On Discrete-Time Loop Transfer Recovery

Zhang, Zhihong; Freudenberg, J.S.

doi:10.23919/acc.1991.4791793

Cited by 10 publications

(6 citation statements)

References 13 publications

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“…where S ( z ) is given in (6). This shows that the error transfer matrix Ep(z) is indeed the error of the sensitivity matrix of the p-step delay compensator loop relative to that of the target This shows that any inherent delay in the plant has the same effect on the error matrix as the induced delay in the feedback loop.…”

Section: Remarkmentioning

confidence: 85%

Discrete‐time loop transfer recovery with multistep delays

Shen

Ray

1992

Optim Control Appl Methods

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SUMMARYThis paper focuses on delay compensation as an extension of the loop transfer recovery (LTR) procedure from one-step prediction to the general case of p-step prediction ( p 2 1). The steady state minimum variance filter gain is shown to be the H2-minimal solution of the relative error between the target sensitivity matrix and the actual sensitivity matrix for p-step prediction ( p 2 1). This result is useful for synthesis of robust delay compensators in multiple-inputlmultiple-output (MIMO) discrete-time systems.

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Section: Remarkmentioning

confidence: 85%

Discrete‐time loop transfer recovery with multistep delays

Shen

Ray

1992

Optim Control Appl Methods

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“…Recently, extension of the linear quadratic gaussian with loop transfer recovery (LQGILTR) design techniques to discrete-time systems has been studied by a number of researchers. 6- 9 The motivation for such an interest is due to the following two reasons: firstly, guaranteed feedback properties for the discrete-time LQ optimal regulator or Kalman filter do exist, 1 1 -1 3 although they are not as attractive as in the continuous-time case. Naturally, it is desirable to have a method of recovering these properties.…”

Section: Introductionmentioning

confidence: 99%

Discrete‐time loop transfer recovery via generalized sampled‐data hold functions based compensator

Anderson

1994

Intl J Robust & Nonlinear

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Loop transfer recovery (LTR) techniques are known to enhance the input or output robustness properties of linear quadratic gaussian (LQG) designs. One restriction of the existing discrete‐time LQG/LTR methods is that they can obtain arbitrarily good recovery only for minimum‐phase plants. A number of researchers have attempted to devise new techniques to cope with non‐minimum‐phase plants and have achieved some degrees of success.6‐9 Nevertheless, their methods only work for a restricted class of non‐minimum‐phase systems. Here, we explore the zero placement capability of generalized sampled‐data hold functions (GSHF) developed in Reference 14 and show that using the arbitrary zero placement capability of GSHF, the discretized plant can always be made minimum‐phase. As a consequence, we are able to achieve discrete‐time perfect recovery using a GSHF‐based compensator irrespective of whether the underlying continuous‐time plant is minimum‐phase or not.

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“…(3.5) i=l Note that this factorization is slightly different from that given in Zhang and Freudenberg (1991), even when si is a real zero. This, however, by 110 means is surprising, as such factorizations are generally nonunique.…”

Section: W H S ( S ) = W Hmentioning

confidence: 92%

“…Finally, we remark that a nonminimum phase transfer function also adnuts an outprt facforization (Zhang and Freudenberg, 1991) analogous to the input factorization. Our subsequent results, however, can be applied to both types of factorizations.…”

Section: W H S ( S ) = W Hmentioning

confidence: 93%

“…A transfer function matrix is said to be nonminimum phase if it has a nonminimum phase zero, and otherwise is said to be minimum phase. As in continuous-time systems Wall et al, 1980), a nonminimum phase transfer function may be factorize6 into a minimum phase part and an all pass factor (Zhang and Freudenberg, 1991). Let si, lsil > 1, i = 1,. .…”

Section: The Extended Poisson Integralsmentioning

confidence: 99%

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Bode integrals for multivariable discrete-time systems

Chen

Nett²

Proceedings of 32nd IEEE Conference on Decision and Control

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The purpose of this paper is to develop integral formulae for singular values of the sensitivity function to express design constraints in multivariable discretetime systems. We present extensions to both the classical Poisson integral and Bode's sensitivity integral formulae. The main utility of these results is that they can be used to quantify design limitations that arise i u niultivariable discretetime systems, due to such system characterist,ics as open loop unstable poles and nonininiinum phase zeros, and to such design requirements as stability and bandwidth constraints. These formulae are similar to those for multivariable continuous-time systems obtained elsewhere, and they reveal that the limitations on the sensitivity design depend on directionality properties of the sensitivity function, as well as on those of unstable poles and nonn~inin~uni phase zeros i n the open loop transfer function.

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On Discrete-Time Loop Transfer Recovery

Cited by 10 publications

References 13 publications

Discrete‐time loop transfer recovery with multistep delays

Discrete‐time loop transfer recovery with multistep delays

Discrete‐time loop transfer recovery via generalized sampled‐data hold functions based compensator

Bode integrals for multivariable discrete-time systems

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