Multi(2)-Rate Control From a 2-Periodic Perspective: Generalized 2-Rate Control

Chakraborty, Sayantan; Das, Sarit K.

doi:10.1109/tac.2015.2478132

Cited by 12 publications

(23 citation statements)

References 32 publications

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“…However, such PTV controllers may cause large ripples in the responses. 7,10,11 Multirate controllers, 8,9,[12][13][14][15][16] in particular, the 2-rate ones, 4,17,18 have also been used in literature to effect zero-placement. A 2-rate control scheme is one in which, either the plant output or the control input to the plant is sampled at a rate two times faster than the other.…”

Section: Introductionmentioning

confidence: 99%

LQ‐optimal 2‐rate control of a class of single‐input single‐output discrete‐time plants

Bhattacharya

Garg

Das

2022

Intl J Robust & Nonlinear

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Use of 2‐rate controllers for robust control via zero‐placement is a topic of interest in current literature. This paper proposes a 2‐degree‐of‐freedom, 2‐rate, dynamic, output feedback controller to compensate single‐input single‐output (SISO), unstable, non‐minimum phase (NMP), discrete, linear time‐invariant (LTI) plants of relative degree unity; and achieves exactly the same loop and input‐output properties as can be achieved by a linear quadratic regulator (LQR) for the equivalent lifted LTI plant using state feedback. Such LQR‐like loop and input‐output properties, it may be noted, cannot be attained by LTI or even the existing 2‐rate output feedback controllers for plants with NMP zeros. Examples presented illustrate the efficacy of the proposed controller with respect to the existing ones.

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Section: Introductionmentioning

confidence: 99%

LQ‐optimal 2‐rate control of a class of single‐input single‐output discrete‐time plants

Bhattacharya

Garg

Das

2022

Intl J Robust & Nonlinear

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“…Periodic controllers, owing to their zero‐placement capabilities, have been used in literature to obtain improved gain, phase margin compensations, 1‐15 infinite sector absolute stability, 16 and to remove decentralized fixed modes 1,17,18 for non‐minimum phase (NMP), linear time‐invariant (LTI) plants. The additional parameters of periodic controllers also help achieve simultaneous stabilization; see Reference 18 and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…The sampled‐data‐based periodic controllers, such as generalized‐sampled‐data‐hold‐function (GSHF) 8‐11 or multi‐rate 12,13 controllers, on the other hand, often suffer from the problem of inter‐sample ripples in the output, which makes them difficult to employ in practice. To circumvent this, recently, a discrete‐time periodic controller which is a generalized version of 2‐rate control is proposed for gain margin improvement via zero‐placement, while ensuring no inter‐sample ripples in control input and output at steady state 14 …”

Section: Introductionmentioning

confidence: 99%

“…Among the (nonadaptive) linear periodic controllers above, although the controllers such as in References 3 and 14 are physically implementable, no result is yet available to robustly compensate a system where the parameters, and not only gain, are uncertain. Also it would be interesting to study if periodic controllers would be of any help for minimum phase plants in presence of general parametric uncertainties, although as is well known, they are not advantageous with respect to gain uncertainties.…”

Section: Introductionmentioning

confidence: 99%

“…Also it would be interesting to study if periodic controllers would be of any help for minimum phase plants in presence of general parametric uncertainties, although as is well known, they are not advantageous with respect to gain uncertainties. The main limitation behind studying these problems appears to be the fact that the design approaches of References 3 and 14 are polynomial‐based, where it is extremely difficult to handle parametric uncertainties excepting gain variation. Now, very recently, the authors in Reference 22 have proposed a 2‐DOF, high frequency, continuous‐time, periodic controller and a state‐space‐based method to design the same for LTI plants.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Periodic compensation of continuous‐time linear systems with norm‐bounded parametric uncertainties

Deshmukh

Garg

2021

Intl J Robust & Nonlinear

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This article employs a recently proposed high frequency, continuous‐time periodic controller to compensate single‐input‐single‐output linear plants with norm‐bounded time‐varying uncertainties. To this end, the design of periodic controller is converted into designing a linear time‐invariant (LTI) controller for a single‐input‐two‐output equivalent uncertain system, following averaging technique. To represent this equivalent uncertain system into a standard form of linear uncertain systems, where uncertainties appear in system matrix A and input matrix B, the observer canonical form description of the original uncertain plant is exploited. Using the relationship between quadratic stability and ℋ∞‐norm minimization result available in literature, it is proved that the presence of virtual output with the periodic feedback introduces a feedforward action on the disturbance input of the generalized plant, unlike an LTI one. By virtue of this, the proposed periodic controller can tolerate more uncertainty bound in the input matrix B than its LTI counterpart, while keeping the bound on system matrix A the same. Finally, a linear matrix inequality‐based method is used to design the periodic controller to achieve quadratic stability along with robust linear quadratic performance. Suitable examples are considered to show the superiority of the periodic control as compared to LTI ones.

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Centralized performance of a 2-rate decentralized controller for a class of two-channel systems

Bhattacharya,

Ghosh,

Das

2023

Automatica

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Multi(2)-Rate Control From a 2-Periodic Perspective: Generalized 2-Rate Control

Cited by 12 publications

References 32 publications

LQ‐optimal 2‐rate control of a class of single‐input single‐output discrete‐time plants

LQ‐optimal 2‐rate control of a class of single‐input single‐output discrete‐time plants

Periodic compensation of continuous‐time linear systems with norm‐bounded parametric uncertainties

Centralized performance of a 2-rate decentralized controller for a class of two-channel systems

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