Controller Order Reduction by Model Matching of Frequency Response

Chida, Yuichi; Shigemasa, Takashi

doi:10.9746/sicetr1965.34.660

Cited by 7 publications

(9 citation statements)

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“…5 show the stability margins and unit time responses, respectively. The results are compared with those obtained by using an H ∞ controller and its reduced-order I-PD controller [16], which provides the PID gains, K P = 5.338, K I = 12.38, and K D =1.125. These gains are almost the same as those by the proposed method; accordingly, as shown by the table and the figure, the closed-loop properties of the two systems are close to each other.…”

Section: Fig 2 Bode Diagrams Of the Complementary Sensitivity Functionsmentioning

confidence: 98%

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

Ochi

Kondo

2010

Proceedings of the 2010 American Control Conference

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This paper presents a new design method of a PID (proportional-integral-derivative) controller that provides sufficient stability margins and good time responses. It is possible to design an optimal PID controller with properties of a linear quadratic regulator or LQR by taking advantage of the fact that the integral-type optimal servo, which is a kind of the LQR, designed for a second order system is equivalent to an I-PD (proportional and derivative preceded integral) controller, However, the plant order is generally higher than the second. In such a case, the plant-order is reduced to the second based on the criterion of the ν-gap metric. Even if open-loop properties of the reduced-order plant are very different from those of the original plant, as long as the ν-gap is sufficiently small, a desirable I-PD or PID controller is obtained using the second-order plant model. Several design examples illustrate the effectiveness and usefulness of the method as a practical design tool of a PID controller.

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Section: Fig 2 Bode Diagrams Of the Complementary Sensitivity Functionsmentioning

confidence: 98%

“…Designing an IOS with Q x = 0 2×2 , Q = 150 and R=1, we obtain PID gains as K P = 5.700, K I =12.25, and K D = 1.162. The time constant of the approximate derivative is chosen to be T D = 0.08 s as in [16]. Table IV and Fig.…”

Section: Fig 2 Bode Diagrams Of the Complementary Sensitivity Functionsmentioning

confidence: 99%

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

Ochi

Kondo

2010

Proceedings of the 2010 American Control Conference

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“…are easily calculated by the least-squares method (Chida and Shigemasa, 1998). Here, ω k is the number of specified frequencies within the matching frequency band, in which an attempt is made to match the loop-transfer function of the reduced-order system to that of the full-order system.…”

Section: Controller Order Reductionmentioning

confidence: 99%

“…Therefore the order of the controller was reduced based on the method of the frequency response matching of the loop-transfer function proposed by Chida and Shigemasa (1998)…”

Section: Controller Order Reductionmentioning

confidence: 99%

Identification and frequency shaping control of a vibration isolation system

Chida¹,

Ishihara²,

Okina³

et al. 2008

Control Engineering Practice

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In the present paper, a vibration isolation control problem is considered for the case in which forced vibration disturbances that have a narrow-band frequency component are applied to a system. Such a control problem appears in the vibration isolation control of a rotating machine. Velocity feedback control including notch-filters attenuates the effects of such narrow-band frequency disturbances, but parameter tuning of a controller is difficult because the vibration isolation performance changes dramatically according to slight discrepancies in the controller parameters. In such cases, a direct frequency shaping method such as the H ∞ control is suitable for the controller design. In the present paper, a vibration isolation control problem for a mechanical experimental system, which simulates the characteristics of a rotating machine in space, is considered. A system model was created by performing system identification experiments, and a controller was designed by a frequency shaping method based on the H ∞ control. Control experiments were carried out successfully, and the controller was verified to provide the expected performance.

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“…If the frequency response of the discretized system agrees with the continuous-time system within the frequency range from ω L to ω H , then the discrete frequency data ω k , which is sampled at N-points within the frequency range, are used, and the following error index function J is introduced [17], [18]:…”

Section: Frequency Matching Conditionmentioning

confidence: 99%

Discretization Method of Continuous-Time Controllers Based on Frequency Response Fitting

Chida

Nishimura

2008

SICE Journal of Control, Measurement, and System Integration

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: In the present paper, a digital redesign problem that converts continuous-time controllers into digital controllers is considered. A new discretization method based on matching of the frequency response of a continuous-time control system is proposed. The frequency response is matched using the least squares method based on data of discrete frequency points. The matching problem is described using an LMI, and the stability condition of the closed-loop system and the redesigned controller are described as additional conditions of LMIs. An optimizing problem described by some LMI conditions is solved by an iterative procedure. Examples are presented that prove the superior performance of the proposed method.

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Controller Order Reduction by Model Matching of Frequency Response

Cited by 7 publications

References 0 publications

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

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

Identification and frequency shaping control of a vibration isolation system

Discretization Method of Continuous-Time Controllers Based on Frequency Response Fitting

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