MATLAB: Is the Krall and Fornaro’s method not implemented to obtain root locus for systems with time delay in the Control Systems Toolbox 8.1 (R2008a)

Control System Toolbox

To obtain the root locus for systems with time delay, I need to first get a transfer function with the Pade approximation using the PADE command in the Control Systems Toolbox. I am wondering why I cannot use not Krall and Fornaro's algorithm, which takes the delay directly as an input:

http://portal.acm.org/citation.cfm?id=363212

Best Answer

Control Systems Toolbox 8.1 (R2008a) does not implement the Krall and Fornaro's algorithm for root locus of systems with time delays.

As a workaround, you can obtain a system transfer function using the Pade approximation (see help for PADE command in the Control Systems Toolbox), and then obtain the root locus.

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MATLAB: Do the plots using the Spectrum Analyzer block in Simulink not agree with the Bode plot of a continuous system

The discrete-time spectrum analyzer coupled with a discrete-time input is not well suited to the task of identification of a continuous-time system.

If instead of using a white noise input, a continuous chirp signal is used, the spectrum analyzer shows a better approximation of the transfer function. This is because a discrete-time white noise signal is sampled and held (ZOH) when it is passed as an input to a continuous transfer function. Therefore, the output signal is the same as the output of the transfer function for a continuous white noise passed through the equivalent ZOH transfer function. Hence the spectrum of the output signal is not the same as when a continuous time white noise signal is fed to a continuous time transfer function. In essence in the above case the spectrum analyzer is displaying the frequency response of a ZOH and a first order continuous time transfer function connected in series. The ZOH causes a roll off in the phase.

There are several products which are better suited than the Spectrum Analyzer block for obtaining a linear estimate of a non-linear Simulink model.

First, Simulink has the ability to linearize a model. This can be done with functions such as LINMOD, LINMOD2, etc... For more information, execute the following command at the MATLAB prompt:

doc linmod

or visit the following URL:

http://www.mathworks.com/help/simulink/ug/linearizing-models.html

Second, Simulink Control Design is an add-on to Simulink which has enhanced linearization features and includes the Simulink Control Design GUI. More information is available at the following URL:

http://www.mathworks.com/products/simcontrol/

Finally, there is the System Identification toolbox which allows you to retrieve system parameters based on measured input and output. More information is available at the following URL:

http://www.mathworks.com/products/sysid/

MATLAB: How to use the “prewarp” method with the C2D command in Control System Toolbox 5.2.1 (R13SP1)

This bug has been fixed for Release 14 (R14). For previous releases, please read below for any possible workarounds:

There is a difference in the information available from the MATLAB file help and from the documentation on the C2D function in Control System Toolbox 5.2.1 (R13SP1). If you wish to view the help for C2D, which includes a brief description of the critical frequency parameter and how to specify it, type the following at the MATLAB command prompt:

help c2d

The correct syntax is:

 SYSD = C2D(SYSC,Ts,'prewarp',Wc)

where Wc is the critical frequency. The critical frequency is the frequency where it is desired that the phase and gain in the digital spectrum exactly match the (original) analog spectrum. We have verified that documentation on the additional parameter for C2D with the "prewarp" method is missing from the Control System Toolbox.

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Related Solutions

MATLAB: Do the plots using the Spectrum Analyzer block in Simulink not agree with the Bode plot of a continuous system

MATLAB: How to use the “prewarp” method with the C2D command in Control System Toolbox 5.2.1 (R13SP1)

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