Continuous-time quadratic regulators and pseudo-continuous-time quadratic regulators with pole placement in a specific region

Shieh, S. Leang; Dib, M. Hani; Ganesan, Subramaniam

doi:10.1049/ip-d.1987.0056

Cited by 7 publications

(3 citation statements)

References 5 publications

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“…With the design of the PI-type controller, the controlled system has the augmented structure, and this structure may result in an uncontrollable augmented controlled system. In paper [16], the authors present a method which is placed in the closed-loop system eigenvalues on the left of the negative vertical that lies by the selected non-positive constant; hence, the proposed method is utilized to overcome the uncontrollable issue in this paper. Since the forward gain cannot be designed by using the traditional LQAT approach due to the method in [16], therefore, the final-value theorem can be adopted to overcome this problem by discussing the final-value theorem for the proposed robust tracker design in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization

et al. 2019

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A robust linear quadratic analog tracker (LQAT) consisting of proportional-integral-derivative (PID) controller, sliding mode control (SMC), and perturbation estimator is proposed for a class of nonlinear systems with unknown nonlinear perturbation and direct feed-through term. Since the derivative type (D-type) controller is very sensitive to the state varying, a new D-type controller design algorithm is developed to avoid an unreasonable large value of the controller gain. Moreover, the boundary of D-type controller is discussed. To cope with the unknown perturbation effect, SMC is utilized. Based on the fast response of SMC controlled systems, the proposed perturbation estimator can estimate unknown nonlinear perturbation and improve the tracking performance. Furthermore, in order to tune the PID controller gains in the designed tracker, the nonlinear perturbation is eliminated by the SMC-based perturbation estimator first, then a hybrid Taguchi real coded DNA (HTRDNA) algorithm is newly proposed for the PID controller optimization. Compared with traditional DNA, a new HTRDNA is developed to improve the convergence performance and effectiveness. Numerical simulations are given to demonstrate the performance of the proposed method.

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Section: Introductionmentioning

confidence: 99%

“…[16] Let A pid , B pid1 be the pair of the given open-loop system and h ≥ 0 represent the prescribed degree of relative stability. The eigenvalues of the closed-loop system A pid − B pid1 R −1 B pid1 T P lie on the left of the −h vertical line with the matrix P being the solution of the Riccati equation…”

mentioning

confidence: 99%

Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization

et al. 2019

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“…[22,23]). Let (A, B) be the pair for the given open-loop system, and let h ≥ 0 represent a prescribed degree of relative stability.…”

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confidence: 99%

A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems

Tsai

Chen

et al. 2020

Applied Sciences

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This paper presents the design of a linear quadratic analog tracker (LQAT) based on the observer–Kalman-filter identification (OKID) method and the design of a modified functional observer-based equivalent input disturbance (EID) estimator for unknown square–non-square singular analog systems with unknown input and output disturbances. First, an equivalent mathematical model of the singular analog system is presented to simulate the time response of continuous-time linear singular analog systems to arbitrary inputs via the model conversion method. Then, for the unknown singular analog system, it constructs a linear quadratic analog tracker with state feedback and feed-forward gains based on the off-line OKID method. Furthermore, it extends the design methodology of the EID estimator for strictly proper regular systems with unknown matched–mismatched input and output disturbances to proper regular systems. It is important to mention that the newly developed modified functional observer for proper systems is used to estimate the unknown EID of singular analog systems and that the constraints on the dimensions of unknown disturbances can be eliminated by using the newly proposed EID estimation method. The contributions of this paper can be listed as follows: (1) based on both the OKID method and the discrete-to-continuous model conversion, the simulation of the time responses of the continuous-time linear singular models (which are not feasible using existing MATLAB toolboxes) become feasible; (2) for effective control of the unknown singular analog system, an off-line OKID method is proposed to design an LQAT with state feedback and feed-forward gains; and (3) based on the newly developed modified functional observer for the reduced-order proper regular system, the original EID estimator in the literature is newly extended to estimate the EID from the unknown strictly proper singular analog system, without the original dimensional constraints of the disturbances. It is important to mention that the disturbances of interest can be unknown matched–mismatched input and output disturbances.

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Model conversion and digital redesign of singular systems

Tsai¹,

Wang²,

Shieh³

1993

Journal of the Franklin Institute

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Continuous-time quadratic regulators and pseudo-continuous-time quadratic regulators with pole placement in a specific region

Cited by 7 publications

References 5 publications

Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization

Design of Robust Trackers and Unknown Nonlinear Perturbation Estimators for a Class of Nonlinear Systems: HTRDNA Algorithm for Tracker Optimization

A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems

Model conversion and digital redesign of singular systems

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