PID controller design based on optimal servo and v-gap metric

The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the controller effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective optimal state-feedback regulator design while minimizing another time domain integral performance index, comprising of a weighted sum of Integral of Time multiplied Squared Error (ITSE) and the controller effort. The proposed methodology is extended for a new kind of fractional order (FO) integral performance indices. The impact of fractional order (as any arbitrary real order) cost function on the LQR tuned PID control loops is highlighted in the present work, along with the achievable cost of control. Guidelines for the choice of integral order of the performance index are given depending on the characteristics of the process, to be controlled.

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“…It has been shown in [26] that minimization of cost function (9) gives the state feedback control law as:…”

Section: Fig1 Lqr Formulation Of Pid Controller For Second Order Prmentioning

confidence: 99%

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

Das

Pan

Halder

et al. 2013

Applied Mathematical Modelling

123

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“…Although it is generally difficult to find a pair (P r (s), K(s)) that satisfies (16), such a pair can probably be obtained, if δ ν is sufficiently smaller than 1, because the ν-gap is the supremum of Ψ( jω). This means that if P r (s) that makes δ ν sufficiently smaller than 1 is found, then the design of K(s) that stabilizes (P(s), K(s)) is likely possible.…”

Section: Model Error and Closed-loop Stabilitymentioning

confidence: 99%

“…The authors of this paper also have tackled the problem of PID controller design using the modern control approach and have proposed a simple design method for SISO plants [16]- [18]. This method is based on an integral-type optimal servomechanism (IOS) [19], which is a type of linear quadratic regulator (LQR), and plant model reduction using the criterion of the ν-gap metric [20].…”

Section: Introductionmentioning

confidence: 99%

“…This method is based on an integral-type optimal servomechanism (IOS) [19], which is a type of linear quadratic regulator (LQR), and plant model reduction using the criterion of the ν-gap metric [20]. In this design method, a given plant model, which is assumed to be an SISO linear-time-invariant system, a given model is reduced to a second-order model, in which the plant parameters are determined, so that the ν-gap between the original plant and the reduced plant becomes as small as possible by using a parameter space search [16], the homotopy method [17], closed-loop balanced truncation [18], or an optimization method, such as the simplex method. Next, an IOS is designed using the reduced plant model.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Geng et al [19][20][21][22] adopted this algorithm to study the errors-in-variables (EIV) model identification. Therefore, developing an even more efficient algorithm for minimization of the v-gap metric is of great importance for its widespread applications in control and identification [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

A convex optimization algorithm for frequency‐domain identification in the v‐gap metric

Geng

Cui

et al. 2014

Adaptive Control & Signal

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This paper proposes a convex optimization algorithm to minimize the v-gap metric for parameter estimation of a SISO system using frequency-domain measurements. According to a geometrical interpretation for this metric, its evaluation for two SISO linear systems is the supreme of sine values of the apertures between their normalized right graph symbols. As a result, the minimization of the v-gap metric becomes that of the maximum of sine values of those apertures at sampling frequencies and can be efficiently solved by a sequence of feasibility problems with a decreasing line search. Compared with the related algorithms, the proposed one has global convergence and much lower computational loads. Finally, a numerical simulation shows the effectiveness of the proposed algorithm.

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PID controller design based on optimal servo and v-gap metric

Cited by 9 publications

References 12 publications

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

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

A convex optimization algorithm for frequency‐domain identification in the v‐gap metric

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