A Higher-Order Method for Dynamic Optimization of Controllable LTI Systems

2011 ◽  
Author(s):  
Damiano Zanotto ◽  
Sunil K. Agrawal ◽  
Giulio Rosati
Keyword(s):  
Differential Equations ◽  
Dynamic Optimization ◽  
Linear Time ◽  
Traditional Approach ◽  
Linear Time Invariant ◽  
System P ◽  
Lti System ◽  
Higher Order Method ◽  
Time Invariant ◽  
Controllability Index

This work describes a new procedure for dynamic optimization of controllable Linear time-invariant (LTI) systems. Unlike the traditional approach, which results in 2n first order differential equations, the method proposed here yields a set of m differential equations, whose highest order is twice the controllability index of the system p. This paper generalizes the approach presented in a previous work [1] to any controllable LTI system.

A Higher-Order Method for Dynamic Optimization of Controllable Linear Time-Invariant Systems

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Damiano Zanotto ◽  
Giulio Rosati ◽  
Sunil K. Agrawal
Keyword(s):  
Differential Equations ◽  
Dynamic Optimization ◽  
Linear Time ◽  
Traditional Approach ◽  
Linear Time Invariant ◽  
System P ◽  
Lti System ◽  
Higher Order Method ◽  
Linear Time Invariant Systems ◽  
Time Invariant

This work describes a new procedure for dynamic optimization of controllable linear time-invariant (LTI) systems. Unlike the traditional approach, which results in 2 n first-order differential equations, the method proposed here yields a set of m differential equations, whose highest order is twice the controllability index of the system p. This paper generalizes the approach presented in a previous work to any controllable LTI system.

scholarly journals Complete Controllability of Impulsive Fractional Linear Time-Invariant Systems with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xian-Feng Zhou ◽  
Song Liu ◽  
Wei Jiang
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Linear Time ◽  
Complete Controllability ◽  
Linear Time Invariant ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential ◽  
Linear Time Invariant Systems ◽  
Time Invariant

Some flaws on impulsive fractional differential equations (systems) have been found. This paper is concerned with the complete controllability of impulsive fractional linear time-invariant dynamical systems with delay. The criteria on the controllability of the system, which is sufficient and necessary, are established by constructing suitable control inputs. Two examples are provided to illustrate the obtained results.

Basics to Multirate Systems

2009 ◽  
pp. 23-63
Author(s):  
Ljiljana Milic
Keyword(s):  
Linear Time ◽  
Sampling Rate ◽  
Multirate Systems ◽  
Linear Time Invariant ◽  
Lti System ◽  
Linear Time Invariant Systems ◽  
Time Invariant ◽  
The Given

Linear time-invariant systems operate at a single sampling rate i.e. the sampling rate is the same at the input and at the output of the system, and at all the nodes inside the system. Thus, in an LTI system, the sampling rate doesn’t change in different stages of the system. Systems that use different sampling rates at different stages are called the multirate systems. The multirate techniques are used to convert the given sampling rate to the desired sampling rate, and to provide different sampling rates through the system without destroying the signal components of interest. In this chapter, we consider the sampling rate alterations when changing the sampling rate by an integer factor. We describe the basic sampling rate alteration operations, and the effects of those operations on the spectrum of the signal.

Reduction in the Number of Gain-Scheduling Parameters Using Dimensional Transformation

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Haftay Hailu ◽  
Sean Brennan
Keyword(s):  
Linear Time ◽  
Gain Scheduling ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Lti System ◽  
Gain Scheduled Controller ◽  
Parameter Dependent ◽  
Time Invariant ◽  
Linear Parameter Varying System ◽  
Gain Scheduled

A method is presented that can often reduce the number of scheduling parameters for gain-scheduled controller implementation by transformation of the system representation using parameter-dependent dimensional transformations. In some cases, the reduction in parameter dependence is so significant that a linear parameter-varying system can be transformed to an equivalent linear time invariant (LTI) system, and a simple example of this is given. A general analysis of the parameter-dependent dimensional transformation using a matrix-based approach is then presented. It is shown that, while some transformations simplify gain scheduling, others may increase the number of scheduling parameters. This work explores the mathematical conditions causing an increase or decrease in varying parameters resulting from a given transformation, thereby allowing one to seek transformations that most reduce the number of gain-scheduled parameters in the controller synthesis step.

scholarly journals Active Unmatched Disturbance Cancellation and Estimation by State--Derivative Feedback for Plants Modeled as an LTI System

