MATLAB: Bode Plot Phase Angles are greater than 180 degrees.

Simulink Control Design

I followed the example for Pade approximation below

>> s = tf('s');
>> sys = exp(-0.1*s);
>> sysx = pade(sys,3)
>> bodeplot(sys,sysx)

When I plot the bode plot of the approximated transfer function ('sysx'), the plot shows +720 degree phase shift relative to the pure delay ('sys'). This seems to be a large phase difference. How can I fix this?

Best Answer

The goal in this case is to bring us back to within -180 to 180 degrees. To resolve the issue we can use the 'PhaseWrapping' property of "bodeplot".

Please have a look at 'PhaseWrapping' in documentation below

https://www.mathworks.com/help/releases/R2018b/ident/ref/bodeoptions.html#brin365-1

When Phase Wrapping is on we are able to wrap around 'PhaseWrappingBranch' angle as soon as we exceed an angle limit in range (currently -180,180).

Using the set of lines below:

>> s = tf('s');
>> sys = exp(-0.1*s);
>> sysx = pade(sys,3);
>> opts = bodeoptions('cstprefs');
>> opts.PhaseWrapping='on'
>> bodeplot(sys,sysx,opts)

This will display the angle within (-180,180) range.

Related Solutions

MATLAB: Does there seem to be a discrepancy in TuningGoal.Overshoot specification and visualization of the goal using viewGoal

You can create a TuningGoal.Overshoot class following the example here:

https://www.mathworks.com/help/control/ref/tuninggoal.overshoot-class.html#btz8lez-2

>> Req = TuningGoal.Overshoot('r','y',20);

then view the goal in a plot:

>> viewGoal(Req)

then right click the plot > Properties > Units > change the Magnitude filed to absolute.

The yellow colored section on the plot shows areas in which the TuningGoal.Overshoot is not satisfied. You would expect the yellow region to start at 1.2 ( 20% over 1), but instead it is greater than 1.23. As another example if you specify an overshoot of 50% the yellow area starts at 2.37.

The yellow region displayed on the bode plot by viewGoal for TuningGoal.Overshoot is actually correct.

It is mentioned in the documentation page of TuningGoal.Overshoot

https://www.mathworks.com/help/control/ref/tuninggoal.overshoot-class.html

"The overshoot tuning goal is evaluated as a constraint on the peak system gain, assuming second-order model characteristics."

The peak system gain/response is the peak gain of dynamic system frequency response, which can be observed in a bode plot. It is not the gain observed in the time-domain step response, but instead the peak gain at the peak frequency. While the peak gain in the time domain step response is just at one frequency. For example, you can show a second-order dynamic system:

>> zeta = 0.25;
>> w0 = 3;
>> sys = tf(w0^2,[1,2*zeta*w0,w0^2])

Using the 'step' command, you can see that the overshoot is about 44%. Generating the bode plot shows a peak gain of about 6.3 dB, an absolute value of 2.06. This result can be confirmed by using the command 'getPeakGain' or checking the infinity norm:

>> [ninf,fpeak] = norm(sys,Inf)
>> [gpeak,fpeak] = getPeakGain(sys)

The result would be the same if you check the following tuning goal:

>> Req = TuningGoal.Overshoot('r','y',44);
>> viewGoal(Req)

The start of the yellow region is the peak response of the bode plot of the system, 'sys', described earlier. As a result, there is no discrepancy between the tuning goal and the overshoot settings.

MATLAB: Bode Diagram

You need to use bodeoptions command and set PhaseWrapping to on. Here is an example showing how to do it:

>>s=tf('s'); %define Laplace variable

>>freq=logspace(-1,2,1000); %define frequency vector

>>sys=1/(s^3+2*s^2+3*s+1); %some tf with phase <-180

>>bode(sys,freq) %phase is not within -180:180

>>p=bodeoptions

>>p.PhaseWrapping='on'

>>bode(sys,freq,p) %phase is wrapped inside -180:180

HTH, Arkadiy

Best Answer

Related Solutions

MATLAB: Does there seem to be a discrepancy in TuningGoal.Overshoot specification and visualization of the goal using viewGoal

MATLAB: Bode Diagram

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