Self-excited systems arise in many applications,
such as biochemical systems, mechanical systems with fluidstructure
interaction, and fuel-driven systems with combustion
dynamics. This paper presents a Lur’e model that exhibits
biased oscillations under constant inputs. The model involves
arbitrary asymptotically stable linear dynamics, time delay, a
washout filter, and a saturation nonlinearity. For all sufficiently
large scalings of the loop transfer function, these components
cause divergence under small signal levels and decay under
large signal amplitudes, thus producing an oscillatory response.
A bias-generation mechanism is used to specify the mean of
the oscillation. The main contribution of the paper is the
presentation and analysis of a discrete-time version of this
model.
more »
« less
Identification of Self-Excited Systems Using Discrete-Time, Time-Delayed Lur’e Models
This paper considers system identification for
systems whose output is asymptotically periodic under constant
inputs. The model used for system identification is a discretetime
Lur’e model consisting of asymptotically stable linear
dynamics, a time delay, a washout filter, and a static nonlinear
feedback mapping. For sufficiently large scaling of the loop
transfer function, these components cause divergence under
small signal levels and decay under large signal amplitudes,
thus producing an asymptotically oscillatory output. A leastsquares
technique is used to estimate the coefficients of the
linear model as well as the parameters of a piecewise-linear
approximation of the feedback mapping.
more »
« less
- Award ID(s):
- 1634709
- NSF-PAR ID:
- 10283703
- Date Published:
- Journal Name:
- Proceedings of the American Control Conference
- ISSN:
- 2378-5861
- Page Range / eLocation ID:
- 3929-3934
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A self-excited system is a nonlinear system with the property that a constant input yields a bounded, nonconvergent response. Nonlinear identification of self-excited systems is considered using a Lur'e model structure, where a linear model is connected in feedback with a nonlinear feedback function. To facilitate identification, the nonlinear feedback function is assumed to be continuous and piecewise affine (CPA). The present paper uses least-squares optimization to estimate the coefficients of the linear dynamics and the slope vector of the CPA nonlinearity, as well as mixed-integer optimization to estimate the order of the linear dynamics and the breakpoints of the CPA function. The proposed identification technique requires only output data, and thus no measurement of the constant input is required. This technique is illustrated on a diverse collection of low-dimensional numerical examples as well as data from a gas-turbine combustor.more » « less
-
more » « less
Abstract Methods in system identification are used to obtain linear time-invariant state-space models that describe how horizontal averages of temperature and humidity of a large cumulus ensemble evolve with time under small forcing. The cumulus ensemble studied here is simulated with cloud-system-resolving models in radiative–convective equilibrium. The identified models extend steady-state linear response functions used in past studies and provide accurate descriptions of the transfer function, the noise model, and the behavior of cumulus convection when coupled with two-dimensional gravity waves. A novel procedure is developed to convert the state-space models into an interpretable form, which is used to elucidate and quantify memory in cumulus convection. The linear problem studied here serves as a useful reference point for more general efforts to obtain data-driven and interpretable parameterizations of cumulus convection.
-
more » « less
Abstract Bounded input delay frequently arises in discrete‐time linear systems. The standard predictor feedback design requires the exact knowledge of the delay. Such a requirement on the availability of the delay knowledge poses challenges in the design of robust control laws when only the knowledge of an upper bound of the delay is known. We propose such a design in this article. Based on the delay‐independent truncated predictor state feedback design, an observer‐based output feedback law is constructed that does not contain any explicit information of the delay. For a general, possibly exponentially unstable, discrete‐time linear system, the proposed output feedback law stabilizes the system as long as the delay does not exceed a certain amount. For the special case of systems with all the open‐loop poles on or inside the unit circle, a low gain feedback design is presented. This low gain design allows us to establish that, when all the open‐loop poles of a system are at
z = 1 -
This paper introduces a new identification‐ and singularity‐robust conditional quasi‐likelihood ratio (SR‐CQLR) test and a new identification‐ and singularity‐robust Anderson and Rubin (1949) (SR‐AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2 + γ bounded moments for some γ > 0. No conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions. The SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification (for all k ≥ p , where k and p are the numbers of moment conditions and parameters, respectively). The SR‐CQLR test reduces asymptotically to Moreira's CLR test when p = 1 in the homoskedastic linear IV model. The same is true for p ≥ 2 in most, but not all, identification scenarios. We also introduce versions of the SR‐CQLR and SR‐AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identified. The subvector SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
