Pointwise frequency responses framework for stability analysis in periodically time-varying systems

In this paper a time varying control for doubly salient machines is proposed. The mathematical model of a switched reluctance motor drive (a typical representative of doubly salient machines) can be represented as a linear time variant system, if the rotor angular velocity is assumed constant. A Floquet transformation is derived which makes it possible to represent the same system as a linear time invariant model with a time dependent control. Next, a torque follower control is proposed for the new model. It was possible to obtain an explicit (closed form) solution for the nonlinear control which is feasible in real time. Conceptually this approach can be used for any other time variant system and serve the same purpose as control design via feedback linearization for nonlinear systems. For the class of time variant systems the feedback linearization results have not been studied yet.

In this paper, we propose and solve the problem of feedback linearization of single-input control affine time-varying nonlinear systems. Feedback linearizability of time-varying is shown to be equivalent to the orbital feedback linearizability (or feedback linearization by state-dependent time scaling) of an extended version of the time-varying system. Necessary and sufficient conditions for feedback linearizability are presented. The conditions are simple and can be checked directly from the data of the problem. Using an exterior calculus approach, a simple algorithm is developed to compute state-dependent time scaling that yield state-feedback linearizable time-varying systems.

A control scheme is proposed to stabilise a class of time-varying nonlinear systems. The scheme is based on the feedback-linearisation scheme and is developed via the newly proposed time-varying diffeomorphism concept, which results in the transformation of time-varying systems into equivalent time-invariant linear systems. As a result, feedback linearisation of time-varying nonlinear systems is achieved and it provides the stabilisation of a class of nonlinear time-varying systems. In addition, the approximate feedback LTIsation concept is introduced for its practicability.

Given a feedback system containing a linear, time-varying (LTV) plant with significant plant uncertainty, it is required that the system response to command and disturbance inputs satisfy specified tolerances over the range of plant uncertainty. The synthesis procedure guarantees the latter satisfied, providing that they are of the following form. Let h(t',\tau) be the system response at t'= t - \tau due to a command input \delta(t - \tau) , and h_{\tau}(s)=\int \liminf{0}\limsup{infty}h(t',\tau)e^-{st'}dt' is the Laplace transform of h(t',\tau) . There is given a set M_{\tau}(\omega)=\{m_{\tau}(\omega)\} , \omega \in[0, \infty) , with the requirement that |h_{\tau}(j\omega)| \in M_{\tau}(\omega) , over the range of plant uncertainty. The disturbance response tolerances are of the same form, in response to a disturbance input \delta (t- \tau) . The acceptable response set M_{\tau}(\omega) can depend on τ. The design emerges with a fixed pair of LTV compensation networks and can be considered applicable to time-domain response tolerances, to the extent that a set of bounds on a time function can be translated into an equivalent set on its frequency response. The design procedure utilizes only time-invariant frequency response concepts and is conceptually easy to follow and implement. At any fixed τ, the time-varying system is converted into an equivalent time-invariant one with plant uncertainty, for which an exact solution is available, with frozen time-invariant compensation. Schauder's fixed-point theorem is used to prove the equivalence of the two systems. The ensemble over τ of the time-invariant compensation gives the final required LTV compensation. It is proven that the design is stable and nonresonant for all bounded inputs.

Modelling of uncertain systems via linear programming

In this study, linear quadratic regulator (LQR) and linear matrix inequalities (LMI) based optimal controllers that guaranteed the stability of the vehicle are designed and performed in the double lane change problem. The simulation case is created according to a scenario frequently encountered in traffic. It is assumed that since the vehicle is positioned safely in the moving lane and the path following controllers provide double lane change maneuver to avoid the collision possibility. A nonlinear model of the vehicle is created and linearized to design the controller to provide automated steering. In the vehicle model, lateral and heading look-ahead errors are used as state variables and performance indexes are created to minimize them accordingly. While the LQR design is made for both linear time-invariant (LTI) and linear parameter-varying (LPV) models, LMI-based state and output feedback controllers are designed using the linear time-invariant model in a way that aims to minimize the H∞ norm of the system. In the simulation studies, the effect of minimizing the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> and H∞ norms on the look-ahead error, as well as the advantages of the LPV model-based controller design compared to the LTI design, are examined.

Periodic Motions for Estimation of the Attraction Domain in the Wheeled Robot Stabilization Problem

Voltage ripple in single-phase ac-dc converters is usually disregarded to design the dc-link voltage control system, since large dc-link electrolytic capacitors are typically employed. However, replacement of electrolytic capacitors by film capacitors has been widely considered for increasing reliability. Consequently, due to cost constraints, such replacement usually employ low capacitance and may be combined with fast dc-bus voltage controllers. This paper shows that the conventional linear time-invariant (LTI) model may not represent the real converter behavior for reduced capacitance and/or faster controllers, leading to poor system performance or even instability. In this way, for any of these cases, the linear time-periodic (LTP) model is highly encouraged for stability and transient analysis as a tool for the controller design. Experimental results confirm that stability margins are precisely obtained from the LTP model but may not from the LTI model. Finally, this paper also compares both LTI and LTP models while considering the control gain and the dc-bus capacitance size. It is graphically revealed that the phase margin of the LTI model diverges from the LTP model for low dc-bus capacitances and high control gains.

Design of optimal PID controller for multivariable time-varying delay discrete-time systems using non-monotonic Lyapunov-Krasovskii approach

Stability analysis of nonlinear control systems with characteristics equations having complex coefficients

Most newcomers to acoustic signal processing understand that linear time-invariant (LTI) filters can remove out-of-band noise from time series signals. What many acoustics researchers may not realize is that LTI models can be applied much more broadly, including to non-linear and time-variant systems. This presentation covers an overview of the autoregressive (AR), moving-average (MA), and autoregressive moving-average (ARMA) family of LTI models and their many useful applications in acoustics. Examples include analytic time-frequency processing of multi-component echolocation signals, fractional-delay filtering for acoustic time series simulations, broadband acoustic array beamforming, adaptive filtering for noise cancelation, and system identification for acoustic equalizers (i.e., flattening the frequency response of a source-receiver pair). This talk serves as a brief tutorial and inspiration for researchers who want to expand their use of signal processing, especially those in the fields of animal bioacoustics, aerial acoustics, and underwater acoustics.

Modeling dynamic radial contrast enhanced MRI with linear time invariant systems for motion correction in quantitative assessment of kidney function.

Trade-offs in linear control system design

A linear time-invariant model for solid-phase diffusion in physics-based lithium ion cell models

Several methods for analysis of linear time periodic (LTP) systems have successfully been demonstrated using harmonic decompositions. One method recently examined is to create a linear time invariant (LTI) model approximation by expansion of the LTP system states into various harmonic state representations, and formulating corresponding linear time invariant models. Although this method has shown success, it relies on a second order formulation of the original LTP system. This second order formulation can prove problematic for degrees of freedom not explicitly represented in second order form. Specifically, difficulties arise when performing the harmonic decomposition of body and inflow states as well as interpretation of LTI velocities. Instead this paper will present a more generalized LTI formulation using a first order formulation for harmonic decomposition. The new first order approach is evaluated for a UH-60 rotorcraft model, and is used to show the significance of particular harmonic terms; specifically that the coupling of harmonic components of body and inflow states with the rotor states has a significant contribution to the LTI model fidelity in the prediction of vibratory hub loads.