Conference Paper

Checking if controllers are stabilizing using closed-loop data

Res. Sch. of Inf. Sci. & Eng., Australian Nat. Univ., Canberra, ACT
DOI: 10.1109/CDC.2006.377549 Conference: Decision and Control, 2006 45th IEEE Conference on
Source: IEEE Xplore

ABSTRACT

Suppose an unknown plant is stabilized by a known controller. Suppose also that some knowledge of the closed-loop system is available and on the basis of that knowledge, the use of a new controller appears attractive, as may arise in iterative control and identification algorithms, and multiple-model adaptive control. The paper presents tests using a limited amount of experimental data obtained with the existing known controller for verifying that introduction of the new controller will stabilize the plant

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    • "The designed controller is then implemented in two parts such that˜V −1 appears in the forward path and˜U appears in the feedback path. The architecture in Figure 1 from [28], [29] with (X,Y ) = (M, N) is equivalent to the feedback architecture in [30], yet, the advantage of Figure 1 is that the controller C b does not need to be split up into two parts. Hence, we focus on the feedback architecture of Figure 1 to propose an enhanced tracking control design for nanopositioning systems and this control architecture will be considered in the rest of the paper. "
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    ABSTRACT: This paper proposes a systematic synthesis methodology for a combined feedforward/feedback architecture to control multiple-input, multiple-output nanopositioning systems. Coprime factorization of the open loop model is used to design the reference and feedforward filters of the proposed control scheme to achieve enhanced tracking, eliminate the limitation of the feedback on tracking performance, and increase the bandwidth of the closed-loop system. Two types of coprime factorization, namely inner–outer factorization and normalized coprime factorization are discussed. A case study based on hardware experiment is presented to analyze the proposed control architecture and demonstrate its superiority over feedback-only control. In addition to the no-load case, the performance of the system is also tested with loads on the nanopositioning stage.
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    • "This paper proposes a two degree of freedom MIMO feedforward/feedback control scheme for nanopositioning stages based on the structure given in [18]. Inner-outer factorisation is used as a special case of coprime factorisation to design the reference and feedforward filters. "
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    ABSTRACT: This paper proposes a two degree of freedom control using a combined feedforward/feedback architecture for MIMO nanopositioning stages. The proposed control system provides higher bandwidth and better performance compared with a single degree of freedom feedback controller. The paper proposes a systematic synthesis methodology to design the controller based on closed loop performance. The results are verified via simulation and hardware experiment.
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    • "In Section III, we will present a framework for implementing controllers in a specialized way, which enables presentation of the proposed experimental setting. This builds on our earlier results [28], [29] and leads to the development of the proposed novel validation tests of Section IV for SISO/MIMO systems. Simulation examples of Section V show the versatility and applicability of the proposed tests. "
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    ABSTRACT: We introduce novel tests utilizing a limited amount of experimental and possibly noisy data obtained with an existing known stabilizing controller connected to an unknown plant for verifying that the introduction of a proposed new controller will stabilize the plant. The tests depend on the assumption that the unknown plant is stabilized by a known controller and that some knowledge of the closed-loop system, such as noisy frequency response data, is available and on the basis of that knowledge, the use of a new controller appears attractive. The desirability of doing this arises in iterative identification and control algorithms, multiple-model adaptive control, and multi-controller adaptive switching. The proposed tests can be used for SISO and/or MIMO linear time-invariant systems.
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