Adjustable Notch Filter help

Question

I'm converting the simulink diagram found in this paper to C code. I'm not familiar with matlab/simulink(too expensive) so need help interpreting the diagram. The problem I experience is that once a value like $\theta$, or $x_1$ becomes zero, zero is propagated everywhere due to the multiplication. The paper states that the integrators are initialized to zero, so I don't see how the system works.

Any ideas?

Below is the simulink diagram and my C code:

The block diagram is found in the paper above as Figure 1 and Figure 2 :

typedef struct  { float zeta,gamma;} PARAM_ANFfloat;
typedef struct  { float err,regressor,x1,theta;} STATE_ANFfloat;

typedef struct {PARAM_ANFfloat p;STATE_ANFfloat s;} ANFfloat;

void dspANFfloat_perform(ANFfloat *anf, float y)
{
    anf->s.err = y - anf->s.regressor;

    anf->s.theta = -anf->p.gamma * anf->s.x1 * anf->s.theta * anf->s.err;

    anf->s.x1 = anf->s.theta * anf->s.err * 2 * anf->p.zeta - anf->s.x1 * - anf->s.theta * anf->s.theta;

    anf->s.regressor = anf->s.x1;

}

Answer 1

In this line:

anf->s.theta = -anf->p.gamma * anf->s.x1 * anf->s.theta * anf->s.err;

you seem to be conflating $\theta$ and $\dot{\theta}$ (the derivative).

Equation 5 of the paper is:

$$ \dot{\theta} = -\gamma x_1 \theta \left[ y(t) - \sum_{l=1}^n \dot{x}_l \right] $$

Note that the left-hand term is the derivative of $\theta$, not $\theta$ itself.