Control zeros and nonminimum phase LTI mimo systems

Latawiec, Krzysztof J.; Bańka, Stanisław; Tokarzewski, Jerzy

doi:10.1016/s1367-5788(00)90021-x

Cited by 10 publications

(8 citation statements)

References 12 publications

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“…Observe that the T -inverses have been originally used in the introduction of control zeros, being an extension of transmission zeros [6], [15]. For example, control zeros for right-invertible systems can be generated by the inverse B R1 0 (q −1 ).…”

Section: Remarkmentioning

confidence: 99%

“…A number of examples showing the diversified behavior of MVC for various selections of poles and zeros of the inverses can be found in [6], [15], [16], [17], [18], [19], [20], [21], [22], [23], [26].…”

Section: New Inverse Of a Nonsquare Polynomial Matrixmentioning

confidence: 99%

“…Actually, our interest in right/left inverses of polynomial matrices has evolved from MVC/perfect control applications [6], [15], [21] which are now being expanded towards robust MVC/perfect control [16], [17], [18], [20], [22], [23]. Quite similar families of applications include distortionless (or perfect) reception in error-control coding [7], [8], [9], [10], [11], [27], [28], perfect precoding and equalization [29], [30], [31], [32], [33], [34], [35], perfect signal reconstruction, including perfect reconstruction filter banks [12], [13], [14], [36], [37], [38] and perfect deconvolution [39], [40], also in the problem of image recovery [41], [42].…”

Section: Actual and Potential Applicationsmentioning

confidence: 99%

“…The employment of the minimum-norm right or leastsquares left inverses has also been the authors' first choice when solving the problem of generation of the so-called 'control zeros' for a nonsquare LTI MIMO system, the zeros defined as poles of an inverse system or poles of a closedloop minimum variance control (MVC) system [6], [15]. The limited usefulness of the minimum-norm right or least-squares left inverses, to be in the sequel called the T -inverses, has soon brought us to the point where we have introduced the so-called τ -inverses and σ-inverses of nonsquare polynomial matrices [16], [17], [18].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Right/Left inverses of polynomial matrices for control, communications and vision

Hunek

Latawiec

Łukaniszyn

2010

2010 11th International Conference on Control Automation Robotics &Amp; Vision

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This paper reviews various right/left inverses of polynomial matrices, introduced by the authors as a result of their research works on minimum variance control for LTI MIMO systems. In consequence, a new, general, Smith-factorization based inverse is presented. The problem of selection of stable inverses, in particular pole-free inverses, is also tackled. Applications in control, communications and vision, in particular concerning perfect signal transmission/recovery, are indicated.Index Terms-MIMO channels/systems, right/left inverses of polynomial matrices, Smith factorization, minimum variance control.

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Section: Remarkmentioning

confidence: 99%

Section: New Inverse Of a Nonsquare Polynomial Matrixmentioning

confidence: 99%

Section: Actual and Potential Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Right/Left inverses of polynomial matrices for control, communications and vision

Hunek

Latawiec

Łukaniszyn

2010

2010 11th International Conference on Control Automation Robotics &Amp; Vision

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“…Output setpoint regulation was studied in [18]. Optimal control that drives an NMPH discrete-time (DT) linear system from a known constant initial to a known constant final position was studied in [19].…”

Section: Introductionmentioning

confidence: 99%

Output tracking in causal nonminimum phase systems using discrete-time stable system center

Iskrenovic-Momcilovic

2013

IETE J Res

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Output tracking is considered for discrete-time causal single input single output n th order linear time invariant system with nonminimum phase zeros via discrete-time variable structure control. The stable system center method was developed originally for controlling the output in continuous time nonminimum phase causal system using sliding mode control. The developed discrete-time stable system center technique transforms an output tracking problem to a corresponding state variable tracking problem. The causal disturbances and output tracking profiles are assumed to obey a linear exogenous system with known characteristic polynomial. The theoretical results are confirmed by discrete variable structure control synthesis for the tracking of const signal.

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On the role of subspace zeros in retrospective cost adaptive control of non-square plants

Sumer

Bernstein

2014

International Journal of Control

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We consider adaptive control of non-square plants, that is, plants that have an unequal number of inputs and outputs. In particular, we focus on retrospective cost adaptive control (RCAC), which is a direct, discrete-time adaptive control algorithm that is applicable to stabilisation, command following, disturbance rejection, and model reference control problems. Previous studies on RCAC have focused on control of square plants. In the square case, RCAC requires knowledge of the first non-zero Markov parameter and the non-minimum-phase (NMP) transmission zeros of the plant, if any. No additional information about the plant or the exogenous signals need be known. The goal of the present paper is to consider RCAC for non-square plants. Unlike the square case, we show that the assumption that the non-square plant is minimum phase does not guarantee closed-loop stability and signal boundedness. The main purpose of this paper is to establish the existence of time-invariant input and output subspaces corresponding to the adaptive controller. In particular, we show that RCAC implicitly squares down non-square plants through pre-/post-compensation of the non-square plant with a constant matrix. We show that, for wide plants, the control input generated by RCAC lies in a time-invariant 'input subspace', which is equivalent to pre-compensating the plant with a constant matrix. On the other hand, for tall plants, we show that the controller update is driven by the output of the plant post-compensated with a constant matrix. Accordingly, in either case, signal boundedness properties of the closed-loop system are determined by the transmission zeros of the squared system, which we call the 'subspace zeros'. To deal with NMP subspace zeros, we introduce a robustness modification, which prevents RCAC from cancelling the NMP subspace zeros.

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Control zeros and nonminimum phase LTI mimo systems

Cited by 10 publications

References 12 publications

Right/Left inverses of polynomial matrices for control, communications and vision

Right/Left inverses of polynomial matrices for control, communications and vision

Output tracking in causal nonminimum phase systems using discrete-time stable system center

On the role of subspace zeros in retrospective cost adaptive control of non-square plants

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