Extending the LQR to the design of PID type‐ii and type‐iii control loops

Liu, Chao; Duan, Qianwen; Zhang, Chao; Luo, Yong; Qiu, Xiaoxia; Xia, Wenqiang; Li, Hong; Mao, Yao

doi:10.1049/cth2.12392

Cited by 3 publications

(3 citation statements)

References 41 publications

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“…Meanwhile, 𝑚 ≫ 𝜁 𝑐𝑙 𝜔 𝑐𝑙 , which ensures that the closed-loop pole is at the dominant pole position [31]. We call this 𝑚 as the relative dominance and as per the literature [21] its value should be chosen around 3 or more.…”

Section: The Rslqr Controllermentioning

confidence: 99%

“…And, the state space of the controlled plant is modeled as Assuming that the correlation weighting matrices 𝑸, 𝑹 and 𝑷 are consistent with Eq. (21). By taking Eq.…”

Section: The Rslqr Controller Based On Lesomentioning

confidence: 99%

“…The LQR method can control the tradeoff between system state and control energy well by choosing weighting matrix. Meanwhile, the optimal control law obtained by LQR method has many excellent properties, including closed-loop stability and robustness [20,21]. This excellent property makes it widely used in engineering applications.…”

Section: Introductionmentioning

confidence: 99%

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The RSLQR Control Method Based on the Linear Extended State Observer in the Electro-Optical Tracking System

Liu,

Wang,

Qiu

et al. 2024

IEEE Photonics J.

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This paper presents a Robust Servo Linear Quadratic Regulator (RSLQR) method based on the Linear Extended State Observer (LESO), which solves the problem of optimal tracking control of electrooptical system under disturbance. For the problem that the accuracy of the electro-optical tracking system is reduced due to disturbance and modeling error, the LESO is adopted in this paper to obtain and compensate the influence of internal and external disturbances in the controlled object model, so as to improve the disturbance suppression ability of the electro-optical tracking system. Considering the influence of weighting matrix in the RSLQR method on system's dynamic response performance, this paper presents a selection criterion of weighting matrix in the RSLQR to meet the performance requirements of closed-loop system. Through simulation analysis and experimental verification, the design method proposed in this paper has great reference value for the optimization of the dynamic response performance of the electro-optical tracking system and the improvement of the disturbance suppression ability.

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Section: The Rslqr Controllermentioning

confidence: 99%

“…And, the state space of the controlled plant is modeled as Assuming that the correlation weighting matrices 𝑸, 𝑹 and 𝑷 are consistent with Eq. (21). By taking Eq.…”

Section: The Rslqr Controller Based On Lesomentioning

confidence: 99%

See 1 more Smart Citation

The RSLQR Control Method Based on the Linear Extended State Observer in the Electro-Optical Tracking System

Liu,

Wang,

Qiu

et al. 2024

IEEE Photonics J.

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The PID high-type controller based on LQR and model-assisted LESO

Liu,

Qiu,

Mao

2024

Proceedings of the Institution of Mechanical Engineers, Part I:

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The work described in this paper proposes a PID high-type controller turning via Linear Quadratic Regulator (LQR) approach and pole-placement technique to level up dynamic response performance and disturbance suppression ability of the system. Meanwhile, considering the influence of the modeling error and uncertain disturbance on the stability of the control system, this paper extends the design method of the Linear Extended State Observer (LESO) to PID high-type control loop. In this paper, the tuning rule of PID high-type controller parameters without delay factor and the tuning rule of PID high-type controller parameters with delay factor are given. Finally, the simulation analysis and experimental results show that performance of the PID high-type controller are superior to the PD controller in traditional LESO and the PID type-i controller. Specifically, the system under the PID high-type controller not only eliminates the high-order steady-state error, but also can achieve high-precision tracking when the reference signal changes quickly. Meanwhile, disturbance suppression ability of the system and the dynamic response performance of the system such as rise time, settling time are significantly improved.

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Disturbance-Observer-Based LQR Tracking Control for Electro-Optical System

2023

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To improve the dynamic property and the disturbance suppression ability of an electro-optical tracking system, this paper presents a disturbance-observer-based LQR tracking control method. The disturbance-observer-based robust controller is composed of three parts: one is the LQR tracking controller, one is the reference model controller and the other is a compensatory controller designed with the output of the disturbance observer. The uncertainty and disturbances are considered in the controller design. By Lyapunov stability theory and linear matrix inequality (LMI) technique, the sufficient conditions for observer gain and controller gain of the tracking reference model of the electro-optical system are given. Simulation and experimental results show that the proposed method in this paper not only improved the disturbance suppression ability of the electro-optical tracking system but also improved the dynamic property of the electro-optical tracking system, such as rise time, settling time and system overshoot. Specially, compared with other methods in this paper, the tracking accuracy and the disturbance suppression ability of the proposed method are about two to three times higher. The method presented in this paper has important reference value in the field of electro-optical system applications. But, with the development of electro-optical system applications, the tracking accuracy and disturbance suppression ability of the proposed method cannot meet the actual requirements of an electro-optical system. The next step of this paper will consider a variety of practical requirements, such as the controller saturation problem and tracking reference target with strong maneuverability, and further optimize the proposed method.

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Extending the LQR to the design of PID type‐ii and type‐iii control loops

Cited by 3 publications

References 41 publications

The RSLQR Control Method Based on the Linear Extended State Observer in the Electro-Optical Tracking System

The RSLQR Control Method Based on the Linear Extended State Observer in the Electro-Optical Tracking System

The PID high-type controller based on LQR and model-assisted LESO

Disturbance-Observer-Based LQR Tracking Control for Electro-Optical System

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