Estimating unstable poles in simulations of microwave circuits

Abstract

The impedance of a microwave circuit has an infinite number of poles due to the distributed elements. This complicates locating those poles with a rational approximation. In this paper, we propose an algorithm to locate the unstable poles of a circuit with distributed elements. The proposed method exploits the fact that a realistic circuit can only have a finite number of unstable poles. We first determine the unstable part whose poles coincide with the unstable poles of the circuit. A rational approximation of the unstable part is used to estimate the unstable poles.

Interpolation-based irrational model control design and stability analysis

“…So far, the control design has been done in a fairly standard way, involving the approximated rational model. Instead of designing a controller on the basis of a rational reduced-order model, as the true system's behaviour is known through (5), a data-driven control strategy, based on the approach presented in [10], is followed. Authors stress that the main contribution of this section with respect to [10] stands in the comparison of the datadriven approach with the model-based one, resulting, as we will see later in the chapter, in exactly similar results.…”

From Reference Model Selection to Controller Validation: Application to Loewner Data-Driven Control

“…The proposed method is based on frequency-domain data. It relies on a data-driven instability detection technique introduced in [8]. Then, once the instabilities of the plant are detected, it is possible to build an achievable reference model.…”

“…In this paper, we propose to build a stable reference model that satisfies (5). First, the plant's instabilities are estimated using the method proposed in [8], recalled in the next section. Then the construction of the reference model is proposed in Section IV and applied on the example of the flexible transmission in Section VI.…”

“…The estimation of instabilities proposed in [8] is based on the Principal Hankel Components (PHC) method.It relies on the Hankel matrix containing the Fourier coefficients corresponding to the anti-stable projection P as . In practice, a truncation Φ n F of the infinite dimensionnal matrix Φ is used, see (8).…”

“…The number of poles n p is the number of non-zero singular values in (9). The value of the corresponding RHP poles can be deduced from the truncated Hankel matrix, see [8].…”