When is Naive Low-Pass Filtering of Noisy Measurements Counter-Productive for the Dynamics of Controlled Systems?

Rauh, Andreas; Romig, Swantje; Aschemann, Harald

doi:10.1109/mmar.2018.8486099

Cited by 6 publications

(30 citation statements)

References 7 publications

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“…As shown in [26], a linear low-pass output filtering, as well as the derivative estimation of the scalar measured variables y m,i , i ∈ {1, . .…”

Section: Linear Output Filteringmentioning

confidence: 99%

“…Generalizing the statements from [26], the minimization of the ellipsoid volume-with a simultaneous maximization of the error domain for which the linear feedback signals are bounded by some positive constant according to [34] after introducing the denominator terms depending on Q and Q f,i -leads to the cost…”

Section: Optimal Output Feedback Controlmentioning

confidence: 99%

“…The required steps are summarized in Appendix B. Comparison of a heuristic D-type control approach with an optimized observer from the previous work [26].…”

Section: Comparison With a Heuristic D-type Control Parameterizationmentioning

confidence: 99%

See 2 more Smart Citations

Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Rauh

Romig

2021

Sensors

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Linear matrix inequalities (LMIs) have gained much importance in recent years for the design of robust controllers for linear dynamic systems, for the design of state observers, as well as for the optimization of both. Typical performance criteria that are considered in these cases are either H2 or H∞ measures. In addition to bounded parameter uncertainty, included in the LMI-based design by means of polytopic uncertainty representations, the recent work of the authors showed that state observers can be optimized with the help of LMIs so that their error dynamics become insensitive against stochastic noise. However, the joint optimization of the parameters of the output feedback controllers of a proportional-differentiating type with a simultaneous optimization of linear output filters for smoothening measurements and for their numeric differentiation has not yet been considered. This is challenging due to the fact that the joint consideration of both types of uncertainties, as well as the combined control and filter optimization lead to a problem that is constrained by nonlinear matrix inequalities. In the current paper, a novel iterative LMI-based procedure is presented for the solution of this optimization task. Finally, an illustrating example is presented to compare the new parameterization scheme for the output feedback controller—which was jointly optimized with a linear derivative estimator—with a heuristically tuned D-type control law of previous work that was implemented with the help of an optimized full-order state observer.

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“…As shown in [26], a linear low-pass output filtering, as well as the derivative estimation of the scalar measured variables y m,i , i ∈ {1, . .…”

Section: Linear Output Filteringmentioning

confidence: 99%

Section: Optimal Output Feedback Controlmentioning

confidence: 99%

See 1 more Smart Citation

Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Rauh

Romig

2021

Sensors

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“…The stability of the closed-loop control structure can be verified by computing the total time derivative of the sliding surface s(x) defined in (48) according to:…”

Section: Verification Of Stabilitymentioning

confidence: 99%

“…Straightforwardly, also generalizations to the identification of domains in the state space, for which the stability of stochastic differential equations cannot be verified, became possible. Such domains were derived in [48].…”

Section: Conclusion and Outlook On Future Workmentioning

confidence: 99%

Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System

2019

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In recent years, many applications, as well as theoretical properties of interval analysis have been investigated. Without any claim for completeness, such applications and methodologies range from enclosing the effect of round-off errors in highly accurate numerical computations over simulating guaranteed enclosures of all reachable states of a dynamic system model with bounded uncertainty in parameters and initial conditions, to the solution of global optimization tasks. By exploiting the fundamental enclosure properties of interval analysis, this paper aims at computing invariant sets of nonlinear closed-loop control systems. For that purpose, Lyapunov-like functions and interval analysis are combined in a novel manner. To demonstrate the proposed techniques for enclosing invariant sets, the systems examined in this paper are controlled via sliding mode techniques with subsequently enclosing the invariant sets by an interval based set inversion technique. The applied methods for the control synthesis make use of a suitably chosen Gröbner basis, which is employed to solve Bézout’s identity. Illustrating simulation results conclude this paper to visualize the novel combination of sliding mode control with an interval based computation of invariant sets.

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A Novel Thick Ellipsoid Approach for Verified Outer and Inner State Enclosures of Discrete-Time Dynamic Systems

Rauh

Jaulin

2021

IFAC-PapersOnLine

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When is Naive Low-Pass Filtering of Noisy Measurements Counter-Productive for the Dynamics of Controlled Systems?

Cited by 6 publications

References 7 publications

Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System

A Novel Thick Ellipsoid Approach for Verified Outer and Inner State Enclosures of Discrete-Time Dynamic Systems

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