Digital redesign of H8 controller via bilinear approximation method for state-delayed systems

Shieh, Leang-San; Wang, Weimin; Tsai, Jason Sheng‐Hong

doi:10.1080/002071798222073

Cited by 33 publications

(30 citation statements)

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“…The discretization technique for multiple inputdelay systems is well developed and can be found in [1]. However, the discretization scheme for continuous-time multiple state/output time-delay systems with each delay time being a fractional number of a sampling period has not yet been fully developed [7,22]. In this paper, we propose a discretization method via the Chebyshev quadrature formula together with a linear interpolation method to construct an equivalent discrete-time model from the continuous-time multiple time-delay system in (1).…”

Section: Digital Modeling Of Mimo Continuous-time Systems With Multipmentioning

confidence: 99%

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Digital Modeling and PID Controller Design for MIMO Analog Systems with Multiple Delays in States, Inputs and Outputs

Chang

Shieh

Liu

et al. 2008

Circuits Syst Signal Process

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This paper presents a discrete-time state-space methodology for the digital modeling and design of an optimal digital proportional-integral-derivative (PID) plus state-feedback controller for multiple-input, multiple-output (MIMO) continuoustime systems with multiple time delays in states, inputs and outputs. To implement the digital design, first the Chebyshev quadrature formula together with a linear interpolation method is employed to obtain an extended discrete-time state-space model from the continuous-time multiple time-delay system. Then, a partially predetermined digital PID controller and the extended discrete-time state-space model are formulated as an augmented discrete-time state-space system utilizing state-feedforward and state-feedback linear-quadratic regulator (LQR) design. As a result, the parameters of the optimal PID controller and its associated state-feedback controller can be determined by tuning the weighting matrices in the LQR performance criteria. Further, an optimal discrete-time observer is jointly constructed for the multivariable system with multiple delays in states, inputs and outputs. The proposed design methodology can be applied to general MIMO continuous-time multiple time-delay 112 Circuits Syst Signal Process (2009) 28: 111-145 systems for performance improvement and disturbance rejection. An illustrative example is given to demonstrate the effectiveness of the developed method.

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Section: Digital Modeling Of Mimo Continuous-time Systems With Multipmentioning

confidence: 99%

“…For example, the discretization scheme for multivariable continuoustime state-space systems with multiple time delays in states, inputs and outputs has only been partially developed in [7,22].…”

Section: Introductionmentioning

confidence: 99%

Digital Modeling and PID Controller Design for MIMO Analog Systems with Multiple Delays in States, Inputs and Outputs

Chang

Shieh

Liu

et al. 2008

Circuits Syst Signal Process

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“…In the recent work of Shieh et al [7], the bilinear approximation method, together with the linear interpolation method, are first utilized to determine an equivalent discrete-time, statedelayed model for the continuous-time, state-delayed system. Then, based on the closed-loop bilinear approximation method, a state-matching digital redesign method [7] is developed to determine the observer-based digital controller for the continuous-time, state-delayed system.…”

Section: Introductionmentioning

confidence: 99%

“…The authors show that the digitally redesigned controller closely matches the states of the digitally controlled sampled-data, state-delayed system, with those of the original analog controlled continuous-time, state-delayed system. Both the state-delayed digital modeling method and the state-matching digital redesign method [7] are also further extended, to discretize a cascaded continuous-time controller for the continuous-time input-state delayed system [8,9]. In References [8,9], the Newton extrapolation formula in conjunction with the Chebyshev quadrature formula are utilized to determine both the discrete-time, input-state delayed model and the equivalent cascaded digital controller for the continuoustime input-state delayed system, under the assumption that all states are available for measurement.…”

Section: Introductionmentioning

confidence: 99%

“…Then, based on the closed-loop bilinear approximation method, a state-matching digital redesign method [7] is developed to determine the observer-based digital controller for the continuous-time, state-delayed system. The authors show that the digitally redesigned controller closely matches the states of the digitally controlled sampled-data, state-delayed system, with those of the original analog controlled continuous-time, state-delayed system.…”

Section: Introductionmentioning

confidence: 99%

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The observer‐based linear quadratic sub‐optimal digital tracker for analog systems with input and state delays

Huang

Tsai

Provence

et al. 2003

Optim Control Appl Methods

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SUMMARYThis paper presents a new observer-based sub-optimal digital tracker for the continuous-time system with input and state time delays. We directly convert the continuous-time input-state delayed system into an equivalent discrete-time input-state delayed model and its extended discrete-time delay-free model. In addition, we directly discretize the linear quadratic performance index specified in the continuoustime domain into an equivalent decoupled discrete-time performance index using the newly developed extended delay-free model. As a consequence, the well-developed discrete-time optimal control theory for discrete-time delay-free system can be applied to determine the optimal digital tracker for the continuous-time input-state delayed system. When the states of the continuous-time input-state delayed system are not available for measurements, we develop a sub-optimal digital observer for the original continuous-time input-state delayed system using the state-matching digital redesign technique and the digital-to-analog model conversion technique. As a result, the proposed observer-based linear quadratic digital tracker is able to make the output of the digitally controlled continuous-time input-state delayed system sub-optimally track the desired reference signals. An illustrative example is presented to demonstrate the effectiveness of the proposed design methodology.

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Stabilization of Multirate Sampled-Data Fuzzy Systems Based on an Approximate Discrete-Time Model

Kim

Park

Joo

2006

Fuzzy Systems and Knowledge Discovery

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This paper studies a stabilization problem for a multirate digital control of fuzzy systems based on the approximately discretized model. In the multirate control scheme, a numerical integration scheme is used to approximately predict the current state from the state measured at the sampling points. It is shown that the multirate digital fuzzy controller stabilizing an approximate discrete-time fuzzy model would also stabilize the sampled-data fuzzy system in the sufficiently small control update time. Furthermore, some sufficient conditions for the stabilization of the approximate discrete-time fuzzy model are provided under the delta-operator frame work, which are expressed as the linear matrix inequalities (LMIs) and thereby easily tractable by the convex optimization techniques. A numerical example is demonstrated to visualize the feasibility of the developed methodology.

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Digital redesign of H8 controller via bilinear approximation method for state-delayed systems

Cited by 33 publications

References 0 publications

Digital Modeling and PID Controller Design for MIMO Analog Systems with Multiple Delays in States, Inputs and Outputs

Digital Modeling and PID Controller Design for MIMO Analog Systems with Multiple Delays in States, Inputs and Outputs

The observer‐based linear quadratic sub‐optimal digital tracker for analog systems with input and state delays

Stabilization of Multirate Sampled-Data Fuzzy Systems Based on an Approximate Discrete-Time Model

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