Discrepancy between Built-in Integrator and C-Script Implementation

PLECS
,
1

Hello everyone,

I am currently working on implementing a Discrete Integrator using a C-Script block to compare it with the standard PLECS library block.

For the comparison, I set the integration method of the standard Discrete Integrator to ‘Forward Euler’ and applied both integrators to a PLL (Phase Locked Loop) system.

- Figure 1 shows the simulation results using the standard Discrete Integrator block.

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- Figure 2 shows the results using my C-Script based integrator.

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As you can see, there is a difference between the two results. In the first figure, i_d and v_d remain at 0, while i_q and v_q stably maintain a constant negative value. However, when the C-Script integrator is applied, the signals oscillate significantly, and eventually, the polarity reverses.

Below is the code I wrote for the Forward Euler method. Logic-wise, it seems correct to me, so I am struggling to understand what causes this significant divergence compared to the built-in block.

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< Code declarations >
#define u Input(0)
#define reset Input(1)
#define y Output(0)
#define x DiscState(0)
#define u_prev DiscState(1)

float Ts;
float init_val;

< Start function code >
Ts = 0.0001;
init_val = 0.0;
x = 0;
u_prev = 0;

< Output function code >
y = x;

< Update function code >
if (reset != 0.0) {
  x = init_Val;
}
else {
  x = x + Ts*u_prev;
}
u_prev = u

Could anyone shed some light on what I might be missing here?

I have attached two simulation models for youre reference.

  1. simulation model using the standard discrete integrator

260116_frame_convert_test_with_default_integ.plecs (62.9 KB)
2. simulation model using the C-Script based integrator

260116_frame_convert_test_with_c-script_integ.plecs (69.6 KB)

I would really appreciate it if you could take a look at the models and share your feedback.
Thank you in advance for your help!

Could anyone advise on what might be causing this discrepancy?

2

Your Update function code introduces a one-step delay on the input signal. You should write this:

if (reset != 0.0) {
  x = init_Val;
}
else {
  x = x + Ts*u;
}

(and eliminate u_prev).

3

Hi Wolfgang,
thank you very much for your reply.

I updated my C-Script integrator as yo suggested by removing u_prev and using the current input u in the state update.

However, I still observe a discrepancy compared to the built-in Discrete Integrator block configured with Forward Euler. When using the library block, the i_dq and v_dq waveforms remain stable over the entire simulation time. In contrast, when the C-Script integrator is used, the signals start to deviate and their polarity flips after 0.7 sec(in Fig. 2).

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Fig.1. simulation results using the default Discrete integrator block

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Fig. 2. simulation results using the C-Script integrator

If the built-in Discrete Integrator is set to Forward Euler, shouldn’t it’s behavior be equivalent to y[k] = x[k] + Ts*u[k-1]? The C-Script implementations follows this update equation directly, so I would expect both implementations to behave identically.

Could you please help clarify why this polarity reversal still occuers in the C-Script case?

<for your reference)

260116_frame_convert_test_with_default_integ.plecs (62.9 KB)

frame_convert_test_260116_v02.plecs (68.8 KB) (modified c-script integrator)

4

Yes, it should - if you have defined Ts correctly.

I just noticed that you have defined it as a single precision floating point number in your Code declarations section:

float Ts;

The single-precision representation of 0.0001 is slightly smaller than the double-precision one, which is what the Pulse Generation uses to execute your Triggered Subsystem that contains the C-Script block. As a result, your C-Script integrator has an effective gain that is slightly smaller than 1.

You should change your code to this:

static double Ts;
static double init_val;

(The static is recommended to avoid linker errors if you ever generate C code for your model.)

5

Wow, that was exactly the problem! I changed it to static double as you suggested, and the issue is resolved. I appreciate your help!!