed-loop system. Finally, in [15] and [16], a MIMO PID controller is obtained by solving a similar static output-feedback problem using linear matrix inequality (LMI) methods. A disadvantage with all of these techniques is that the controller synthesis requires solving various subproblems multiple times before obtaining a stabilizing controller (if one exists), and therefore the complexity of the procedures increases greatly with the system size.…”

Section: Introductionmentioning

confidence: 99%

Multivariable three-term optimal controller design for large-scale systems

Davison

Lam

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-This paper deals with the design of controllers for large-scale linear time-invariant multi-input multi-output systems, such as those that often arise in process control. We focus on two standard controller objectives: (i) asymptotic regulation subject to unmeasurable constant disturbances, and/or (ii) asymptotic tracking of constant set-points. In either case, standard output-feedback controller design methodologies typically result in controllers that have order at least as large as that of the plant; for large-scale systems, the controller order can consequently be impractically large. The purpose of this paper is to introduce, for the subclass of plants that are open-loop stable, a low-order three-term (i.e., PID) multivariable control design approach that is practical to compute numerically, even for large-scale systems. A design algorithm and existence results to construct such a controller are given, and the approach is applied to several examples. Remarkably, at least for the examples considered, the three-term controller's performance is quite similar to that achieved by the standard (much higher order) controller that solves the servomechanism problem.

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On the design of multivariable PID controllers via LMI approach

Cited by 236 publications

References 4 publications

Multivariable Pid Control Via Ilmis: Performances Assessment

Multivariable Pid Control Via Ilmis: Performances Assessment

Design of a MIMO PID Controller by Integral-Type Optimal Servomechanism and Fractional Balanced Reduction

Multivariable three-term optimal controller design for large-scale systems

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