Biorthogonal Wavelet Based Identification of Fast Linear Time-Varying Systems—Part II: Algorithms and Performance Analysis12

2000 ◽  
Vol 123 (4) ◽  
pp. 593-600 ◽  
Author(s):  
Haipeng Zhao ◽  
Joseph Bentsman
Keyword(s):  
System Dynamics ◽  
High Speed ◽  
Linear Time ◽  
A Priori ◽  
Time Varying ◽  
Function Decomposition ◽  
Time Varying Systems ◽  
Random Disturbances ◽  
And Performance ◽  
Short Time

The present work proposes a new class of algorithms for identification of fast linear time-varying systems on short time intervals, based on the biorthogonal function decomposition. When certain features of the system dynamics are known a priori, the algorithms admit their embedding into the identification procedure through the choice of the matching bases, yielding the rapidly convergent identification laws. The speed-up is attained via utilizing both time and frequency localized bases, permitting identification of fewer coefficients without noticeable loss of accuracy. Simulation shows that the resulting high speed identification algorithms can reject small persistent random disturbances as well as capture the fast changes in system dynamics. The algorithm development is based on the results of Part I where it is shown that the sets of all bounded-input-bounded-output (BIBO) stable or l2-stable linear discrete-time-varying (LTV) systems are Banach spaces, and modeling and identification of these systems are reducible to linear approximation problems in a Banach space setting.

scholarly journals Damping Effects Induced by a Mass Moving along a Pendulum

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
E. Gandino ◽  
S. Marchesiello ◽  
A. Bellino ◽  
A. Fasana ◽  
L. Garibaldi
Keyword(s):  
Linear Time ◽  
Damping Ratio ◽  
System Response ◽  
Time Varying ◽  
Simple Method ◽  
Equivalent Damping ◽  
Stochastic Subspace Identification ◽  
Time Varying Systems ◽  
Instantaneous Frequencies ◽  
Short Time

The experimental study of damping in a time-varying inertia pendulum is presented. The system consists of a disk travelling along an oscillating pendulum: large swinging angles are reached, so that its equation of motion is not only time-varying but also nonlinear. Signals are acquired from a rotary sensor, but some remarks are also proposed as regards signals measured by piezoelectric or capacitive accelerometers. Time-varying inertia due to the relative motion of the mass is associated with the Coriolis-type effects appearing in the system, which can reduce and also amplify the oscillations. The analytical model of the pendulum is introduced and an equivalent damping ratio is estimated by applying energy considerations. An accurate model is obtained by updating the viscous damping coefficient in accordance with the experimental data. The system is analysed through the application of a subspace-based technique devoted to the identification of linear time-varying systems: the so-called short-time stochastic subspace identification (ST-SSI). This is a very simple method recently adopted for estimating the instantaneous frequencies of a system. In this paper, the ST-SSI method is demonstrated to be capable of accurately estimating damping ratios, even in the challenging cases when damping may turn to negative due to the Coriolis-type effects, thus causing amplifications of the system response.

Robust Adaptive Controllers for Interconnected Mechanical Systems: Influence of Types of Interconnections on Time-Invariant and Time-Varying Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 456-473 ◽  
Author(s):  
Sunil K. Singh ◽  
Lin Shi
Keyword(s):  
State Space ◽  
High Speed ◽  
Linear Time ◽  
Direct Method ◽  
Time Varying ◽  
Adaptive Controllers ◽  
First Order ◽  
Time Varying Systems ◽  
Robust Adaptive ◽  
Time Invariant

We investigate robust adaptive controller designs for interconnected systems when no exact knowledge about the structure of the nonlinear interconnections between various subsystems is available. In this study, we concentrate on several different types of systems. We deal with both linear time-invariant (LTI) and linear time-varying (LTV) systems with nonlinear interconnections. For LTI systems, we examine the following types of interconnections: • interconnections that are bounded by first order polynomials in state space; • slowly time varying interconnections; • interconnections bounded by higher-order polynomials in state-space together with input channel interconnections. For LTV systems we deal with interconnections bounded by first-order polynomials in state space. We show that the nature of the nonlinear interactions influences the adaptation laws. We use the direct method of Lyapunov for the design of adaptive controllers for tracking in such systems. We investigate issues such as stability, transient performance and steady-state errors, and derive quantitative estimates and analytical bounds for various different adaptive controllers. For time-varying systems, we analyze the effect of the time variations of parameters and interactions and propose a modified adaptive control scheme with better performance. Simulation results are presented to validate our conclusions. We also investigate these results experimentally on a two-link robot manipulator. Experimental results validate theoretical conclusions and demonstrate the usefulness of such robust adaptive controllers for high-speed motions in uncertain systems.

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

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