MATLAB: Is it possible to linearize a phase-lock-loop using the linear analysis GUI

Question

I have a phase lock loop system similar to this:

https://www.mathworks.com/help/physmod/sps/examples/phase-locked-loop.html

I am interested in the frequency response characteristics of this system. Is it possible to use the Model Linearizer app and the Linear Analysis Tool to perform this analysis?

I have tried adding model I/Os and using the Linear Analysis Tool, but the resulting Bode plot is empty (linearized to zero). Is this expected?

Answer 1

Since switching is an intrinsic part of phase lock loops, the "linearize-to-zero" result from the exact linearization is expected for a PLL. These switches introduced discontinuities in the signals that form the PLL feedback loop.

To obtain the frequency response of the loop transfer function, we need to conduct frequency response estimation, i.e. using the "Estimation" tab. There is an example which you may find helpful in learning the workflow to create a "sinestream" input signal, conduct the frequency response estimation and create a Bode plot in the App.

https://www.mathworks.com/help/slcontrol/ug/design-controller-for-power-electronics-model-using-frequency-response-data.htmlPlease note that the frequency response estimation in the reproduction model may take a long simulation time. 

Some additional things to pay attention to:

• The frequency points of the "sinestream" input signal need to be chosen carefully, especially over the low-frequency range. This is because the simulation for low-frequency signals would take a long time.You may want to start with only a few points before trying to get a high-resolution bode plot.
• Another critical value is the amplitude of the "sinestream", which needs to be large enough to make sure the model is properly excited and not too large to deviate from the operating point.