Harmonic transfer functions based controllers for linear time-periodic systems

Abstract

The analysis, identification and control of periodic systems has gained increasing interest during the last few decades due to the increased use of dynamical systems that exhibit periodic motion. The vast majority of these studies focus on the analysis and control problem for a known state-space formulation of the linear time-periodic (LTP) system. On the other hand, there are also some studies that focus on data-driven identification of LTP systems with unknown state-space formulations. However, most of these methods provide numerical estimates for the harmonic transfer functions (HTFs) of an LTP system that are extremely difficult to work with during controller design. The goal of this paper is to provide a simple controller design methodology for unknown LTP systems by utilizing so-called HTFs estimates. To this end, we first build a mathematical basis of LTP controller design for known LTP systems using the Nyquist diagrams and analytically derived HTFs. We propose a new methodology to design P-, PD-and PIDtype controllers for LTP systems using Nyquist diagrams and the eigenlocus of the HTFs. Having established the HTF-based controller design procedure, we extend our methodology to unknown LTP systems by presenting a new sum-of-cosine signal-based data-driven system identification method. We show that the proposed data-driven controller design method allows estimation of the HTFs and it provides simple tools for optimizing certain time-domain performance metrics. We provide numerical examples for both known and unknown LTP system cases to illustrate the performance of the proposed controller design methodology.

Modeling of Power Electronics Systems and PWM Modulators in Harmonic-State Space

“…This is one of the challenges of HSS. Some efforts have been made to develop Black Box models for the HSS model in [36] and [37], but more input can reap good rewards.…”

Frequency-Domain Subspace Identification of Linear Time-Periodic (LTP) Systems

“…As stated earlier, each cosine input at ω m produces an output spectra at ±ω m ±kω p for k ∈ Z, since cosine triggers both ±ω m . Hence the input frequencies should be carefully selected to avoid any coincidence of harmonic responses (see [26] for illustrative explanations). Once this is satisfied, we can separate the inputoutput response of each individual cosine signal in frequency domain.…”

“…Let the output of (1) to inputs u + c (t), u − c (t) and u c (t) be y + c (t), y − c (t) and y c (t), respectively where y c (t) = y + c (t) + y − c (t). Ensuring that ω m = 0.5kω p for k ∈ Z, one can also guarantee that there will be no coincidence in harmonic responses of the single-cosine input [26]. Thus, we can simulate (1) with u c (t) and only use y + c (t) as the output assuming that our input was u + c (t).…”

Frequency scanning of weakly damped single-phase VSCs with chirp error control

“…The majority of impedance-based stability analyses which incorporate coupling effects have since relied on single-tone sweeps for model verification [15]- [17] and even black-box input-output identification [18]. Some examples from other fields adopt wideband injections by either performing multiple independent injections [19] or by carefully designing the input signal to avoid spectral overlap [20], [21]. Either way introduces additional complexity to the design and post-processing procedures.…”