System Parameter Estimation with Projection Algorithm

[rfrederic]

I am recently trying to identify system parameters with projection algorithm, but faced a problem, and the dynamic model is the following:
[itex]\ddot{y}(t)+a\cdot\dot{y}(t)=b\cdot e(t)[/itex]

The true value of [itex]a[/itex] is [itex]2.8[/itex], [itex]b[/itex] is [itex]0.1[/itex].

While inputing volt [itex]e(t)=12sin(2\pi t)+5sin(2t)[/itex], I can get a good result showed in 1c_PA_r0.1_a0.jpg, and both of a and b are convergent to the true value.

But while [itex]e(t)=24[/itex], the result showed in doesn't seem right.

My question is: will [itex]e(t)[/itex] affect the convergence of parameters? And why?
By the way, I had also tried to use the least square to identify parameters while [itex]e(t)=24[/itex], the result also seems good.

 

[anorlunda]

will e(t)e(t)e(t) affect the convergence of parameters? And why?

Why not? Different e(t) are different cases. There is no reason to expect that all cases are equally easy to identify.