The averaging method for control design and stability analysis of practical switched systems

Pedicini, Carmen; Iannelli, Luigi; Vasca, Francesco

doi:10.1109/cca.2012.6402375

Cited by 9 publications

(6 citation statements)

References 29 publications

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“…Theorem 1: Consider the switched DAE system (1) with initial value x 0 ∈ R n and P modes satisfying the following assumptions (i) the switching signal σ is periodic of period p and given by (11) with d i ∈ (0, 1) ∀ i = 1, . .…”

Section: Averaging For Switched Daesmentioning

confidence: 99%

“…The paper [10] presents an overview on the averaging results for switched systems which commute among modes each representable by means of possibly nonlinear ordinary differential equations. Averaging of fast switching systems is also an effective technique used in many engineering applications [11]. However in modeling switched systems a representation by means of switching ordinary differential equations (ODEs) might limit the description of switched systems behavior.…”

Section: Introductionmentioning

confidence: 99%

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An averaging result for switched DAEs with multiple modes

Iannelli

Pedicini

Trenn

et al. 2013

52nd IEEE Conference on Decision and Control

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The major motivation of the averaging technique for switched systems is the construction of a smooth average system whose state trajectory approximates in some sense the state trajectory of the switched system. Averaging of dynamic systems represented by switched ordinary differential equations (ODEs) has been widely analyzed in the literature. The averaging approach can be useful also for the analysis of switched differential algebraic equations (DAEs). Indeed by analyzing the evolution of the switched DAEs state it is possible to conjecture the existence of an average model. However a trivial generalization of the ODE case is not possible due to the presence of state jumps. In this paper we discuss the averaging approach for switched DAEs and an approximation result is derived for homogenous switched linear DAE with periodic switching signals commuting among several modes. This approximation result extends a recent averaging result for switched DAEs with only two modes. Numerical simulations confirm the validity of the averaging approach for switched DAEs.

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Section: Averaging For Switched Daesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An averaging result for switched DAEs with multiple modes

Iannelli

Pedicini

Trenn

et al. 2013

52nd IEEE Conference on Decision and Control

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“…Due to the nonlinearity of closed-loop control system, the average analysis method is exploited to analyze its stabilization [31]. According to Equation (3), the differential equation between the input of the system ( Vi ) and the output of preamplifier ( Vo ), demodulation result ( VL ) and output of PI controller ( Vt ) can be, respectively, deduced as lefttrueVo¨+ws0QtrueVo˙+(ws02−bVt2)Vo=Kf−emsVitrueVL˙=β(VoVi−VL)trueVt˙=Ki(VL−C) where β represents the cut-off frequency of low pass filter (LPF), and Ki and C are the integral coefficient and reference voltage of PI controller, respectively.…”

Section: Digital Excitation-calibration Control Systemmentioning

confidence: 99%

A Digital Calibration Technique of MEMS Gyroscope for Closed-Loop Mode-Matching Control

Yang

Guo

et al. 2019

Micromachines

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A digital excitation-calibration technique of dual-mass MEMS gyroscope for closed-loop mode-matching control is presented in this paper. The technique, which takes advantage of the symmetrical amplitude response of MEMS gyroscope, exploits a two-side excitation signal to actuate the sense mode to obtain the corresponding DC tuning voltage. The structural characteristics of dual-mass decoupled MEMS gyroscope and the tuning principle of excitation-calibration technique are introduced firstly. Then, the scheme of digital excitation-calibration system for the real-time mode-matching control is presented. Simultaneously, open-loop analysis and closed-loop analysis are deduced, respectively, to analyze the sources of tuning error and system stability. To verify the validity of the scheme and theoretical analysis, the system model was established by SIMULINK. The simulation results are proved to be consistent with the theoretical analysis, verifying the feasibility of the digital excitation-calibration technique. The control algorithms of the system were implemented with a FPGA device. Experimental results demonstrate that digital excitation-calibration technique can realize mode-matching within 1 s. The prototype with real-time mode-matching control has a bias instability of 0.813 ∘ /h and an ARW (Angular Random Walk) of 0.0117 ∘ / h . Compared to the mode-mismatching condition, the bias instability and ARW are improved by 3.25 and 4.49 times respectively.

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“…Averaging techniques, discussed in literature (Pedicini et al 2012;Krein et al 1989;Sanders et al 1990;Lehman & Bass 1994;Ren et al 2000;Jalla et al 2004;Chung et al 2009), include state-space and switching cycle averaging methods. State-space averaging technique is a matrix based technique, increasing the computational effort (Vuthchhay & Bunlaksananusorn 2008).…”

Section: Introductionmentioning

confidence: 99%

Computationally efficient models for simulation of non-ideal DC–DC converters operating in continuous and discontinuous conduction modes

Krishna

Saritha

Narayanan

2015

Sadhana

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This paper discusses dynamic modeling of non-isolated DC-DC converters (buck, boost and buck-boost) under continuous and discontinuous modes of operation. Three types of models are presented for each converter, namely, switching model, average model and harmonic model. These models include significant nonidealities of the converters. The switching model gives the instantaneous currents and voltages of the converter. The average model provides the ripple-free currents and voltages, averaged over a switching cycle. The harmonic model gives the peak to peak values of ripple in currents and voltages. The validity of all these models is established by comparing the simulation results with the experimental results from laboratory prototypes, at different steady state and transient conditions. Simulation based on a combination of average and harmonic models is shown to provide all relevant information as obtained from the switching model, while consuming less computation time than the latter.

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The averaging method for control design and stability analysis of practical switched systems

Cited by 9 publications

References 29 publications

An averaging result for switched DAEs with multiple modes

An averaging result for switched DAEs with multiple modes

A Digital Calibration Technique of MEMS Gyroscope for Closed-Loop Mode-Matching Control

Computationally efficient models for simulation of non-ideal DC–DC converters operating in continuous and discontinuous conduction modes

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