2018 ◽  
Vol 8 (2) ◽  
pp. 237-249
Author(s):  
Halil Ibrahim Basturk
Keyword(s):  
Linear Time ◽  
Position Information ◽  
Linear Time Invariant ◽  
Lti System ◽  
Disturbance Cancellation ◽  
Disturbance Model ◽  
The Stability ◽  
Linear Time Invariant System ◽  
Time Invariant ◽  
Two Degree Of Freedom

We design adaptive algorithms for both cancellation and estimation of unknown periodic disturbance, by feedback of state--derivatives ( i.e.,} without position information for mechanical systems) for the plants which are modeled as a linear time invariant system. We consider a series of unmatched unknown sinusoidal signals as the disturbance.The first step of the design consists of the parametrization of the disturbance model and the development of observer filters.The result obtained in this step allows us to use adaptive control techniques for the solution of the problem.In order to handle the unmatched condition, a backstepping technique is employed. Since the partial measurement of the virtual inputs is not available, we design a state observer and the estimates of these signals are used in the backstepping design.Finally, the stability of the equilibrium of the adaptive closed loop system with the convergence of states is proven.As a numerical example, a two-degree of freedom system is considered and the effectiveness of the algorithms are shown.

scholarly journals Identification of Linear Time Invariant Systems Using FMCW Signals and Stretch Processing Receivers

2019 ◽  
Vol 8 (2) ◽  
pp. 35
Author(s):  
Stephan Häfner ◽  
Reiner Thomä
Keyword(s):  
Continuous Wave ◽  
Linear Time ◽  
Practical Applications ◽  
Fmcw Radar ◽  
Linear Time Invariant ◽  
Time Bandwidth Product ◽  
Lti System ◽  
Baseband Signal ◽  
Linear Time Invariant Systems ◽  
Time Invariant

The paper deals with the identification of linear time invariant (LTI) systems by a special observer. An observer emitting an frequency modulated continuous wave (FMCW) signal and having a stretch processor as receiver will be considered for system identification. A thorough derivation of the gathered baseband signal for arbitrary LTI systems will be given. It is shown, that the received signal is approximately given by the transfer function of the LTI system over the frequency sweep of the FMCW signal. The proof relies on an infinite large time-bandwidth product of the transmit signal, such that errors remain in practical applications with a finite time-bandwidth product. Monte–Carlo simulations are conducted to verify the approximation and to quantify its accuracy and remaining errors. The findings are important for e.g. calibration or derivation of a device model in FMCW radar applications.

scholarly journals On a parameter adaptive self-organizing system in the presence of large outliers in observations

2009 ◽  
Vol 50 ◽  
Author(s):  
Rimantas Pupeikis
Keyword(s):  
Gaussian Noise ◽  
Linear Time ◽  
Minimum Variance ◽  
Linear Time Invariant ◽  
Lti System ◽  
Current Value ◽  
Is Development ◽  
Time Invariant ◽  
The Given ◽  
Time Linear

The aim of the given paper is development of a minimum variance control (MVC) approach for a closed-loopdiscrete-time linear time-invariant (LTI) system when the parameters of a dynamic system as well as that of a controller are not known and ought to be estimated by processing observations in the case of additive Gaussian noise on the output with contaminating outliers uniformly spread in it. Afterwards, the current value of the control signal is found in each operation, and it is used to generate the output of the system. The results of numerical simulation by computer are presented and discussed here, too.

Signal Distortion Compensation of Linear Time-Invariant Measurement System

2000 ◽  
Author(s):  
Changting Wang ◽  
Robert X. Gao
Keyword(s):  
Measurement System ◽  
Precision Measurement ◽  
Linear Time ◽  
Signal Distortion ◽  
Charge Amplifier ◽  
Distortion Compensation ◽  
Linear Time Invariant ◽  
Lti System ◽  
Invariant Measurement ◽  
Time Invariant

Abstract Non-distortion is an important aspect in precision measurement, calibration and signal processing. In this paper, the distortion error of a linear time-invariant measurement system is derived for periodical and non-periodical signal inputs, using Fourier Series and Fourier Transformation. The signal distortion is measured by the error-to-signal energy ratio. A charge amplifier circuit has been analyzed as an example, which shows that the distortion of an LTI system can not be simply neglected if precision measurement is required. Direct compensation and adaptive control methods have been discussed to reduce the LTI system distortion. The applications of these two methods to the charge amplifier design are discussed, which demonstrated good results.

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