Continuous to discrete model conversion for the system with a singular system matrix based on matrix sign function

Tsai, Jason Sheng Hong; Huang, Chih Cheng; Guo, Shu‐Mei; Shieh, Leang-San

doi:10.1016/j.apm.2011.02.009

Cited by 12 publications

(4 citation statements)

References 18 publications

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“…Furthermore, in order to design the DTLQR scheme to preserve the stability and tracking of the EMS system, the discrete-time of the EMS system is required. Although, there have been various approaches that can formulate a discrete time model from the continuous model form [42,43], in this study, it is converted by adopting the Taylor series since it has a computationally fast and numerically stable function among other methods [44]. To compute the discrete form of the EMS system based on the Taylor series, the following computation in Equation ( 14) must be computed.…”

Section: Standard Solution Of the Dtlqr Problemmentioning

confidence: 99%

Adaptive dynamic programming discrete‐time LQR control on electromagnetic levitation system

Abdollahzadeh

2023

IET Control Theory & Appl

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In this paper, an adaptive dynamic programming discrete‐time linear quadratic Riccati (ADP‐DTLQR) control is designed for an electromagnetic levitation system (EMS) to track the reference trajectories and preserve stability in severe situations efficiently. The EMS system has a strongly nonlinear and unstable dynamic in nature. The ADP‐DTLQR approach is a novel method based on the Q‐learning algorithm for unknown discrete‐time systems in a causal manner. The ADP‐DTLQR can determine the online gains of the controller in different conditions as a model‐free structure, which can minimize the combination of state errors and control efforts of the systems. Moreover, the DTLQR controller and linear matrix inequality controller on the EMS system are designed and compared with the present strategy in different scenarios in the simulation section to verify the robustness and strongness of the proposed method. The evaluation of simulation results demonstrates that the proposed control scheme is suitable not only for preserving the levitated object stability but also for compensating the disturbances and uncertainties in the EMS structure.

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Section: Standard Solution Of the Dtlqr Problemmentioning

confidence: 99%

Adaptive dynamic programming discrete‐time LQR control on electromagnetic levitation system

Abdollahzadeh

2023

IET Control Theory & Appl

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“…When A −1 does not exist, a computationally fast analytic solution of H can also be found in . Obviously, the varied control input u d ( k T ) at time instant k T includes varied state x d ( k T ), a constant term C d , and varied reference input r * ( k T ).…”

Section: Observer‐based Linear Quadratic Tracker For the Sample‐data mentioning

confidence: 99%

A new optimal linear quadratic observer‐based tracker under input constraint for the unknown system with a direct feed‐through term

Tsai

Lee

et al. 2014

Optim Control Appl Methods

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SUMMARYThis paper develops a new optimal linear quadratic observer-based tracker with input constraint for the linear unknown system with a direct transmission term from input to measured output. The off-line observer/Kalman filter identification method is used to determine the linear sampled-data model with a direct feed-through term. On the basis of this model, a high-gain optimal linear quadratic analog observer-based tracker is proposed, so that it can effectively induce a high quality performance on the state estimation and the trajectory tracking design. Besides, the prediction-based digital redesign method is utilized to obtain a relatively low-gain and implementable observer and digital tracker from the theoretically well-designed high-gain analog observer and tracker for the linear system with a direct transmission term from input to output. To reduce the magnitude of control input, which is caused by the high-gain property to fit the requirement of the input constraint, the modified linear quadratic analog tracker is proposed. Thus, the control input can be compressed effectively without losing the original high performance of tracking much.

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“…When A −1 d,k does not exist, a computationally fast analytic solution of H d,k can also be found in [Tsai et al, 2011b]. The receiver design method makes use of the proposed prediction-based adaptive observer with actuator and state faults.…”

Section: Fault-diagnosis and Performance Recoverymentioning

confidence: 99%

From Fault-Diagnosis and Performance Recovery of a Controlled System to Chaotic Secure Communication

Hsu

Tsai

Guo

et al. 2014

Int. J. Bifurcation Chaos

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Chaotic systems are often applied to encryption on secure communication, but they may not provide high-degree security. In order to improve the security of communication, chaotic systems may need to add other secure signals, but this may cause the system to diverge. In this paper, we redesign a communication scheme that could create secure communication with additional secure signals, and the proposed scheme could keep system convergence. First, we introduce the universal state-space adaptive observer-based fault diagnosis/estimator and the high-performance tracker for the sampled-data linear time-varying system with unanticipated decay factors in actuators/system states. Besides, robustness, convergence in the mean, and tracking ability are given in this paper. A residual generation scheme and a mechanism for auto-tuning switched gain is also presented, so that the introduced methodology is applicable for the fault detection and diagnosis (FDD) for actuator and state faults to yield a high tracking performance recovery. The evolutionary programming-based adaptive observer is then applied to the problem of secure communication. Whenever the tracker induces a large control input which might not conform to the input constraint of some physical systems, the proposed modified linear quadratic optimal tracker (LQT) can effectively restrict the control input within the specified constraint interval, under the acceptable tracking performance. The effectiveness of the proposed design methodology is illustrated through tracking control simulation examples. Assumption 2 [Wei et al., 2011]. Let Υ(kT ) ∈ n×m be a matrix of signals generated by the following system Υ(kT + T ) = G d (kT )Υ(kT ) + Φ d (kT ). (10) Assume that G(kT )−L d (kT +T )CG(kT ) is globally asymptotically stable and Φ d (kT + T ) = [Φ(kT ) − L d (kT + T )CΦ(kT )] is a persistently excited signal. 1450151-5 Int. J. Bifurcation Chaos 2014.24. Downloaded from www.worldscientific.com by UNIVERSIDAD POLITECNICA DE MADRID SERVICIO DE BIBLIOTECA UNIVERSITARIA on 01/05/15. For personal use only. W.-T. Hsu et al. 1450151-6 Int. J. Bifurcation Chaos 2014.24. Downloaded from www.worldscientific.com by UNIVERSIDAD POLITECNICA DE MADRID SERVICIO DE BIBLIOTECA UNIVERSITARIA on 01/05/15. For personal use only. Fault-Diagnosis and Performance Recovery Application of the adaptive fault estimator to secure communicationLet the transmitter be the nonlinear time-varying system, and according to the communication structure in Fig. 6 (due to which state masks the message), the equation of the transmitter can be written askT ) + M 1 m(kT )) + H d,k u d (kT ) 1450151-23 Int. J. Bifurcation Chaos 2014.24. Downloaded from www.worldscientific.com by UNIVERSIDAD POLITECNICA DE MADRID SERVICIO DE BIBLIOTECA UNIVERSITARIA on 01/05/15. For personal use only.

show abstract

Continuous to discrete model conversion for the system with a singular system matrix based on matrix sign function

Cited by 12 publications

References 18 publications

Adaptive dynamic programming discrete‐time LQR control on electromagnetic levitation system

Adaptive dynamic programming discrete‐time LQR control on electromagnetic levitation system

A new optimal linear quadratic observer‐based tracker under input constraint for the unknown system with a direct feed‐through term

From Fault-Diagnosis and Performance Recovery of a Controlled System to Chaotic Secure Communication

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